id	sid	tid	token	lemma	pos
ejpam-3003	1	1	european	european	PROPN
ejpam-3003	1	2	journal	journal	PROPN
ejpam-3003	1	3	of	of	ADP
ejpam-3003	1	4	pure	pure	ADJ
ejpam-3003	1	5	and	and	CCONJ
ejpam-3003	1	6	applied	apply	VERB
ejpam-3003	1	7	mathematics	mathematic	NOUN
ejpam-3003	1	8	vol	vol	NOUN
ejpam-3003	1	9	.	.	PROPN
ejpam-3003	2	1	10	10	NUM
ejpam-3003	2	2	,	,	PUNCT
ejpam-3003	2	3	no	no	INTJ
ejpam-3003	2	4	.	.	NOUN
ejpam-3003	2	5	4	4	NUM
ejpam-3003	2	6	,	,	PUNCT
ejpam-3003	2	7	2017	2017	NUM
ejpam-3003	2	8	,	,	PUNCT
ejpam-3003	2	9	668	668	NUM
ejpam-3003	2	10	-	-	SYM
ejpam-3003	2	11	701	701	NUM
ejpam-3003	2	12	issn	issn	PROPN
ejpam-3003	2	13	1307	1307	NUM
ejpam-3003	2	14	-	-	SYM
ejpam-3003	2	15	5543	5543	NUM
ejpam-3003	2	16	–	–	PUNCT
ejpam-3003	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3003	2	18	published	publish	VERB
ejpam-3003	2	19	by	by	ADP
ejpam-3003	2	20	new	new	PROPN
ejpam-3003	2	21	york	york	PROPN
ejpam-3003	2	22	business	business	PROPN
ejpam-3003	2	23	global	global	ADJ
ejpam-3003	2	24	existence	existence	PROPN
ejpam-3003	2	25	,	,	PUNCT
ejpam-3003	2	26	nonexistence	nonexistence	NOUN
ejpam-3003	2	27	and	and	CCONJ
ejpam-3003	2	28	decay	decay	NOUN
ejpam-3003	2	29	estimate	estimate	NOUN
ejpam-3003	2	30	of	of	ADP
ejpam-3003	2	31	global	global	ADJ
ejpam-3003	2	32	solutions	solution	NOUN
ejpam-3003	2	33	for	for	ADP
ejpam-3003	2	34	a	a	DET
ejpam-3003	2	35	viscoelastic	viscoelastic	ADJ
ejpam-3003	2	36	wave	wave	NOUN
ejpam-3003	2	37	equation	equation	NOUN
ejpam-3003	2	38	with	with	ADP
ejpam-3003	2	39	nonlinear	nonlinear	ADJ
ejpam-3003	2	40	boundary	boundary	ADJ
ejpam-3003	2	41	damping	damp	VERB
ejpam-3003	2	42	and	and	CCONJ
ejpam-3003	2	43	internal	internal	ADJ
ejpam-3003	2	44	source	source	NOUN
ejpam-3003	2	45	terms	term	NOUN
ejpam-3003	2	46	huafei	huafei	PROPN
ejpam-3003	2	47	di1	di1	NOUN
ejpam-3003	2	48	,	,	PUNCT
ejpam-3003	2	49	yadong	yadong	ADJ
ejpam-3003	2	50	shang1,∗	shang1,∗	NOUN
ejpam-3003	2	51	1	1	NUM
ejpam-3003	2	52	school	school	NOUN
ejpam-3003	2	53	of	of	ADP
ejpam-3003	2	54	mathematics	mathematic	NOUN
ejpam-3003	2	55	and	and	CCONJ
ejpam-3003	2	56	information	information	NOUN
ejpam-3003	2	57	science	science	NOUN
ejpam-3003	2	58	,	,	PUNCT
ejpam-3003	2	59	guangzhou	guangzhou	PROPN
ejpam-3003	2	60	university	university	PROPN
ejpam-3003	2	61	,	,	PUNCT
ejpam-3003	2	62	guangdong	guangdong	PROPN
ejpam-3003	2	63	,	,	PUNCT
ejpam-3003	2	64	p	p	PROPN
ejpam-3003	2	65	r	r	PROPN
ejpam-3003	2	66	china	china	PROPN
ejpam-3003	2	67	abstract	abstract	NOUN
ejpam-3003	2	68	.	.	PUNCT
ejpam-3003	3	1	in	in	ADP
ejpam-3003	3	2	this	this	DET
ejpam-3003	3	3	paper	paper	NOUN
ejpam-3003	3	4	,	,	PUNCT
ejpam-3003	3	5	we	we	PRON
ejpam-3003	3	6	consider	consider	VERB
ejpam-3003	3	7	the	the	DET
ejpam-3003	3	8	initial	initial	ADJ
ejpam-3003	3	9	boundary	boundary	ADJ
ejpam-3003	3	10	value	value	NOUN
ejpam-3003	3	11	problem	problem	NOUN
ejpam-3003	3	12	for	for	ADP
ejpam-3003	3	13	a	a	DET
ejpam-3003	3	14	viscoelastic	viscoelastic	ADJ
ejpam-3003	3	15	wave	wave	NOUN
ejpam-3003	3	16	equation	equation	NOUN
ejpam-3003	3	17	with	with	ADP
ejpam-3003	3	18	nonlinear	nonlinear	ADJ
ejpam-3003	3	19	boundary	boundary	ADJ
ejpam-3003	3	20	damping	damp	VERB
ejpam-3003	3	21	and	and	CCONJ
ejpam-3003	3	22	internal	internal	ADJ
ejpam-3003	3	23	source	source	NOUN
ejpam-3003	3	24	terms	term	NOUN
ejpam-3003	3	25	.	.	PUNCT
ejpam-3003	4	1	we	we	PRON
ejpam-3003	4	2	first	first	ADV
ejpam-3003	4	3	prove	prove	VERB
ejpam-3003	4	4	the	the	DET
ejpam-3003	4	5	existence	existence	NOUN
ejpam-3003	4	6	of	of	ADP
ejpam-3003	4	7	global	global	ADJ
ejpam-3003	4	8	weak	weak	ADJ
ejpam-3003	4	9	solutions	solution	NOUN
ejpam-3003	4	10	by	by	ADP
ejpam-3003	4	11	the	the	DET
ejpam-3003	4	12	combination	combination	NOUN
ejpam-3003	4	13	of	of	ADP
ejpam-3003	4	14	galerkin	galerkin	ADJ
ejpam-3003	4	15	approximation	approximation	NOUN
ejpam-3003	4	16	,	,	PUNCT
ejpam-3003	4	17	potential	potential	ADJ
ejpam-3003	4	18	well	well	ADV
ejpam-3003	4	19	and	and	CCONJ
ejpam-3003	4	20	monotonicity	monotonicity	NOUN
ejpam-3003	4	21	-	-	PUNCT
ejpam-3003	4	22	compactness	compactness	NOUN
ejpam-3003	4	23	methods	method	NOUN
ejpam-3003	4	24	.	.	PUNCT
ejpam-3003	5	1	then	then	ADV
ejpam-3003	5	2	,	,	PUNCT
ejpam-3003	5	3	we	we	PRON
ejpam-3003	5	4	give	give	VERB
ejpam-3003	5	5	an	an	DET
ejpam-3003	5	6	explicit	explicit	ADJ
ejpam-3003	5	7	decay	decay	NOUN
ejpam-3003	5	8	rate	rate	NOUN
ejpam-3003	5	9	estimate	estimate	NOUN
ejpam-3003	5	10	of	of	ADP
ejpam-3003	5	11	the	the	DET
ejpam-3003	5	12	energy	energy	NOUN
ejpam-3003	5	13	by	by	ADP
ejpam-3003	5	14	making	make	VERB
ejpam-3003	5	15	use	use	NOUN
ejpam-3003	5	16	of	of	ADP
ejpam-3003	5	17	the	the	DET
ejpam-3003	5	18	perturbed	perturb	VERB
ejpam-3003	5	19	energy	energy	NOUN
ejpam-3003	5	20	method	method	NOUN
ejpam-3003	5	21	.	.	PUNCT
ejpam-3003	6	1	finally	finally	ADV
ejpam-3003	6	2	,	,	PUNCT
ejpam-3003	6	3	the	the	DET
ejpam-3003	6	4	finite	finite	ADJ
ejpam-3003	6	5	time	time	NOUN
ejpam-3003	6	6	blow	blow	VERB
ejpam-3003	6	7	up	up	ADP
ejpam-3003	6	8	result	result	NOUN
ejpam-3003	6	9	of	of	ADP
ejpam-3003	6	10	the	the	DET
ejpam-3003	6	11	solutions	solution	NOUN
ejpam-3003	6	12	is	be	AUX
ejpam-3003	6	13	investigated	investigate	VERB
ejpam-3003	6	14	under	under	ADP
ejpam-3003	6	15	certain	certain	ADJ
ejpam-3003	6	16	assumptions	assumption	NOUN
ejpam-3003	6	17	on	on	ADP
ejpam-3003	6	18	the	the	DET
ejpam-3003	6	19	relaxation	relaxation	NOUN
ejpam-3003	6	20	function	function	NOUN
ejpam-3003	6	21	g	g	NOUN
ejpam-3003	6	22	and	and	CCONJ
ejpam-3003	6	23	initial	initial	ADJ
ejpam-3003	6	24	data	datum	NOUN
ejpam-3003	6	25	.	.	PUNCT
ejpam-3003	7	1	2010	2010	NUM
ejpam-3003	7	2	mathematics	mathematic	NOUN
ejpam-3003	7	3	subject	subject	NOUN
ejpam-3003	7	4	classifications	classification	NOUN
ejpam-3003	7	5	:	:	PUNCT
ejpam-3003	7	6	35l35	35l35	NUM
ejpam-3003	7	7	,	,	PUNCT
ejpam-3003	7	8	35l75	35l75	NUM
ejpam-3003	7	9	,	,	PUNCT
ejpam-3003	7	10	35r15	35r15	NUM
ejpam-3003	7	11	key	key	ADJ
ejpam-3003	7	12	words	word	NOUN
ejpam-3003	7	13	and	and	CCONJ
ejpam-3003	7	14	phrases	phrase	NOUN
ejpam-3003	7	15	:	:	PUNCT
ejpam-3003	7	16	viscoelastic	viscoelastic	ADJ
ejpam-3003	7	17	equation	equation	NOUN
ejpam-3003	7	18	,	,	PUNCT
ejpam-3003	7	19	nonlinear	nonlinear	ADJ
ejpam-3003	7	20	boundary	boundary	ADJ
ejpam-3003	7	21	damping	damping	NOUN
ejpam-3003	7	22	,	,	PUNCT
ejpam-3003	7	23	internal	internal	ADJ
ejpam-3003	7	24	source	source	NOUN
ejpam-3003	7	25	,	,	PUNCT
ejpam-3003	7	26	blow	blow	VERB
ejpam-3003	7	27	up	up	ADP
ejpam-3003	7	28	,	,	PUNCT
ejpam-3003	7	29	decay	decay	NOUN
ejpam-3003	7	30	rate	rate	NOUN
ejpam-3003	7	31	estimate	estimate	NOUN
ejpam-3003	7	32	,	,	PUNCT
ejpam-3003	7	33	perturbed	perturb	VERB
ejpam-3003	7	34	energy	energy	NOUN
ejpam-3003	7	35	method	method	NOUN
ejpam-3003	7	36	1	1	NUM
ejpam-3003	7	37	.	.	PUNCT
ejpam-3003	8	1	introduction	introduction	NOUN
ejpam-3003	8	2	we	we	PRON
ejpam-3003	8	3	are	be	AUX
ejpam-3003	8	4	concerned	concerned	ADJ
ejpam-3003	8	5	with	with	ADP
ejpam-3003	8	6	the	the	DET
ejpam-3003	8	7	following	follow	VERB
ejpam-3003	8	8	initial	initial	ADJ
ejpam-3003	8	9	boundary	boundary	ADJ
ejpam-3003	8	10	value	value	NOUN
ejpam-3003	8	11	problem	problem	NOUN
ejpam-3003	8	12	of	of	ADP
ejpam-3003	8	13	the	the	DET
ejpam-3003	8	14	viscoelastic	viscoelastic	ADJ
ejpam-3003	8	15	wave	wave	NOUN
ejpam-3003	8	16	equation	equation	NOUN
ejpam-3003	8	17	with	with	ADP
ejpam-3003	8	18	nonlinear	nonlinear	ADJ
ejpam-3003	8	19	boundary	boundary	ADJ
ejpam-3003	8	20	damping	damp	VERB
ejpam-3003	8	21	and	and	CCONJ
ejpam-3003	8	22	internal	internal	ADJ
ejpam-3003	8	23	source	source	NOUN
ejpam-3003	8	24	terms	terms	PROPN
ejpam-3003	8	25	|ut|ρ−1utt	|ut|ρ−1utt	NOUN
ejpam-3003	9	1	−4u+	−4u+	NOUN
ejpam-3003	10	1	∫	∫	PROPN
ejpam-3003	10	2	t	t	PROPN
ejpam-3003	10	3	0	0	NUM
ejpam-3003	10	4	g(t−	g(t−	PROPN
ejpam-3003	10	5	s)4u(s)ds	s)4u(s)d	NOUN
ejpam-3003	10	6	=	=	SYM
ejpam-3003	10	7	|u|p−1u	|u|p−1u	INTJ
ejpam-3003	10	8	,	,	PUNCT
ejpam-3003	10	9	in	in	ADP
ejpam-3003	10	10	ω×	ω×	PROPN
ejpam-3003	10	11	(	(	PUNCT
ejpam-3003	10	12	0,∞	0,∞	NUM
ejpam-3003	10	13	)	)	PUNCT
ejpam-3003	10	14	,	,	PUNCT
ejpam-3003	10	15	u(x	u(x	PROPN
ejpam-3003	10	16	,	,	PUNCT
ejpam-3003	10	17	t	t	PROPN
ejpam-3003	10	18	)	)	PUNCT
ejpam-3003	10	19	=	=	SYM
ejpam-3003	10	20	0	0	NUM
ejpam-3003	10	21	,	,	PUNCT
ejpam-3003	10	22	on	on	ADP
ejpam-3003	10	23	γ0	γ0	PROPN
ejpam-3003	10	24	×	×	PROPN
ejpam-3003	10	25	(	(	PUNCT
ejpam-3003	10	26	0,∞	0,∞	NOUN
ejpam-3003	10	27	)	)	PUNCT
ejpam-3003	10	28	,	,	PUNCT
ejpam-3003	10	29	∂u	∂u	PROPN
ejpam-3003	10	30	∂ν	∂ν	PROPN
ejpam-3003	11	1	−	−	PROPN
ejpam-3003	11	2	∫	∫	PROPN
ejpam-3003	11	3	t	t	PROPN
ejpam-3003	11	4	0	0	NUM
ejpam-3003	11	5	g(t−	g(t−	PROPN
ejpam-3003	11	6	s)∂u∂ν	s)∂u∂ν	PROPN
ejpam-3003	11	7	(	(	PUNCT
ejpam-3003	11	8	s)ds+	s)ds+	NOUN
ejpam-3003	11	9	|ut|q−1ut	|ut|q−1ut	PROPN
ejpam-3003	11	10	=	=	SYM
ejpam-3003	11	11	0	0	NUM
ejpam-3003	11	12	,	,	PUNCT
ejpam-3003	11	13	on	on	ADP
ejpam-3003	11	14	γ1	γ1	PROPN
ejpam-3003	11	15	×	×	PROPN
ejpam-3003	11	16	(	(	PUNCT
ejpam-3003	11	17	0,∞	0,∞	NUM
ejpam-3003	11	18	)	)	PUNCT
ejpam-3003	11	19	,	,	PUNCT
ejpam-3003	11	20	u(x	u(x	NOUN
ejpam-3003	11	21	,	,	PUNCT
ejpam-3003	11	22	0	0	NUM
ejpam-3003	11	23	)	)	PUNCT
ejpam-3003	11	24	=	=	SYM
ejpam-3003	11	25	u0(x	u0(x	NOUN
ejpam-3003	11	26	)	)	PUNCT
ejpam-3003	11	27	,	,	PUNCT
ejpam-3003	11	28	ut(x	ut(x	NOUN
ejpam-3003	11	29	,	,	PUNCT
ejpam-3003	11	30	0	0	NUM
ejpam-3003	11	31	)	)	PUNCT
ejpam-3003	11	32	=	=	SYM
ejpam-3003	12	1	u1(x	u1(x	NOUN
ejpam-3003	12	2	)	)	PUNCT
ejpam-3003	12	3	,	,	PUNCT
ejpam-3003	12	4	x	x	PUNCT
ejpam-3003	12	5	∈	∈	PROPN
ejpam-3003	12	6	ω	ω	PROPN
ejpam-3003	12	7	,	,	PUNCT
ejpam-3003	12	8	(	(	PUNCT
ejpam-3003	12	9	1.1	1.1	NUM
ejpam-3003	12	10	)	)	PUNCT
ejpam-3003	12	11	where	where	SCONJ
ejpam-3003	12	12	ρ	ρ	NOUN
ejpam-3003	12	13	,	,	PUNCT
ejpam-3003	12	14	p	p	X
ejpam-3003	12	15	,	,	PUNCT
ejpam-3003	12	16	q	q	X
ejpam-3003	12	17	≥	≥	NOUN
ejpam-3003	12	18	1	1	NUM
ejpam-3003	12	19	,	,	PUNCT
ejpam-3003	12	20	and	and	CCONJ
ejpam-3003	12	21	ω	ω	PROPN
ejpam-3003	12	22	is	be	AUX
ejpam-3003	12	23	a	a	DET
ejpam-3003	12	24	bounded	bounded	ADJ
ejpam-3003	12	25	domain	domain	NOUN
ejpam-3003	12	26	of	of	ADP
ejpam-3003	12	27	rn	rn	PROPN
ejpam-3003	12	28	with	with	ADP
ejpam-3003	12	29	a	a	DET
ejpam-3003	12	30	smooth	smooth	ADJ
ejpam-3003	12	31	boundary	boundary	ADJ
ejpam-3003	12	32	γ	γ	X
ejpam-3003	12	33	.	.	PUNCT
ejpam-3003	12	34	let	let	AUX
ejpam-3003	12	35	{	{	PUNCT
ejpam-3003	12	36	γ0,γ1	γ0,γ1	PRON
ejpam-3003	12	37	}	}	PUNCT
ejpam-3003	12	38	be	be	AUX
ejpam-3003	12	39	a	a	DET
ejpam-3003	12	40	partition	partition	NOUN
ejpam-3003	12	41	of	of	ADP
ejpam-3003	12	42	its	its	PRON
ejpam-3003	12	43	boundary	boundary	ADJ
ejpam-3003	12	44	γ	γ	NOUN
ejpam-3003	12	45	such	such	ADJ
ejpam-3003	12	46	that	that	SCONJ
ejpam-3003	12	47	γ	γ	PROPN
ejpam-3003	12	48	=	=	SYM
ejpam-3003	12	49	γ0	γ0	PROPN
ejpam-3003	12	50	∪	∪	PROPN
ejpam-3003	12	51	γ1	γ1	NOUN
ejpam-3003	12	52	,	,	PUNCT
ejpam-3003	12	53	γ0	γ0	NOUN
ejpam-3003	12	54	∩	∩	ADJ
ejpam-3003	12	55	γ1	γ1	NOUN
ejpam-3003	12	56	=	=	SYM
ejpam-3003	12	57	∅	∅	NOUN
ejpam-3003	12	58	and	and	CCONJ
ejpam-3003	12	59	meas(γ0	meas(γ0	NOUN
ejpam-3003	12	60	)	)	PUNCT
ejpam-3003	12	61	>	>	X
ejpam-3003	12	62	0	0	X
ejpam-3003	12	63	.	.	PUNCT
ejpam-3003	13	1	here	here	ADV
ejpam-3003	13	2	,	,	PUNCT
ejpam-3003	13	3	ν	ν	PROPN
ejpam-3003	13	4	is	be	AUX
ejpam-3003	13	5	the	the	DET
ejpam-3003	13	6	unit	unit	NOUN
ejpam-3003	13	7	outward	outward	VERB
ejpam-3003	13	8	normal	normal	ADJ
ejpam-3003	13	9	to	to	ADP
ejpam-3003	13	10	γ	γ	X
ejpam-3003	13	11	,	,	PUNCT
ejpam-3003	13	12	and	and	CCONJ
ejpam-3003	13	13	g	g	PROPN
ejpam-3003	13	14	represents	represent	VERB
ejpam-3003	13	15	the	the	DET
ejpam-3003	13	16	kernel	kernel	NOUN
ejpam-3003	13	17	of	of	ADP
ejpam-3003	13	18	memory	memory	NOUN
ejpam-3003	13	19	term	term	NOUN
ejpam-3003	13	20	,	,	PUNCT
ejpam-3003	13	21	namely	namely	ADV
ejpam-3003	13	22	the	the	DET
ejpam-3003	13	23	relaxation	relaxation	NOUN
ejpam-3003	13	24	function	function	NOUN
ejpam-3003	13	25	,	,	PUNCT
ejpam-3003	13	26	satisfying	satisfy	VERB
ejpam-3003	13	27	certain	certain	ADJ
ejpam-3003	13	28	conditions	condition	NOUN
ejpam-3003	13	29	to	to	PART
ejpam-3003	13	30	be	be	AUX
ejpam-3003	13	31	specified	specify	VERB
ejpam-3003	13	32	later	later	ADV
ejpam-3003	13	33	.	.	PUNCT
ejpam-3003	14	1	∗corresponding	∗corresponde	VERB
ejpam-3003	14	2	author	author	NOUN
ejpam-3003	14	3	.	.	PUNCT
ejpam-3003	15	1	email	email	NOUN
ejpam-3003	15	2	addresses	address	NOUN
ejpam-3003	15	3	:	:	PUNCT
ejpam-3003	15	4	dihuafei@yeah.net	dihuafei@yeah.net	PROPN
ejpam-3003	15	5	(	(	PUNCT
ejpam-3003	15	6	h.f	h.f	PROPN
ejpam-3003	15	7	.	.	PROPN
ejpam-3003	15	8	di	di	PROPN
ejpam-3003	15	9	)	)	PUNCT
ejpam-3003	15	10	,	,	PUNCT
ejpam-3003	15	11	gzydshang@126.com	gzydshang@126.com	PROPN
ejpam-3003	15	12	(	(	PUNCT
ejpam-3003	15	13	y.d	y.d	PROPN
ejpam-3003	15	14	.	.	PROPN
ejpam-3003	15	15	shang	shang	PROPN
ejpam-3003	15	16	)	)	PUNCT
ejpam-3003	15	17	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3003	16	1	668	668	NUM
ejpam-3003	16	2	c	c	AUX
ejpam-3003	16	3	©	©	PROPN
ejpam-3003	16	4	2017	2017	NUM
ejpam-3003	16	5	ejpam	ejpam	NOUN
ejpam-3003	16	6	all	all	DET
ejpam-3003	16	7	rights	right	NOUN
ejpam-3003	16	8	reserved	reserve	VERB
ejpam-3003	16	9	.	.	PUNCT
ejpam-3003	17	1	h.f	h.f	PROPN
ejpam-3003	17	2	.	.	PROPN
ejpam-3003	17	3	di	di	PROPN
ejpam-3003	17	4	,	,	PUNCT
ejpam-3003	17	5	y.d	y.d	PROPN
ejpam-3003	17	6	.	.	PROPN
ejpam-3003	17	7	shang	shang	PROPN
ejpam-3003	17	8	/	/	SYM
ejpam-3003	17	9	eur	eur	PROPN
ejpam-3003	17	10	.	.	PUNCT
ejpam-3003	18	1	j.	j.	PROPN
ejpam-3003	18	2	pure	pure	PROPN
ejpam-3003	18	3	appl	appl	PROPN
ejpam-3003	18	4	.	.	PROPN
ejpam-3003	18	5	math	math	PROPN
ejpam-3003	18	6	,	,	PUNCT
ejpam-3003	18	7	10	10	NUM
ejpam-3003	18	8	(	(	PUNCT
ejpam-3003	18	9	4	4	NUM
ejpam-3003	18	10	)	)	PUNCT
ejpam-3003	18	11	(	(	PUNCT
ejpam-3003	18	12	2017	2017	NUM
ejpam-3003	18	13	)	)	PUNCT
ejpam-3003	18	14	,	,	PUNCT
ejpam-3003	18	15	668	668	NUM
ejpam-3003	18	16	-	-	SYM
ejpam-3003	18	17	701	701	NUM
ejpam-3003	18	18	669	669	NUM
ejpam-3003	18	19	it	it	PRON
ejpam-3003	18	20	is	be	AUX
ejpam-3003	18	21	well	well	ADV
ejpam-3003	18	22	known	know	VERB
ejpam-3003	18	23	that	that	SCONJ
ejpam-3003	18	24	viscoelastic	viscoelastic	ADJ
ejpam-3003	18	25	materials	material	NOUN
ejpam-3003	18	26	present	present	VERB
ejpam-3003	18	27	nature	nature	NOUN
ejpam-3003	18	28	damping	damp	VERB
ejpam-3003	18	29	,	,	PUNCT
ejpam-3003	18	30	which	which	PRON
ejpam-3003	18	31	is	be	AUX
ejpam-3003	18	32	due	due	ADJ
ejpam-3003	18	33	to	to	ADP
ejpam-3003	18	34	some	some	DET
ejpam-3003	18	35	special	special	ADJ
ejpam-3003	18	36	properties	property	NOUN
ejpam-3003	18	37	of	of	ADP
ejpam-3003	18	38	these	these	DET
ejpam-3003	18	39	materials	material	NOUN
ejpam-3003	18	40	to	to	PART
ejpam-3003	18	41	keep	keep	VERB
ejpam-3003	18	42	memory	memory	NOUN
ejpam-3003	18	43	of	of	ADP
ejpam-3003	18	44	their	their	PRON
ejpam-3003	18	45	past	past	ADJ
ejpam-3003	18	46	trace	trace	NOUN
ejpam-3003	18	47	.	.	PUNCT
ejpam-3003	19	1	from	from	ADP
ejpam-3003	19	2	the	the	DET
ejpam-3003	19	3	mathematical	mathematical	ADJ
ejpam-3003	19	4	point	point	NOUN
ejpam-3003	19	5	of	of	ADP
ejpam-3003	19	6	view	view	NOUN
ejpam-3003	19	7	,	,	PUNCT
ejpam-3003	19	8	these	these	DET
ejpam-3003	19	9	damping	damp	VERB
ejpam-3003	19	10	effects	effect	NOUN
ejpam-3003	19	11	are	be	AUX
ejpam-3003	19	12	modeled	model	VERB
ejpam-3003	19	13	by	by	ADP
ejpam-3003	19	14	integro	integro	ADJ
ejpam-3003	19	15	-	-	PUNCT
ejpam-3003	19	16	differential	differential	NOUN
ejpam-3003	19	17	operators	operator	NOUN
ejpam-3003	19	18	.	.	PUNCT
ejpam-3003	20	1	this	this	DET
ejpam-3003	20	2	type	type	NOUN
ejpam-3003	20	3	of	of	ADP
ejpam-3003	20	4	equations	equation	NOUN
ejpam-3003	20	5	with	with	ADP
ejpam-3003	20	6	viscoelastic	viscoelastic	ADJ
ejpam-3003	20	7	term	term	NOUN
ejpam-3003	20	8	describes	describe	VERB
ejpam-3003	20	9	a	a	DET
ejpam-3003	20	10	variety	variety	NOUN
ejpam-3003	20	11	of	of	ADP
ejpam-3003	20	12	important	important	ADJ
ejpam-3003	20	13	physical	physical	ADJ
ejpam-3003	20	14	processes	process	NOUN
ejpam-3003	20	15	,	,	PUNCT
ejpam-3003	20	16	such	such	ADJ
ejpam-3003	20	17	as	as	ADP
ejpam-3003	20	18	the	the	DET
ejpam-3003	20	19	analysis	analysis	NOUN
ejpam-3003	20	20	of	of	ADP
ejpam-3003	20	21	heat	heat	NOUN
ejpam-3003	20	22	conduction	conduction	NOUN
ejpam-3003	20	23	in	in	ADP
ejpam-3003	20	24	viscoelastic	viscoelastic	ADJ
ejpam-3003	20	25	materials	material	NOUN
ejpam-3003	20	26	,	,	PUNCT
ejpam-3003	20	27	electric	electric	ADJ
ejpam-3003	20	28	signals	signal	NOUN
ejpam-3003	20	29	in	in	ADP
ejpam-3003	20	30	nonlinear	nonlinear	ADJ
ejpam-3003	20	31	telegraph	telegraph	NOUN
ejpam-3003	20	32	line	line	NOUN
ejpam-3003	20	33	with	with	ADP
ejpam-3003	20	34	nonlinear	nonlinear	ADJ
ejpam-3003	20	35	damping	damp	VERB
ejpam-3003	20	36	,	,	PUNCT
ejpam-3003	20	37	viscous	viscous	ADJ
ejpam-3003	20	38	flow	flow	NOUN
ejpam-3003	20	39	in	in	ADP
ejpam-3003	20	40	viscoelastic	viscoelastic	ADJ
ejpam-3003	20	41	materials	material	NOUN
ejpam-3003	20	42	[	[	X
ejpam-3003	20	43	1	1	NUM
ejpam-3003	20	44	]	]	PUNCT
ejpam-3003	20	45	,	,	PUNCT
ejpam-3003	20	46	vibration	vibration	NOUN
ejpam-3003	20	47	of	of	ADP
ejpam-3003	20	48	nonlinear	nonlinear	ADJ
ejpam-3003	20	49	elastic	elastic	ADJ
ejpam-3003	20	50	rod	rod	NOUN
ejpam-3003	20	51	with	with	ADP
ejpam-3003	20	52	viscosity	viscosity	NOUN
ejpam-3003	20	53	[	[	X
ejpam-3003	20	54	2	2	NUM
ejpam-3003	20	55	]	]	PUNCT
ejpam-3003	20	56	,	,	PUNCT
ejpam-3003	20	57	nonlinear	nonlinear	ADJ
ejpam-3003	20	58	bidirectional	bidirectional	ADJ
ejpam-3003	20	59	shallow	shallow	ADJ
ejpam-3003	20	60	water	water	NOUN
ejpam-3003	20	61	waves	wave	NOUN
ejpam-3003	20	62	[	[	X
ejpam-3003	20	63	3	3	NUM
ejpam-3003	20	64	]	]	PUNCT
ejpam-3003	20	65	,	,	PUNCT
ejpam-3003	20	66	and	and	CCONJ
ejpam-3003	20	67	the	the	DET
ejpam-3003	20	68	velocity	velocity	NOUN
ejpam-3003	20	69	evolution	evolution	NOUN
ejpam-3003	20	70	of	of	ADP
ejpam-3003	20	71	ion	ion	NOUN
ejpam-3003	20	72	-	-	PUNCT
ejpam-3003	20	73	acoustic	acoustic	ADJ
ejpam-3003	20	74	waves	wave	NOUN
ejpam-3003	20	75	in	in	ADP
ejpam-3003	20	76	a	a	DET
ejpam-3003	20	77	collision	collision	NOUN
ejpam-3003	20	78	less	less	ADJ
ejpam-3003	20	79	plasma	plasma	NOUN
ejpam-3003	20	80	when	when	SCONJ
ejpam-3003	20	81	a	a	DET
ejpam-3003	20	82	ion	ion	NOUN
ejpam-3003	20	83	viscosity	viscosity	NOUN
ejpam-3003	20	84	is	be	AUX
ejpam-3003	20	85	invoked	invoke	VERB
ejpam-3003	20	86	[	[	X
ejpam-3003	20	87	4	4	NUM
ejpam-3003	20	88	]	]	PUNCT
ejpam-3003	20	89	and	and	CCONJ
ejpam-3003	20	90	so	so	ADV
ejpam-3003	20	91	on	on	ADV
ejpam-3003	20	92	.	.	PUNCT
ejpam-3003	21	1	for	for	ADP
ejpam-3003	21	2	the	the	DET
ejpam-3003	21	3	nonlinear	nonlinear	ADJ
ejpam-3003	21	4	viscoelastic	viscoelastic	PROPN
ejpam-3003	21	5	wave	wave	NOUN
ejpam-3003	21	6	equations	equation	NOUN
ejpam-3003	21	7	with	with	ADP
ejpam-3003	21	8	homogeneous	homogeneous	ADJ
ejpam-3003	21	9	dirichlet	dirichlet	PROPN
ejpam-3003	21	10	boundary	boundary	PROPN
ejpam-3003	21	11	condition	condition	NOUN
ejpam-3003	21	12	,	,	PUNCT
ejpam-3003	21	13	many	many	ADJ
ejpam-3003	21	14	authors	author	NOUN
ejpam-3003	21	15	have	have	AUX
ejpam-3003	21	16	given	give	VERB
ejpam-3003	21	17	attention	attention	NOUN
ejpam-3003	21	18	to	to	ADP
ejpam-3003	21	19	them	they	PRON
ejpam-3003	21	20	for	for	ADP
ejpam-3003	21	21	quite	quite	DET
ejpam-3003	21	22	a	a	DET
ejpam-3003	21	23	long	long	ADJ
ejpam-3003	21	24	time	time	NOUN
ejpam-3003	21	25	.	.	PUNCT
ejpam-3003	22	1	there	there	PRON
ejpam-3003	22	2	are	be	VERB
ejpam-3003	22	3	extensive	extensive	ADJ
ejpam-3003	22	4	literature	literature	NOUN
ejpam-3003	22	5	on	on	ADP
ejpam-3003	22	6	the	the	DET
ejpam-3003	22	7	existence	existence	NOUN
ejpam-3003	22	8	or	or	CCONJ
ejpam-3003	22	9	nonexistence	nonexistence	NOUN
ejpam-3003	22	10	of	of	ADP
ejpam-3003	22	11	global	global	ADJ
ejpam-3003	22	12	solutions	solution	NOUN
ejpam-3003	22	13	,	,	PUNCT
ejpam-3003	22	14	blow	blow	VERB
ejpam-3003	22	15	up	up	ADP
ejpam-3003	22	16	results	result	NOUN
ejpam-3003	22	17	in	in	ADP
ejpam-3003	22	18	finite	finite	ADJ
ejpam-3003	22	19	time	time	NOUN
ejpam-3003	22	20	,	,	PUNCT
ejpam-3003	22	21	and	and	CCONJ
ejpam-3003	22	22	the	the	DET
ejpam-3003	22	23	asymptotic	asymptotic	ADJ
ejpam-3003	22	24	behavior	behavior	NOUN
ejpam-3003	22	25	of	of	ADP
ejpam-3003	22	26	the	the	DET
ejpam-3003	22	27	solutions	solution	NOUN
ejpam-3003	22	28	for	for	ADP
ejpam-3003	22	29	this	this	DET
ejpam-3003	22	30	type	type	NOUN
ejpam-3003	22	31	of	of	ADP
ejpam-3003	22	32	problems	problem	NOUN
ejpam-3003	22	33	.	.	PUNCT
ejpam-3003	23	1	berrimi	berrimi	NOUN
ejpam-3003	23	2	and	and	CCONJ
ejpam-3003	23	3	messaoudi	messaoudi	ADJ
ejpam-3003	24	1	[	[	X
ejpam-3003	24	2	5	5	NUM
ejpam-3003	24	3	]	]	PUNCT
ejpam-3003	24	4	considered	consider	VERB
ejpam-3003	24	5	the	the	DET
ejpam-3003	24	6	following	follow	VERB
ejpam-3003	24	7	nonlinear	nonlinear	ADJ
ejpam-3003	24	8	viscoelastic	viscoelastic	ADJ
ejpam-3003	24	9	wave	wave	NOUN
ejpam-3003	24	10	equation	equation	NOUN
ejpam-3003	24	11	utt	utt	PROPN
ejpam-3003	25	1	−4u+	−4u+	PROPN
ejpam-3003	25	2	∫	∫	PROPN
ejpam-3003	25	3	t	t	PROPN
ejpam-3003	25	4	0	0	NUM
ejpam-3003	25	5	g(t−	g(t−	PROPN
ejpam-3003	25	6	s)4u(s)ds	s)4u(s)d	NOUN
ejpam-3003	25	7	=	=	SYM
ejpam-3003	25	8	u|u|p−2	u|u|p−2	NOUN
ejpam-3003	25	9	,	,	PUNCT
ejpam-3003	25	10	in	in	ADP
ejpam-3003	25	11	ω×	ω×	PROPN
ejpam-3003	25	12	(	(	PUNCT
ejpam-3003	25	13	0,∞	0,∞	NUM
ejpam-3003	25	14	)	)	PUNCT
ejpam-3003	25	15	,	,	PUNCT
ejpam-3003	25	16	(	(	PUNCT
ejpam-3003	25	17	1.2	1.2	NUM
ejpam-3003	25	18	)	)	PUNCT
ejpam-3003	25	19	in	in	ADP
ejpam-3003	25	20	a	a	DET
ejpam-3003	25	21	bounded	bounded	ADJ
ejpam-3003	25	22	domain	domain	NOUN
ejpam-3003	25	23	and	and	CCONJ
ejpam-3003	25	24	p	p	NOUN
ejpam-3003	25	25	≥	≥	NUM
ejpam-3003	25	26	2	2	NUM
ejpam-3003	25	27	.	.	PUNCT
ejpam-3003	26	1	they	they	PRON
ejpam-3003	26	2	established	establish	VERB
ejpam-3003	26	3	a	a	DET
ejpam-3003	26	4	local	local	ADJ
ejpam-3003	26	5	existence	existence	NOUN
ejpam-3003	26	6	result	result	NOUN
ejpam-3003	26	7	and	and	CCONJ
ejpam-3003	26	8	showed	show	VERB
ejpam-3003	26	9	that	that	SCONJ
ejpam-3003	26	10	the	the	DET
ejpam-3003	26	11	local	local	ADJ
ejpam-3003	26	12	solution	solution	NOUN
ejpam-3003	26	13	is	be	AUX
ejpam-3003	26	14	global	global	ADJ
ejpam-3003	26	15	and	and	CCONJ
ejpam-3003	26	16	decays	decay	VERB
ejpam-3003	26	17	uniformly	uniformly	ADV
ejpam-3003	26	18	if	if	SCONJ
ejpam-3003	26	19	the	the	DET
ejpam-3003	26	20	initial	initial	ADJ
ejpam-3003	26	21	data	datum	NOUN
ejpam-3003	26	22	are	be	AUX
ejpam-3003	26	23	small	small	ADJ
ejpam-3003	26	24	enough	enough	ADV
ejpam-3003	26	25	.	.	PUNCT
ejpam-3003	27	1	kim	kim	PROPN
ejpam-3003	27	2	and	and	CCONJ
ejpam-3003	27	3	han	han	PROPN
ejpam-3003	28	1	[	[	X
ejpam-3003	28	2	6	6	NUM
ejpam-3003	28	3	]	]	PUNCT
ejpam-3003	28	4	proved	prove	VERB
ejpam-3003	28	5	that	that	SCONJ
ejpam-3003	28	6	any	any	DET
ejpam-3003	28	7	weak	weak	ADJ
ejpam-3003	28	8	solution	solution	NOUN
ejpam-3003	28	9	with	with	ADP
ejpam-3003	28	10	negative	negative	ADJ
ejpam-3003	28	11	initial	initial	ADJ
ejpam-3003	28	12	energy	energy	NOUN
ejpam-3003	28	13	blows	blow	VERB
ejpam-3003	28	14	up	up	ADP
ejpam-3003	28	15	in	in	ADP
ejpam-3003	28	16	finite	finite	ADJ
ejpam-3003	28	17	time	time	NOUN
ejpam-3003	28	18	under	under	ADP
ejpam-3003	28	19	suitable	suitable	ADJ
ejpam-3003	28	20	conditions	condition	NOUN
ejpam-3003	28	21	on	on	ADP
ejpam-3003	28	22	the	the	DET
ejpam-3003	28	23	relaxation	relaxation	NOUN
ejpam-3003	28	24	function	function	NOUN
ejpam-3003	28	25	g	g	NOUN
ejpam-3003	28	26	for	for	ADP
ejpam-3003	28	27	the	the	DET
ejpam-3003	28	28	equation	equation	NOUN
ejpam-3003	28	29	(	(	PUNCT
ejpam-3003	28	30	1.2	1.2	NUM
ejpam-3003	28	31	)	)	PUNCT
ejpam-3003	28	32	.	.	PUNCT
ejpam-3003	29	1	in	in	ADP
ejpam-3003	29	2	[	[	X
ejpam-3003	29	3	7	7	NUM
ejpam-3003	29	4	]	]	PUNCT
ejpam-3003	29	5	,	,	PUNCT
ejpam-3003	29	6	wang	wang	PROPN
ejpam-3003	29	7	et	et	PROPN
ejpam-3003	29	8	al	al	PROPN
ejpam-3003	29	9	.	.	PROPN
ejpam-3003	29	10	studied	study	VERB
ejpam-3003	29	11	the	the	DET
ejpam-3003	29	12	following	following	ADJ
ejpam-3003	29	13	nonlinear	nonlinear	ADJ
ejpam-3003	29	14	viscoelastic	viscoelastic	ADJ
ejpam-3003	29	15	wave	wave	NOUN
ejpam-3003	29	16	equation	equation	NOUN
ejpam-3003	29	17	utt	utt	PROPN
ejpam-3003	29	18	−4u+	−4u+	PROPN
ejpam-3003	29	19	∫	∫	PROPN
ejpam-3003	29	20	t	t	PROPN
ejpam-3003	29	21	0	0	NUM
ejpam-3003	29	22	g(t−	g(t−	PROPN
ejpam-3003	29	23	s)4u(s)ds+	s)4u(s)ds+	NOUN
ejpam-3003	29	24	ut	ut	PROPN
ejpam-3003	30	1	=	=	PUNCT
ejpam-3003	30	2	u|u|p−2	u|u|p−2	PROPN
ejpam-3003	30	3	,	,	PUNCT
ejpam-3003	30	4	in	in	ADP
ejpam-3003	30	5	ω×	ω×	PROPN
ejpam-3003	30	6	(	(	PUNCT
ejpam-3003	30	7	0,∞	0,∞	NUM
ejpam-3003	30	8	)	)	PUNCT
ejpam-3003	30	9	.	.	PUNCT
ejpam-3003	31	1	(	(	PUNCT
ejpam-3003	31	2	1.3	1.3	NUM
ejpam-3003	31	3	)	)	PUNCT
ejpam-3003	31	4	under	under	ADP
ejpam-3003	31	5	some	some	DET
ejpam-3003	31	6	appropriate	appropriate	ADJ
ejpam-3003	31	7	assumptions	assumption	NOUN
ejpam-3003	31	8	on	on	ADP
ejpam-3003	31	9	g	g	PROPN
ejpam-3003	31	10	,	,	PUNCT
ejpam-3003	31	11	by	by	ADP
ejpam-3003	31	12	introducing	introduce	VERB
ejpam-3003	31	13	potential	potential	ADJ
ejpam-3003	31	14	wells	well	NOUN
ejpam-3003	31	15	they	they	PRON
ejpam-3003	31	16	obtained	obtain	VERB
ejpam-3003	31	17	the	the	DET
ejpam-3003	31	18	existence	existence	NOUN
ejpam-3003	31	19	of	of	ADP
ejpam-3003	31	20	global	global	ADJ
ejpam-3003	31	21	solution	solution	NOUN
ejpam-3003	31	22	and	and	CCONJ
ejpam-3003	31	23	the	the	DET
ejpam-3003	31	24	explicit	explicit	ADJ
ejpam-3003	31	25	exponential	exponential	ADJ
ejpam-3003	31	26	energy	energy	NOUN
ejpam-3003	31	27	decay	decay	NOUN
ejpam-3003	31	28	estimates	estimate	NOUN
ejpam-3003	31	29	.	.	PUNCT
ejpam-3003	32	1	later	later	ADV
ejpam-3003	32	2	,	,	PUNCT
ejpam-3003	32	3	wang	wang	PROPN
ejpam-3003	32	4	[	[	X
ejpam-3003	32	5	8	8	NUM
ejpam-3003	32	6	]	]	PUNCT
ejpam-3003	32	7	proved	prove	VERB
ejpam-3003	32	8	that	that	SCONJ
ejpam-3003	32	9	solution	solution	NOUN
ejpam-3003	32	10	with	with	ADP
ejpam-3003	32	11	arbitrary	arbitrary	ADJ
ejpam-3003	32	12	positive	positive	ADJ
ejpam-3003	32	13	initial	initial	ADJ
ejpam-3003	32	14	energy	energy	NOUN
ejpam-3003	32	15	blows	blow	VERB
ejpam-3003	32	16	up	up	ADP
ejpam-3003	32	17	in	in	ADP
ejpam-3003	32	18	finite	finite	ADJ
ejpam-3003	32	19	time	time	NOUN
ejpam-3003	32	20	under	under	ADP
ejpam-3003	32	21	some	some	DET
ejpam-3003	32	22	appropriate	appropriate	ADJ
ejpam-3003	32	23	assumptions	assumption	NOUN
ejpam-3003	32	24	on	on	ADP
ejpam-3003	32	25	the	the	DET
ejpam-3003	32	26	relaxation	relaxation	NOUN
ejpam-3003	32	27	function	function	NOUN
ejpam-3003	32	28	g	g	NOUN
ejpam-3003	32	29	and	and	CCONJ
ejpam-3003	32	30	the	the	DET
ejpam-3003	32	31	initial	initial	ADJ
ejpam-3003	32	32	data	datum	NOUN
ejpam-3003	32	33	.	.	PUNCT
ejpam-3003	33	1	messaoudi	messaoudi	PROPN
ejpam-3003	34	1	[	[	X
ejpam-3003	34	2	9	9	NUM
ejpam-3003	34	3	]	]	PUNCT
ejpam-3003	34	4	changed	change	VERB
ejpam-3003	34	5	the	the	DET
ejpam-3003	34	6	linear	linear	ADJ
ejpam-3003	34	7	damping	damp	VERB
ejpam-3003	34	8	term	term	NOUN
ejpam-3003	34	9	ut	ut	PROPN
ejpam-3003	34	10	into	into	ADP
ejpam-3003	34	11	the	the	DET
ejpam-3003	34	12	nonlinear	nonlinear	ADJ
ejpam-3003	34	13	damping	damp	VERB
ejpam-3003	34	14	term	term	NOUN
ejpam-3003	34	15	aut|ut|m−2	aut|ut|m−2	NOUN
ejpam-3003	34	16	.	.	PUNCT
ejpam-3003	35	1	under	under	ADP
ejpam-3003	35	2	suitable	suitable	ADJ
ejpam-3003	35	3	conditions	condition	NOUN
ejpam-3003	35	4	on	on	ADP
ejpam-3003	35	5	g	g	NOUN
ejpam-3003	35	6	,	,	PUNCT
ejpam-3003	35	7	he	he	PRON
ejpam-3003	35	8	proved	prove	VERB
ejpam-3003	35	9	that	that	SCONJ
ejpam-3003	35	10	the	the	DET
ejpam-3003	35	11	solution	solution	NOUN
ejpam-3003	35	12	with	with	ADP
ejpam-3003	35	13	negative	negative	ADJ
ejpam-3003	35	14	initial	initial	ADJ
ejpam-3003	35	15	energy	energy	NOUN
ejpam-3003	35	16	blows	blow	VERB
ejpam-3003	35	17	up	up	ADP
ejpam-3003	35	18	in	in	ADP
ejpam-3003	35	19	finite	finite	ADJ
ejpam-3003	35	20	time	time	NOUN
ejpam-3003	35	21	.	.	PUNCT
ejpam-3003	36	1	this	this	PRON
ejpam-3003	36	2	blow	blow	VERB
ejpam-3003	36	3	up	up	ADP
ejpam-3003	36	4	result	result	NOUN
ejpam-3003	36	5	was	be	AUX
ejpam-3003	36	6	extended	extend	VERB
ejpam-3003	36	7	by	by	ADP
ejpam-3003	36	8	the	the	DET
ejpam-3003	36	9	same	same	ADJ
ejpam-3003	36	10	author	author	NOUN
ejpam-3003	36	11	[	[	X
ejpam-3003	36	12	10	10	NUM
ejpam-3003	36	13	]	]	PUNCT
ejpam-3003	36	14	to	to	ADP
ejpam-3003	36	15	certain	certain	ADJ
ejpam-3003	36	16	solution	solution	NOUN
ejpam-3003	36	17	with	with	ADP
ejpam-3003	36	18	positive	positive	ADJ
ejpam-3003	36	19	initial	initial	ADJ
ejpam-3003	36	20	energy	energy	NOUN
ejpam-3003	36	21	.	.	PUNCT
ejpam-3003	37	1	song	song	NOUN
ejpam-3003	37	2	and	and	CCONJ
ejpam-3003	37	3	zhong	zhong	PROPN
ejpam-3003	38	1	[	[	X
ejpam-3003	38	2	11	11	NUM
ejpam-3003	38	3	]	]	PUNCT
ejpam-3003	38	4	considered	consider	VERB
ejpam-3003	38	5	the	the	DET
ejpam-3003	38	6	nonlinear	nonlinear	ADJ
ejpam-3003	38	7	viscoelastic	viscoelastic	ADJ
ejpam-3003	38	8	wave	wave	NOUN
ejpam-3003	38	9	equation	equation	NOUN
ejpam-3003	38	10	with	with	ADP
ejpam-3003	38	11	strong	strong	ADJ
ejpam-3003	38	12	damping	damp	VERB
ejpam-3003	38	13	term	term	NOUN
ejpam-3003	38	14	utt	utt	PROPN
ejpam-3003	38	15	−4u+	−4u+	PROPN
ejpam-3003	38	16	∫	∫	PROPN
ejpam-3003	38	17	t	t	PROPN
ejpam-3003	38	18	0	0	NUM
ejpam-3003	38	19	g(t−	g(t−	PROPN
ejpam-3003	38	20	s)4u(s)ds−4ut	s)4u(s)ds−4ut	PROPN
ejpam-3003	38	21	=	=	SYM
ejpam-3003	38	22	u|u|p−2	u|u|p−2	PROPN
ejpam-3003	38	23	,	,	PUNCT
ejpam-3003	38	24	in	in	ADP
ejpam-3003	38	25	ω×	ω×	PROPN
ejpam-3003	38	26	(	(	PUNCT
ejpam-3003	38	27	0,∞	0,∞	NUM
ejpam-3003	38	28	)	)	PUNCT
ejpam-3003	38	29	,	,	PUNCT
ejpam-3003	38	30	(	(	PUNCT
ejpam-3003	38	31	1.4	1.4	NUM
ejpam-3003	38	32	)	)	PUNCT
ejpam-3003	38	33	with	with	ADP
ejpam-3003	38	34	homogeneous	homogeneous	ADJ
ejpam-3003	38	35	dirichlet	dirichlet	PROPN
ejpam-3003	38	36	boundary	boundary	PROPN
ejpam-3003	38	37	condition	condition	NOUN
ejpam-3003	38	38	.	.	PUNCT
ejpam-3003	39	1	they	they	PRON
ejpam-3003	39	2	proved	prove	VERB
ejpam-3003	39	3	that	that	SCONJ
ejpam-3003	39	4	the	the	DET
ejpam-3003	39	5	solution	solution	NOUN
ejpam-3003	39	6	with	with	ADP
ejpam-3003	39	7	positive	positive	ADJ
ejpam-3003	39	8	initial	initial	ADJ
ejpam-3003	39	9	energy	energy	NOUN
ejpam-3003	39	10	blows	blow	VERB
ejpam-3003	39	11	up	up	ADP
ejpam-3003	39	12	in	in	ADP
ejpam-3003	39	13	finite	finite	ADJ
ejpam-3003	39	14	time	time	NOUN
ejpam-3003	39	15	.	.	PUNCT
ejpam-3003	40	1	in	in	ADP
ejpam-3003	40	2	[	[	X
ejpam-3003	40	3	12	12	NUM
ejpam-3003	40	4	]	]	PUNCT
ejpam-3003	40	5	,	,	PUNCT
ejpam-3003	40	6	han	han	PROPN
ejpam-3003	40	7	and	and	CCONJ
ejpam-3003	40	8	wang	wang	PROPN
ejpam-3003	40	9	studied	study	VERB
ejpam-3003	40	10	the	the	DET
ejpam-3003	40	11	general	general	ADJ
ejpam-3003	40	12	decay	decay	NOUN
ejpam-3003	40	13	of	of	ADP
ejpam-3003	40	14	energy	energy	NOUN
ejpam-3003	40	15	for	for	ADP
ejpam-3003	40	16	the	the	DET
ejpam-3003	40	17	following	follow	VERB
ejpam-3003	40	18	nonlinear	nonlinear	ADJ
ejpam-3003	40	19	viscoelastic	viscoelastic	ADJ
ejpam-3003	40	20	equation	equation	NOUN
ejpam-3003	40	21	without	without	ADP
ejpam-3003	40	22	source	source	NOUN
ejpam-3003	40	23	term	term	NOUN
ejpam-3003	40	24	utt	utt	PROPN
ejpam-3003	41	1	−4u+	−4u+	PROPN
ejpam-3003	42	1	∫	∫	PROPN
ejpam-3003	42	2	t	t	PROPN
ejpam-3003	42	3	0	0	NUM
ejpam-3003	42	4	g(t−	g(t−	PROPN
ejpam-3003	42	5	s)4u(s)ds−4utt	s)4u(s)ds−4utt	NUM
ejpam-3003	42	6	+	+	CCONJ
ejpam-3003	42	7	ut|ut|m−2	ut|ut|m−2	PROPN
ejpam-3003	42	8	=	=	SYM
ejpam-3003	42	9	0	0	NUM
ejpam-3003	42	10	,	,	PUNCT
ejpam-3003	42	11	in	in	ADP
ejpam-3003	42	12	ω×	ω×	PROPN
ejpam-3003	42	13	(	(	PUNCT
ejpam-3003	42	14	0,∞	0,∞	NUM
ejpam-3003	42	15	)	)	PUNCT
ejpam-3003	42	16	.	.	PUNCT
ejpam-3003	43	1	(	(	PUNCT
ejpam-3003	43	2	1.5	1.5	NUM
ejpam-3003	43	3	)	)	PUNCT
ejpam-3003	43	4	h.f	h.f	PROPN
ejpam-3003	43	5	.	.	PROPN
ejpam-3003	43	6	di	di	PROPN
ejpam-3003	43	7	,	,	PUNCT
ejpam-3003	43	8	y.d	y.d	PROPN
ejpam-3003	43	9	.	.	PROPN
ejpam-3003	43	10	shang	shang	PROPN
ejpam-3003	43	11	/	/	SYM
ejpam-3003	43	12	eur	eur	PROPN
ejpam-3003	43	13	.	.	PUNCT
ejpam-3003	44	1	j.	j.	PROPN
ejpam-3003	44	2	pure	pure	PROPN
ejpam-3003	44	3	appl	appl	PROPN
ejpam-3003	44	4	.	.	PROPN
ejpam-3003	44	5	math	math	PROPN
ejpam-3003	44	6	,	,	PUNCT
ejpam-3003	44	7	10	10	NUM
ejpam-3003	44	8	(	(	PUNCT
ejpam-3003	44	9	4	4	NUM
ejpam-3003	44	10	)	)	PUNCT
ejpam-3003	44	11	(	(	PUNCT
ejpam-3003	44	12	2017	2017	NUM
ejpam-3003	44	13	)	)	PUNCT
ejpam-3003	44	14	,	,	PUNCT
ejpam-3003	44	15	668	668	NUM
ejpam-3003	44	16	-	-	SYM
ejpam-3003	44	17	701	701	NUM
ejpam-3003	44	18	670	670	NUM
ejpam-3003	44	19	more	more	ADV
ejpam-3003	44	20	recently	recently	ADV
ejpam-3003	44	21	,	,	PUNCT
ejpam-3003	44	22	xu	xu	PROPN
ejpam-3003	44	23	,	,	PUNCT
ejpam-3003	44	24	yang	yang	PROPN
ejpam-3003	44	25	and	and	CCONJ
ejpam-3003	44	26	liu	liu	PROPN
ejpam-3003	45	1	[	[	X
ejpam-3003	45	2	13	13	NUM
ejpam-3003	45	3	]	]	PUNCT
ejpam-3003	45	4	investigated	investigate	VERB
ejpam-3003	45	5	the	the	DET
ejpam-3003	45	6	following	follow	VERB
ejpam-3003	45	7	strongly	strongly	ADV
ejpam-3003	45	8	damped	damp	VERB
ejpam-3003	45	9	viscoelastic	viscoelastic	ADJ
ejpam-3003	45	10	wave	wave	NOUN
ejpam-3003	45	11	equation	equation	NOUN
ejpam-3003	45	12	utt	utt	PROPN
ejpam-3003	45	13	−4u+	−4u+	PROPN
ejpam-3003	45	14	∫	∫	PROPN
ejpam-3003	45	15	t	t	PROPN
ejpam-3003	45	16	0	0	NUM
ejpam-3003	45	17	g(t−	g(t−	PROPN
ejpam-3003	45	18	s)4u(s)ds−4ut	s)4u(s)ds−4ut	PROPN
ejpam-3003	45	19	−4utt	−4utt	NOUN
ejpam-3003	45	20	+	+	CCONJ
ejpam-3003	45	21	ut	ut	PROPN
ejpam-3003	45	22	=	=	SYM
ejpam-3003	45	23	u|u|p−1	u|u|p−1	PROPN
ejpam-3003	45	24	,	,	PUNCT
ejpam-3003	45	25	in	in	ADP
ejpam-3003	45	26	ω×	ω×	PROPN
ejpam-3003	45	27	(	(	PUNCT
ejpam-3003	45	28	0,∞	0,∞	NUM
ejpam-3003	45	29	)	)	PUNCT
ejpam-3003	45	30	.	.	PUNCT
ejpam-3003	46	1	(	(	PUNCT
ejpam-3003	46	2	1.6	1.6	NUM
ejpam-3003	46	3	)	)	PUNCT
ejpam-3003	46	4	they	they	PRON
ejpam-3003	46	5	proved	prove	VERB
ejpam-3003	46	6	the	the	DET
ejpam-3003	46	7	existence	existence	NOUN
ejpam-3003	46	8	and	and	CCONJ
ejpam-3003	46	9	nonexistence	nonexistence	NOUN
ejpam-3003	46	10	of	of	ADP
ejpam-3003	46	11	global	global	ADJ
ejpam-3003	46	12	weak	weak	ADJ
ejpam-3003	46	13	solution	solution	NOUN
ejpam-3003	46	14	with	with	ADP
ejpam-3003	46	15	low	low	ADJ
ejpam-3003	46	16	initial	initial	ADJ
ejpam-3003	46	17	energy	energy	NOUN
ejpam-3003	46	18	by	by	ADP
ejpam-3003	46	19	introducing	introduce	VERB
ejpam-3003	46	20	a	a	DET
ejpam-3003	46	21	family	family	NOUN
ejpam-3003	46	22	of	of	ADP
ejpam-3003	46	23	potential	potential	ADJ
ejpam-3003	46	24	wells	well	NOUN
ejpam-3003	46	25	.	.	PUNCT
ejpam-3003	47	1	then	then	ADV
ejpam-3003	47	2	,	,	PUNCT
ejpam-3003	47	3	they	they	PRON
ejpam-3003	47	4	established	establish	VERB
ejpam-3003	47	5	a	a	DET
ejpam-3003	47	6	blow	blow	NOUN
ejpam-3003	47	7	up	up	ADP
ejpam-3003	47	8	result	result	NOUN
ejpam-3003	47	9	for	for	ADP
ejpam-3003	47	10	certain	certain	ADJ
ejpam-3003	47	11	solutions	solution	NOUN
ejpam-3003	47	12	with	with	ADP
ejpam-3003	47	13	arbitrary	arbitrary	ADJ
ejpam-3003	47	14	positive	positive	ADJ
ejpam-3003	47	15	initial	initial	ADJ
ejpam-3003	47	16	energy	energy	NOUN
ejpam-3003	47	17	.	.	PUNCT
ejpam-3003	48	1	messaoudi	messaoudi	ADJ
ejpam-3003	48	2	and	and	CCONJ
ejpam-3003	48	3	tatar	tatar	NOUN
ejpam-3003	48	4	[	[	X
ejpam-3003	48	5	14	14	NUM
ejpam-3003	48	6	]	]	PUNCT
ejpam-3003	48	7	considered	consider	VERB
ejpam-3003	48	8	the	the	DET
ejpam-3003	48	9	following	follow	VERB
ejpam-3003	48	10	nonlinear	nonlinear	ADJ
ejpam-3003	48	11	viscoelastic	viscoelastic	ADJ
ejpam-3003	48	12	equation	equation	NOUN
ejpam-3003	48	13	|ut|ρutt	|ut|ρutt	VERB
ejpam-3003	49	1	−4u+	−4u+	PROPN
ejpam-3003	49	2	∫	∫	PROPN
ejpam-3003	49	3	t	t	PROPN
ejpam-3003	49	4	0	0	NUM
ejpam-3003	49	5	g(t−	g(t−	PROPN
ejpam-3003	49	6	s)4u(s)ds−4utt	s)4u(s)ds−4utt	NUM
ejpam-3003	49	7	=	=	SYM
ejpam-3003	49	8	bu|u|p−1	bu|u|p−1	ADJ
ejpam-3003	49	9	,	,	PUNCT
ejpam-3003	49	10	in	in	ADP
ejpam-3003	49	11	ω×	ω×	PROPN
ejpam-3003	49	12	(	(	PUNCT
ejpam-3003	49	13	0,∞	0,∞	NUM
ejpam-3003	49	14	)	)	PUNCT
ejpam-3003	49	15	,	,	PUNCT
ejpam-3003	49	16	(	(	PUNCT
ejpam-3003	49	17	1.7	1.7	NUM
ejpam-3003	49	18	)	)	PUNCT
ejpam-3003	49	19	with	with	ADP
ejpam-3003	49	20	dirichlet	dirichlet	PROPN
ejpam-3003	49	21	boundary	boundary	PROPN
ejpam-3003	49	22	condition	condition	NOUN
ejpam-3003	49	23	.	.	PUNCT
ejpam-3003	50	1	by	by	ADP
ejpam-3003	50	2	using	use	VERB
ejpam-3003	50	3	the	the	DET
ejpam-3003	50	4	potential	potential	ADJ
ejpam-3003	50	5	well	well	ADJ
ejpam-3003	50	6	method	method	NOUN
ejpam-3003	50	7	,	,	PUNCT
ejpam-3003	50	8	they	they	PRON
ejpam-3003	50	9	proved	prove	VERB
ejpam-3003	50	10	that	that	SCONJ
ejpam-3003	50	11	the	the	DET
ejpam-3003	50	12	viscoelastic	viscoelastic	ADJ
ejpam-3003	50	13	term	term	NOUN
ejpam-3003	50	14	is	be	AUX
ejpam-3003	50	15	enough	enough	ADJ
ejpam-3003	50	16	to	to	PART
ejpam-3003	50	17	ensure	ensure	VERB
ejpam-3003	50	18	the	the	DET
ejpam-3003	50	19	global	global	ADJ
ejpam-3003	50	20	existence	existence	NOUN
ejpam-3003	50	21	and	and	CCONJ
ejpam-3003	50	22	uniform	uniform	ADJ
ejpam-3003	50	23	decay	decay	NOUN
ejpam-3003	50	24	of	of	ADP
ejpam-3003	50	25	solutions	solution	NOUN
ejpam-3003	50	26	provided	provide	VERB
ejpam-3003	50	27	that	that	SCONJ
ejpam-3003	50	28	the	the	DET
ejpam-3003	50	29	initial	initial	ADJ
ejpam-3003	50	30	data	datum	NOUN
ejpam-3003	50	31	are	be	AUX
ejpam-3003	50	32	in	in	ADP
ejpam-3003	50	33	same	same	ADJ
ejpam-3003	50	34	stable	stable	ADJ
ejpam-3003	50	35	set	set	NOUN
ejpam-3003	50	36	.	.	PUNCT
ejpam-3003	51	1	liu	liu	PROPN
ejpam-3003	52	1	[	[	X
ejpam-3003	52	2	15	15	NUM
ejpam-3003	52	3	]	]	PUNCT
ejpam-3003	52	4	proved	prove	VERB
ejpam-3003	52	5	that	that	SCONJ
ejpam-3003	52	6	for	for	ADP
ejpam-3003	52	7	certain	certain	ADJ
ejpam-3003	52	8	class	class	NOUN
ejpam-3003	52	9	of	of	ADP
ejpam-3003	52	10	relaxation	relaxation	NOUN
ejpam-3003	52	11	function	function	NOUN
ejpam-3003	52	12	g	g	NOUN
ejpam-3003	52	13	and	and	CCONJ
ejpam-3003	52	14	certain	certain	ADJ
ejpam-3003	52	15	initial	initial	ADJ
ejpam-3003	52	16	data	datum	NOUN
ejpam-3003	52	17	in	in	ADP
ejpam-3003	52	18	the	the	DET
ejpam-3003	52	19	unstable	unstable	ADJ
ejpam-3003	52	20	set	set	NOUN
ejpam-3003	52	21	,	,	PUNCT
ejpam-3003	52	22	there	there	PRON
ejpam-3003	52	23	are	be	VERB
ejpam-3003	52	24	the	the	DET
ejpam-3003	52	25	solutions	solution	NOUN
ejpam-3003	52	26	with	with	ADP
ejpam-3003	52	27	positive	positive	ADJ
ejpam-3003	52	28	initial	initial	ADJ
ejpam-3003	52	29	energy	energy	NOUN
ejpam-3003	52	30	that	that	PRON
ejpam-3003	52	31	blow	blow	VERB
ejpam-3003	52	32	up	up	ADP
ejpam-3003	52	33	in	in	ADP
ejpam-3003	52	34	finite	finite	ADJ
ejpam-3003	52	35	time	time	NOUN
ejpam-3003	52	36	.	.	PUNCT
ejpam-3003	53	1	cavalcanti	cavalcanti	PROPN
ejpam-3003	53	2	et	et	PROPN
ejpam-3003	53	3	al	al	PROPN
ejpam-3003	53	4	.	.	PUNCT
ejpam-3003	54	1	[	[	X
ejpam-3003	54	2	16	16	NUM
ejpam-3003	54	3	]	]	PUNCT
ejpam-3003	54	4	considered	consider	VERB
ejpam-3003	54	5	the	the	DET
ejpam-3003	54	6	following	follow	VERB
ejpam-3003	54	7	nonlinear	nonlinear	ADJ
ejpam-3003	54	8	viscoelastic	viscoelastic	ADJ
ejpam-3003	54	9	equation	equation	NOUN
ejpam-3003	54	10	without	without	ADP
ejpam-3003	54	11	source	source	NOUN
ejpam-3003	54	12	and	and	CCONJ
ejpam-3003	54	13	weak	weak	ADJ
ejpam-3003	54	14	damping	damp	VERB
ejpam-3003	54	15	terms	term	NOUN
ejpam-3003	54	16	|ut|ρutt	|ut|ρutt	VERB
ejpam-3003	55	1	−4u+	−4u+	PROPN
ejpam-3003	55	2	∫	∫	PROPN
ejpam-3003	55	3	t	t	PROPN
ejpam-3003	55	4	0	0	NUM
ejpam-3003	55	5	g(t−	g(t−	PROPN
ejpam-3003	55	6	s)4u(s)ds−	s)4u(s)ds−	NOUN
ejpam-3003	55	7	γ4ut	γ4ut	X
ejpam-3003	55	8	−4utt	−4utt	NOUN
ejpam-3003	55	9	=	=	SYM
ejpam-3003	55	10	0	0	NUM
ejpam-3003	55	11	,	,	PUNCT
ejpam-3003	55	12	in	in	ADP
ejpam-3003	55	13	ω×	ω×	PROPN
ejpam-3003	55	14	(	(	PUNCT
ejpam-3003	55	15	0,∞	0,∞	NUM
ejpam-3003	55	16	)	)	PUNCT
ejpam-3003	55	17	.	.	PUNCT
ejpam-3003	56	1	(	(	PUNCT
ejpam-3003	56	2	1.8	1.8	NUM
ejpam-3003	56	3	)	)	PUNCT
ejpam-3003	56	4	they	they	PRON
ejpam-3003	56	5	obtained	obtain	VERB
ejpam-3003	56	6	the	the	DET
ejpam-3003	56	7	global	global	ADJ
ejpam-3003	56	8	existence	existence	NOUN
ejpam-3003	56	9	of	of	ADP
ejpam-3003	56	10	weak	weak	ADJ
ejpam-3003	56	11	solution	solution	NOUN
ejpam-3003	56	12	and	and	CCONJ
ejpam-3003	56	13	uniform	uniform	ADJ
ejpam-3003	56	14	decay	decay	NOUN
ejpam-3003	56	15	rates	rate	NOUN
ejpam-3003	56	16	of	of	ADP
ejpam-3003	56	17	the	the	DET
ejpam-3003	56	18	energy	energy	NOUN
ejpam-3003	56	19	by	by	ADP
ejpam-3003	56	20	assuming	assume	VERB
ejpam-3003	56	21	that	that	SCONJ
ejpam-3003	56	22	the	the	DET
ejpam-3003	56	23	relaxation	relaxation	NOUN
ejpam-3003	56	24	g	g	PROPN
ejpam-3003	56	25	has	have	VERB
ejpam-3003	56	26	a	a	DET
ejpam-3003	56	27	exponential	exponential	ADJ
ejpam-3003	56	28	decay	decay	NOUN
ejpam-3003	56	29	.	.	PUNCT
ejpam-3003	57	1	in	in	ADP
ejpam-3003	57	2	[	[	X
ejpam-3003	57	3	17	17	NUM
ejpam-3003	57	4	]	]	PUNCT
ejpam-3003	57	5	,	,	PUNCT
ejpam-3003	57	6	wu	wu	PROPN
ejpam-3003	57	7	studied	study	VERB
ejpam-3003	57	8	the	the	DET
ejpam-3003	57	9	following	follow	VERB
ejpam-3003	57	10	viscoelastic	viscoelastic	ADJ
ejpam-3003	57	11	equation	equation	NOUN
ejpam-3003	57	12	with	with	ADP
ejpam-3003	57	13	nonlinear	nonlinear	ADJ
ejpam-3003	57	14	source	source	NOUN
ejpam-3003	57	15	and	and	CCONJ
ejpam-3003	57	16	weak	weak	ADJ
ejpam-3003	57	17	damping	damp	VERB
ejpam-3003	57	18	terms	term	NOUN
ejpam-3003	57	19	|ut|ρutt	|ut|ρutt	ADJ
ejpam-3003	57	20	−4u−4utt	−4u−4utt	NOUN
ejpam-3003	58	1	+	+	CCONJ
ejpam-3003	58	2	∫	∫	PROPN
ejpam-3003	58	3	t	t	PROPN
ejpam-3003	58	4	0	0	NUM
ejpam-3003	58	5	g(t−	g(t−	PROPN
ejpam-3003	58	6	s)4u(s)ds+	s)4u(s)ds+	NOUN
ejpam-3003	58	7	|ut|mut	|ut|mut	NOUN
ejpam-3003	59	1	=	=	SYM
ejpam-3003	59	2	|u|p−1u	|u|p−1u	INTJ
ejpam-3003	59	3	,	,	PUNCT
ejpam-3003	59	4	in	in	ADP
ejpam-3003	59	5	ω×	ω×	PROPN
ejpam-3003	59	6	(	(	PUNCT
ejpam-3003	59	7	0,∞	0,∞	NUM
ejpam-3003	59	8	)	)	PUNCT
ejpam-3003	59	9	.	.	PUNCT
ejpam-3003	60	1	(	(	PUNCT
ejpam-3003	60	2	1.9	1.9	NUM
ejpam-3003	60	3	)	)	PUNCT
ejpam-3003	60	4	he	he	PRON
ejpam-3003	60	5	discussed	discuss	VERB
ejpam-3003	60	6	the	the	DET
ejpam-3003	60	7	general	general	ADJ
ejpam-3003	60	8	uniform	uniform	ADJ
ejpam-3003	60	9	decay	decay	NOUN
ejpam-3003	60	10	estimate	estimate	NOUN
ejpam-3003	60	11	of	of	ADP
ejpam-3003	60	12	solution	solution	NOUN
ejpam-3003	60	13	energy	energy	NOUN
ejpam-3003	60	14	under	under	ADP
ejpam-3003	60	15	suitable	suitable	ADJ
ejpam-3003	60	16	conditions	condition	NOUN
ejpam-3003	60	17	on	on	ADP
ejpam-3003	60	18	the	the	DET
ejpam-3003	60	19	relaxation	relaxation	NOUN
ejpam-3003	60	20	function	function	NOUN
ejpam-3003	60	21	g	g	NOUN
ejpam-3003	60	22	,	,	PUNCT
ejpam-3003	60	23	the	the	DET
ejpam-3003	60	24	initial	initial	ADJ
ejpam-3003	60	25	data	datum	NOUN
ejpam-3003	60	26	and	and	CCONJ
ejpam-3003	60	27	the	the	DET
ejpam-3003	60	28	parameters	parameter	NOUN
ejpam-3003	60	29	ρ	ρ	PROPN
ejpam-3003	60	30	,	,	PUNCT
ejpam-3003	60	31	m	m	PRON
ejpam-3003	60	32	,	,	PUNCT
ejpam-3003	60	33	p.	p.	NOUN
ejpam-3003	60	34	we	we	PRON
ejpam-3003	60	35	also	also	ADV
ejpam-3003	60	36	note	note	VERB
ejpam-3003	60	37	that	that	SCONJ
ejpam-3003	60	38	the	the	DET
ejpam-3003	60	39	potential	potential	ADJ
ejpam-3003	60	40	well	well	ADJ
ejpam-3003	60	41	method	method	NOUN
ejpam-3003	60	42	is	be	AUX
ejpam-3003	60	43	a	a	DET
ejpam-3003	60	44	very	very	ADV
ejpam-3003	60	45	popular	popular	ADJ
ejpam-3003	60	46	and	and	CCONJ
ejpam-3003	60	47	important	important	ADJ
ejpam-3003	60	48	way	way	NOUN
ejpam-3003	60	49	to	to	PART
ejpam-3003	60	50	study	study	VERB
ejpam-3003	60	51	the	the	DET
ejpam-3003	60	52	global	global	ADJ
ejpam-3003	60	53	existence	existence	NOUN
ejpam-3003	60	54	and	and	CCONJ
ejpam-3003	60	55	finite	finite	ADJ
ejpam-3003	60	56	time	time	NOUN
ejpam-3003	60	57	blow	blow	VERB
ejpam-3003	60	58	up	up	ADP
ejpam-3003	60	59	of	of	ADP
ejpam-3003	60	60	solutions	solution	NOUN
ejpam-3003	60	61	for	for	ADP
ejpam-3003	60	62	nonlinear	nonlinear	ADJ
ejpam-3003	60	63	evolution	evolution	NOUN
ejpam-3003	60	64	equations	equation	NOUN
ejpam-3003	60	65	.	.	PUNCT
ejpam-3003	61	1	this	this	DET
ejpam-3003	61	2	method	method	NOUN
ejpam-3003	61	3	was	be	AUX
ejpam-3003	61	4	first	first	ADV
ejpam-3003	61	5	introduced	introduce	VERB
ejpam-3003	61	6	by	by	ADP
ejpam-3003	61	7	sattinger	sattinger	NOUN
ejpam-3003	61	8	[	[	X
ejpam-3003	61	9	26	26	NUM
ejpam-3003	61	10	]	]	PUNCT
ejpam-3003	61	11	to	to	PART
ejpam-3003	61	12	study	study	VERB
ejpam-3003	61	13	the	the	DET
ejpam-3003	61	14	global	global	ADJ
ejpam-3003	61	15	existence	existence	NOUN
ejpam-3003	61	16	of	of	ADP
ejpam-3003	61	17	solutions	solution	NOUN
ejpam-3003	61	18	for	for	ADP
ejpam-3003	61	19	nonlinear	nonlinear	ADJ
ejpam-3003	61	20	hyperbolic	hyperbolic	ADJ
ejpam-3003	61	21	equations	equation	NOUN
ejpam-3003	61	22	.	.	PUNCT
ejpam-3003	62	1	and	and	CCONJ
ejpam-3003	62	2	it	it	PRON
ejpam-3003	62	3	also	also	ADV
ejpam-3003	62	4	plays	play	VERB
ejpam-3003	62	5	a	a	DET
ejpam-3003	62	6	very	very	ADV
ejpam-3003	62	7	vital	vital	ADJ
ejpam-3003	62	8	role	role	NOUN
ejpam-3003	62	9	in	in	ADP
ejpam-3003	62	10	deriving	derive	VERB
ejpam-3003	62	11	the	the	DET
ejpam-3003	62	12	threshold	threshold	NOUN
ejpam-3003	62	13	results	result	NOUN
ejpam-3003	62	14	between	between	ADP
ejpam-3003	62	15	the	the	DET
ejpam-3003	62	16	global	global	ADJ
ejpam-3003	62	17	existence	existence	NOUN
ejpam-3003	62	18	and	and	CCONJ
ejpam-3003	62	19	nonexistence	nonexistence	NOUN
ejpam-3003	62	20	of	of	ADP
ejpam-3003	62	21	solutions	solution	NOUN
ejpam-3003	62	22	.	.	PUNCT
ejpam-3003	63	1	hence	hence	ADV
ejpam-3003	63	2	,	,	PUNCT
ejpam-3003	63	3	the	the	DET
ejpam-3003	63	4	potential	potential	ADJ
ejpam-3003	63	5	well	well	ADJ
ejpam-3003	63	6	method	method	NOUN
ejpam-3003	63	7	has	have	AUX
ejpam-3003	63	8	been	be	AUX
ejpam-3003	63	9	widely	widely	ADV
ejpam-3003	63	10	used	use	VERB
ejpam-3003	63	11	and	and	CCONJ
ejpam-3003	63	12	extended	extend	VERB
ejpam-3003	63	13	by	by	ADP
ejpam-3003	63	14	many	many	ADJ
ejpam-3003	63	15	authors	author	NOUN
ejpam-3003	63	16	to	to	PART
ejpam-3003	63	17	study	study	VERB
ejpam-3003	63	18	different	different	ADJ
ejpam-3003	63	19	kinds	kind	NOUN
ejpam-3003	63	20	of	of	ADP
ejpam-3003	63	21	evolution	evolution	NOUN
ejpam-3003	63	22	equations	equation	NOUN
ejpam-3003	63	23	,	,	PUNCT
ejpam-3003	63	24	we	we	PRON
ejpam-3003	63	25	refer	refer	VERB
ejpam-3003	63	26	the	the	DET
ejpam-3003	63	27	reader	reader	NOUN
ejpam-3003	63	28	to	to	PART
ejpam-3003	63	29	see	see	VERB
ejpam-3003	63	30	[	[	X
ejpam-3003	63	31	25,27	25,27	NUM
ejpam-3003	63	32	-	-	SYM
ejpam-3003	63	33	29	29	NUM
ejpam-3003	63	34	]	]	PUNCT
ejpam-3003	63	35	and	and	CCONJ
ejpam-3003	63	36	the	the	DET
ejpam-3003	63	37	papers	paper	NOUN
ejpam-3003	63	38	cited	cite	VERB
ejpam-3003	63	39	therein	therein	ADV
ejpam-3003	63	40	.	.	PUNCT
ejpam-3003	64	1	for	for	ADP
ejpam-3003	64	2	the	the	DET
ejpam-3003	64	3	viscoelastic	viscoelastic	ADJ
ejpam-3003	64	4	equation	equation	NOUN
ejpam-3003	64	5	with	with	ADP
ejpam-3003	64	6	nonlinear	nonlinear	ADJ
ejpam-3003	64	7	boundary	boundary	ADJ
ejpam-3003	64	8	condition	condition	NOUN
ejpam-3003	64	9	,	,	PUNCT
ejpam-3003	64	10	there	there	PRON
ejpam-3003	64	11	are	be	VERB
ejpam-3003	64	12	also	also	ADV
ejpam-3003	64	13	some	some	DET
ejpam-3003	64	14	results	result	NOUN
ejpam-3003	64	15	about	about	ADP
ejpam-3003	64	16	the	the	DET
ejpam-3003	64	17	well	well	NOUN
ejpam-3003	64	18	-	-	PUNCT
ejpam-3003	64	19	posedness	posedness	NOUN
ejpam-3003	64	20	for	for	ADP
ejpam-3003	64	21	this	this	DET
ejpam-3003	64	22	type	type	NOUN
ejpam-3003	64	23	of	of	ADP
ejpam-3003	64	24	problems	problem	NOUN
ejpam-3003	64	25	.	.	PUNCT
ejpam-3003	65	1	we	we	PRON
ejpam-3003	65	2	refer	refer	VERB
ejpam-3003	65	3	readers	reader	NOUN
ejpam-3003	65	4	to	to	PART
ejpam-3003	65	5	see	see	VERB
ejpam-3003	65	6	[	[	X
ejpam-3003	65	7	18][22	18][22	X
ejpam-3003	65	8	]	]	PUNCT
ejpam-3003	65	9	and	and	CCONJ
ejpam-3003	65	10	the	the	DET
ejpam-3003	65	11	papers	paper	NOUN
ejpam-3003	65	12	cited	cite	VERB
ejpam-3003	65	13	therein	therein	ADV
ejpam-3003	65	14	.	.	PUNCT
ejpam-3003	66	1	in	in	ADP
ejpam-3003	66	2	[	[	X
ejpam-3003	66	3	18]-[20	18]-[20	X
ejpam-3003	66	4	]	]	PUNCT
ejpam-3003	66	5	,	,	PUNCT
ejpam-3003	66	6	the	the	DET
ejpam-3003	66	7	initial	initial	ADJ
ejpam-3003	66	8	boundary	boundary	ADJ
ejpam-3003	66	9	value	value	NOUN
ejpam-3003	66	10	problem	problem	NOUN
ejpam-3003	66	11	of	of	ADP
ejpam-3003	66	12	the	the	DET
ejpam-3003	66	13	h.f	h.f	PROPN
ejpam-3003	66	14	.	.	PROPN
ejpam-3003	66	15	di	di	PROPN
ejpam-3003	66	16	,	,	PUNCT
ejpam-3003	66	17	y.d	y.d	PROPN
ejpam-3003	66	18	.	.	PROPN
ejpam-3003	66	19	shang	shang	PROPN
ejpam-3003	66	20	/	/	SYM
ejpam-3003	66	21	eur	eur	PROPN
ejpam-3003	66	22	.	.	PUNCT
ejpam-3003	67	1	j.	j.	PROPN
ejpam-3003	67	2	pure	pure	PROPN
ejpam-3003	67	3	appl	appl	PROPN
ejpam-3003	67	4	.	.	PROPN
ejpam-3003	67	5	math	math	PROPN
ejpam-3003	67	6	,	,	PUNCT
ejpam-3003	67	7	10	10	NUM
ejpam-3003	67	8	(	(	PUNCT
ejpam-3003	67	9	4	4	NUM
ejpam-3003	67	10	)	)	PUNCT
ejpam-3003	67	11	(	(	PUNCT
ejpam-3003	67	12	2017	2017	NUM
ejpam-3003	67	13	)	)	PUNCT
ejpam-3003	67	14	,	,	PUNCT
ejpam-3003	67	15	668	668	NUM
ejpam-3003	67	16	-	-	SYM
ejpam-3003	67	17	701	701	NUM
ejpam-3003	67	18	671	671	NUM
ejpam-3003	67	19	viscoelastic	viscoelastic	ADJ
ejpam-3003	67	20	equation	equation	NOUN
ejpam-3003	67	21	with	with	ADP
ejpam-3003	67	22	a	a	PRON
ejpam-3003	67	23	nonlinear	nonlinear	ADJ
ejpam-3003	67	24	boundary	boundary	ADJ
ejpam-3003	67	25	damping	damp	VERB
ejpam-3003	67	26	term	term	PROPN
ejpam-3003	67	27	utt	utt	PROPN
ejpam-3003	67	28	−4u+	−4u+	PROPN
ejpam-3003	67	29	∫	∫	PROPN
ejpam-3003	67	30	t	t	PROPN
ejpam-3003	67	31	0	0	NUM
ejpam-3003	67	32	g(t−	g(t−	PROPN
ejpam-3003	67	33	s)4u(s)ds	s)4u(s)d	NOUN
ejpam-3003	67	34	=	=	SYM
ejpam-3003	67	35	0	0	NUM
ejpam-3003	67	36	,	,	PUNCT
ejpam-3003	67	37	in	in	ADP
ejpam-3003	67	38	ω×	ω×	PROPN
ejpam-3003	67	39	(	(	PUNCT
ejpam-3003	67	40	0,∞	0,∞	NUM
ejpam-3003	67	41	)	)	PUNCT
ejpam-3003	67	42	,	,	PUNCT
ejpam-3003	67	43	u(x	u(x	PROPN
ejpam-3003	67	44	,	,	PUNCT
ejpam-3003	67	45	t	t	PROPN
ejpam-3003	67	46	)	)	PUNCT
ejpam-3003	67	47	=	=	SYM
ejpam-3003	67	48	0	0	NUM
ejpam-3003	67	49	,	,	PUNCT
ejpam-3003	67	50	on	on	ADP
ejpam-3003	67	51	γ0	γ0	PROPN
ejpam-3003	67	52	×	×	PROPN
ejpam-3003	67	53	(	(	PUNCT
ejpam-3003	67	54	0,∞	0,∞	NOUN
ejpam-3003	67	55	)	)	PUNCT
ejpam-3003	67	56	,	,	PUNCT
ejpam-3003	67	57	∂u	∂u	PROPN
ejpam-3003	67	58	∂ν	∂ν	PROPN
ejpam-3003	68	1	−	−	PROPN
ejpam-3003	68	2	∫	∫	PROPN
ejpam-3003	68	3	t	t	PROPN
ejpam-3003	68	4	0	0	NUM
ejpam-3003	68	5	g(t−	g(t−	PROPN
ejpam-3003	68	6	s)∂u∂ν	s)∂u∂ν	PROPN
ejpam-3003	68	7	(	(	PUNCT
ejpam-3003	68	8	s)ds+	s)ds+	NOUN
ejpam-3003	68	9	h(ut	h(ut	PROPN
ejpam-3003	68	10	)	)	PUNCT
ejpam-3003	68	11	=	=	SYM
ejpam-3003	68	12	0	0	NUM
ejpam-3003	68	13	,	,	PUNCT
ejpam-3003	68	14	on	on	ADP
ejpam-3003	68	15	γ1	γ1	PROPN
ejpam-3003	68	16	×	×	PROPN
ejpam-3003	68	17	(	(	PUNCT
ejpam-3003	68	18	0,∞	0,∞	NUM
ejpam-3003	68	19	)	)	PUNCT
ejpam-3003	68	20	,	,	PUNCT
ejpam-3003	68	21	u(x	u(x	NOUN
ejpam-3003	68	22	,	,	PUNCT
ejpam-3003	68	23	0	0	NUM
ejpam-3003	68	24	)	)	PUNCT
ejpam-3003	68	25	=	=	SYM
ejpam-3003	68	26	u0(x	u0(x	NOUN
ejpam-3003	68	27	)	)	PUNCT
ejpam-3003	68	28	,	,	PUNCT
ejpam-3003	68	29	ut(x	ut(x	NOUN
ejpam-3003	68	30	,	,	PUNCT
ejpam-3003	68	31	0	0	NUM
ejpam-3003	68	32	)	)	PUNCT
ejpam-3003	68	33	=	=	SYM
ejpam-3003	69	1	u1(x	u1(x	NOUN
ejpam-3003	69	2	)	)	PUNCT
ejpam-3003	69	3	,	,	PUNCT
ejpam-3003	69	4	x	x	PUNCT
ejpam-3003	69	5	∈	∈	PROPN
ejpam-3003	69	6	ω	ω	PROPN
ejpam-3003	69	7	,	,	PUNCT
ejpam-3003	69	8	(	(	PUNCT
ejpam-3003	69	9	1.10	1.10	NUM
ejpam-3003	69	10	)	)	PUNCT
ejpam-3003	69	11	was	be	AUX
ejpam-3003	69	12	studied	study	VERB
ejpam-3003	69	13	.	.	PUNCT
ejpam-3003	70	1	cavalcanti	cavalcanti	PROPN
ejpam-3003	70	2	et	et	PROPN
ejpam-3003	70	3	al	al	PROPN
ejpam-3003	70	4	.	.	PUNCT
ejpam-3003	71	1	[	[	X
ejpam-3003	71	2	18	18	NUM
ejpam-3003	71	3	]	]	PUNCT
ejpam-3003	71	4	obtained	obtain	VERB
ejpam-3003	71	5	a	a	DET
ejpam-3003	71	6	global	global	ADJ
ejpam-3003	71	7	existence	existence	NOUN
ejpam-3003	71	8	result	result	VERB
ejpam-3003	71	9	for	for	ADP
ejpam-3003	71	10	strong	strong	ADJ
ejpam-3003	71	11	and	and	CCONJ
ejpam-3003	71	12	weak	weak	ADJ
ejpam-3003	71	13	solutions	solution	NOUN
ejpam-3003	71	14	under	under	ADP
ejpam-3003	71	15	the	the	DET
ejpam-3003	71	16	classical	classical	ADJ
ejpam-3003	71	17	assumptions	assumption	NOUN
ejpam-3003	71	18	on	on	ADP
ejpam-3003	71	19	g.	g.	PROPN
ejpam-3003	71	20	some	some	DET
ejpam-3003	71	21	uniform	uniform	ADJ
ejpam-3003	71	22	decay	decay	NOUN
ejpam-3003	71	23	rate	rate	NOUN
ejpam-3003	71	24	results	result	NOUN
ejpam-3003	71	25	were	be	AUX
ejpam-3003	71	26	established	establish	VERB
ejpam-3003	71	27	under	under	ADP
ejpam-3003	71	28	quite	quite	ADV
ejpam-3003	71	29	restrictive	restrictive	ADJ
ejpam-3003	71	30	assumptions	assumption	NOUN
ejpam-3003	71	31	on	on	ADP
ejpam-3003	71	32	both	both	CCONJ
ejpam-3003	71	33	the	the	DET
ejpam-3003	71	34	damping	damp	VERB
ejpam-3003	71	35	term	term	NOUN
ejpam-3003	71	36	h	h	NOUN
ejpam-3003	71	37	and	and	CCONJ
ejpam-3003	71	38	the	the	DET
ejpam-3003	71	39	relaxation	relaxation	NOUN
ejpam-3003	71	40	function	function	NOUN
ejpam-3003	71	41	g.	g.	PROPN
ejpam-3003	71	42	later	later	ADV
ejpam-3003	71	43	,	,	PUNCT
ejpam-3003	71	44	cavalcanti	cavalcanti	PROPN
ejpam-3003	71	45	et	et	PROPN
ejpam-3003	71	46	al	al	PROPN
ejpam-3003	71	47	.	.	PUNCT
ejpam-3003	72	1	[	[	X
ejpam-3003	72	2	19	19	NUM
ejpam-3003	72	3	]	]	PUNCT
ejpam-3003	72	4	studied	study	VERB
ejpam-3003	72	5	the	the	DET
ejpam-3003	72	6	problem	problem	NOUN
ejpam-3003	72	7	(	(	PUNCT
ejpam-3003	72	8	1.10	1.10	NUM
ejpam-3003	72	9	)	)	PUNCT
ejpam-3003	72	10	under	under	ADP
ejpam-3003	72	11	weaker	weak	ADJ
ejpam-3003	72	12	conditions	condition	NOUN
ejpam-3003	72	13	on	on	ADP
ejpam-3003	72	14	the	the	DET
ejpam-3003	72	15	relaxation	relaxation	NOUN
ejpam-3003	72	16	function	function	NOUN
ejpam-3003	72	17	g	g	NOUN
ejpam-3003	72	18	and	and	CCONJ
ejpam-3003	72	19	without	without	ADP
ejpam-3003	72	20	imposing	impose	VERB
ejpam-3003	72	21	a	a	DET
ejpam-3003	72	22	growth	growth	NOUN
ejpam-3003	72	23	assumption	assumption	NOUN
ejpam-3003	72	24	on	on	ADP
ejpam-3003	72	25	the	the	DET
ejpam-3003	72	26	function	function	NOUN
ejpam-3003	72	27	h.	h.	NOUN
ejpam-3003	72	28	they	they	PRON
ejpam-3003	72	29	obtained	obtain	VERB
ejpam-3003	72	30	the	the	DET
ejpam-3003	72	31	decay	decay	NOUN
ejpam-3003	72	32	rate	rate	NOUN
ejpam-3003	72	33	estimates	estimate	NOUN
ejpam-3003	72	34	of	of	ADP
ejpam-3003	72	35	the	the	DET
ejpam-3003	72	36	energy	energy	NOUN
ejpam-3003	72	37	depending	depend	VERB
ejpam-3003	72	38	on	on	ADP
ejpam-3003	72	39	the	the	DET
ejpam-3003	72	40	behavior	behavior	NOUN
ejpam-3003	72	41	of	of	ADP
ejpam-3003	72	42	h	h	NOUN
ejpam-3003	72	43	near	near	ADP
ejpam-3003	72	44	zero	zero	NUM
ejpam-3003	72	45	and	and	CCONJ
ejpam-3003	72	46	on	on	ADP
ejpam-3003	72	47	the	the	DET
ejpam-3003	72	48	behavior	behavior	NOUN
ejpam-3003	72	49	of	of	ADP
ejpam-3003	72	50	the	the	DET
ejpam-3003	72	51	relaxation	relaxation	NOUN
ejpam-3003	72	52	g	g	NOUN
ejpam-3003	72	53	at	at	ADP
ejpam-3003	72	54	infinity	infinity	NOUN
ejpam-3003	72	55	.	.	PUNCT
ejpam-3003	73	1	for	for	ADP
ejpam-3003	73	2	a	a	DET
ejpam-3003	73	3	wider	wide	ADJ
ejpam-3003	73	4	class	class	NOUN
ejpam-3003	73	5	of	of	ADP
ejpam-3003	73	6	relaxation	relaxation	NOUN
ejpam-3003	73	7	function	function	NOUN
ejpam-3003	73	8	g	g	NOUN
ejpam-3003	73	9	and	and	CCONJ
ejpam-3003	73	10	without	without	ADP
ejpam-3003	73	11	imposing	impose	VERB
ejpam-3003	73	12	any	any	DET
ejpam-3003	73	13	restrictive	restrictive	ADJ
ejpam-3003	73	14	growth	growth	NOUN
ejpam-3003	73	15	assumptions	assumption	NOUN
ejpam-3003	73	16	on	on	ADP
ejpam-3003	73	17	the	the	DET
ejpam-3003	73	18	damping	damp	VERB
ejpam-3003	73	19	term	term	NOUN
ejpam-3003	73	20	h	h	NOUN
ejpam-3003	73	21	,	,	PUNCT
ejpam-3003	73	22	messaoudi	messaoudi	PROPN
ejpam-3003	73	23	and	and	CCONJ
ejpam-3003	73	24	mustafa	mustafa	PROPN
ejpam-3003	73	25	[	[	X
ejpam-3003	73	26	20	20	NUM
ejpam-3003	73	27	]	]	PUNCT
ejpam-3003	73	28	also	also	ADV
ejpam-3003	73	29	established	establish	VERB
ejpam-3003	73	30	an	an	DET
ejpam-3003	73	31	explicit	explicit	ADJ
ejpam-3003	73	32	and	and	CCONJ
ejpam-3003	73	33	general	general	ADJ
ejpam-3003	73	34	decay	decay	NOUN
ejpam-3003	73	35	rate	rate	NOUN
ejpam-3003	73	36	result	result	NOUN
ejpam-3003	73	37	for	for	ADP
ejpam-3003	73	38	the	the	DET
ejpam-3003	73	39	problem	problem	NOUN
ejpam-3003	73	40	(	(	PUNCT
ejpam-3003	73	41	1.10	1.10	NUM
ejpam-3003	73	42	)	)	PUNCT
ejpam-3003	73	43	.	.	PUNCT
ejpam-3003	74	1	lu	lu	PROPN
ejpam-3003	74	2	et	et	PROPN
ejpam-3003	74	3	al	al	PROPN
ejpam-3003	74	4	.	.	PUNCT
ejpam-3003	75	1	[	[	X
ejpam-3003	75	2	21	21	NUM
ejpam-3003	75	3	]	]	PUNCT
ejpam-3003	75	4	considered	consider	VERB
ejpam-3003	75	5	the	the	DET
ejpam-3003	75	6	following	following	ADJ
ejpam-3003	75	7	initial	initial	ADJ
ejpam-3003	75	8	boundary	boundary	ADJ
ejpam-3003	75	9	value	value	NOUN
ejpam-3003	75	10	problem	problem	NOUN
ejpam-3003	75	11	of	of	ADP
ejpam-3003	75	12	the	the	DET
ejpam-3003	75	13	viscoelastic	viscoelastic	ADJ
ejpam-3003	75	14	wave	wave	NOUN
ejpam-3003	75	15	equation	equation	NOUN
ejpam-3003	75	16	with	with	ADP
ejpam-3003	75	17	nonlinear	nonlinear	ADJ
ejpam-3003	75	18	boundary	boundary	ADJ
ejpam-3003	75	19	damping	damp	VERB
ejpam-3003	75	20	and	and	CCONJ
ejpam-3003	75	21	source	source	NOUN
ejpam-3003	75	22	terms	terms	PROPN
ejpam-3003	75	23	utt	utt	PROPN
ejpam-3003	75	24	−4u+	−4u+	PROPN
ejpam-3003	75	25	∫	∫	PROPN
ejpam-3003	75	26	t	t	PROPN
ejpam-3003	75	27	0	0	NUM
ejpam-3003	75	28	g(t−	g(t−	PROPN
ejpam-3003	75	29	s)4u(s)ds	s)4u(s)d	NOUN
ejpam-3003	75	30	=	=	SYM
ejpam-3003	75	31	0	0	NUM
ejpam-3003	75	32	,	,	PUNCT
ejpam-3003	75	33	in	in	ADP
ejpam-3003	75	34	ω×	ω×	PROPN
ejpam-3003	75	35	(	(	PUNCT
ejpam-3003	75	36	0,∞	0,∞	NUM
ejpam-3003	75	37	)	)	PUNCT
ejpam-3003	75	38	,	,	PUNCT
ejpam-3003	75	39	u(x	u(x	PROPN
ejpam-3003	75	40	,	,	PUNCT
ejpam-3003	75	41	t	t	PROPN
ejpam-3003	75	42	)	)	PUNCT
ejpam-3003	75	43	=	=	SYM
ejpam-3003	75	44	0	0	NUM
ejpam-3003	75	45	,	,	PUNCT
ejpam-3003	75	46	on	on	ADP
ejpam-3003	75	47	γ0	γ0	PROPN
ejpam-3003	75	48	×	×	PROPN
ejpam-3003	75	49	(	(	PUNCT
ejpam-3003	75	50	0,∞	0,∞	NOUN
ejpam-3003	75	51	)	)	PUNCT
ejpam-3003	75	52	,	,	PUNCT
ejpam-3003	76	1	∂u	∂u	PROPN
ejpam-3003	76	2	∂ν	∂ν	PROPN
ejpam-3003	76	3	−	−	PROPN
ejpam-3003	76	4	∫	∫	PROPN
ejpam-3003	76	5	t	t	PROPN
ejpam-3003	76	6	0	0	NUM
ejpam-3003	76	7	g(t−	g(t−	PROPN
ejpam-3003	76	8	s)∂u∂ν	s)∂u∂ν	PROPN
ejpam-3003	76	9	(	(	PUNCT
ejpam-3003	76	10	s)ds+	s)ds+	NOUN
ejpam-3003	76	11	ut|ut|m−2	ut|ut|m−2	PROPN
ejpam-3003	77	1	=	=	SYM
ejpam-3003	78	1	u|u|p−2	u|u|p−2	NOUN
ejpam-3003	78	2	,	,	PUNCT
ejpam-3003	78	3	on	on	ADP
ejpam-3003	78	4	γ1	γ1	PROPN
ejpam-3003	78	5	×	×	PROPN
ejpam-3003	78	6	(	(	PUNCT
ejpam-3003	78	7	0,∞	0,∞	NUM
ejpam-3003	78	8	)	)	PUNCT
ejpam-3003	78	9	,	,	PUNCT
ejpam-3003	78	10	u(x	u(x	NOUN
ejpam-3003	78	11	,	,	PUNCT
ejpam-3003	78	12	0	0	NUM
ejpam-3003	78	13	)	)	PUNCT
ejpam-3003	78	14	=	=	SYM
ejpam-3003	78	15	u0(x	u0(x	NOUN
ejpam-3003	78	16	)	)	PUNCT
ejpam-3003	78	17	,	,	PUNCT
ejpam-3003	78	18	ut(x	ut(x	NOUN
ejpam-3003	78	19	,	,	PUNCT
ejpam-3003	78	20	0	0	NUM
ejpam-3003	78	21	)	)	PUNCT
ejpam-3003	78	22	=	=	SYM
ejpam-3003	79	1	u1(x	u1(x	NOUN
ejpam-3003	79	2	)	)	PUNCT
ejpam-3003	79	3	,	,	PUNCT
ejpam-3003	79	4	x	x	PUNCT
ejpam-3003	79	5	∈	∈	PROPN
ejpam-3003	79	6	ω	ω	PROPN
ejpam-3003	79	7	.	.	PUNCT
ejpam-3003	80	1	(	(	PUNCT
ejpam-3003	80	2	1.11	1.11	NUM
ejpam-3003	80	3	)	)	PUNCT
ejpam-3003	80	4	they	they	PRON
ejpam-3003	80	5	obtained	obtain	VERB
ejpam-3003	80	6	the	the	DET
ejpam-3003	80	7	global	global	ADJ
ejpam-3003	80	8	existence	existence	NOUN
ejpam-3003	80	9	of	of	ADP
ejpam-3003	80	10	solution	solution	NOUN
ejpam-3003	80	11	and	and	CCONJ
ejpam-3003	80	12	a	a	DET
ejpam-3003	80	13	general	general	ADJ
ejpam-3003	80	14	decay	decay	NOUN
ejpam-3003	80	15	of	of	ADP
ejpam-3003	80	16	the	the	DET
ejpam-3003	80	17	energy	energy	NOUN
ejpam-3003	80	18	under	under	ADP
ejpam-3003	80	19	some	some	DET
ejpam-3003	80	20	appropriate	appropriate	ADJ
ejpam-3003	80	21	assumptions	assumption	NOUN
ejpam-3003	80	22	on	on	ADP
ejpam-3003	80	23	the	the	DET
ejpam-3003	80	24	function	function	NOUN
ejpam-3003	80	25	g	g	NOUN
ejpam-3003	80	26	and	and	CCONJ
ejpam-3003	80	27	certain	certain	ADJ
ejpam-3003	80	28	initial	initial	ADJ
ejpam-3003	80	29	data	datum	NOUN
ejpam-3003	80	30	.	.	PUNCT
ejpam-3003	81	1	in	in	ADP
ejpam-3003	81	2	[	[	X
ejpam-3003	81	3	22	22	NUM
ejpam-3003	81	4	]	]	PUNCT
ejpam-3003	81	5	,	,	PUNCT
ejpam-3003	81	6	liu	liu	PROPN
ejpam-3003	81	7	and	and	CCONJ
ejpam-3003	81	8	yu	yu	PROPN
ejpam-3003	81	9	first	first	ADV
ejpam-3003	81	10	extended	extend	VERB
ejpam-3003	81	11	the	the	DET
ejpam-3003	81	12	decay	decay	NOUN
ejpam-3003	81	13	result	result	NOUN
ejpam-3003	81	14	obtained	obtain	VERB
ejpam-3003	81	15	by	by	ADP
ejpam-3003	81	16	lu	lu	PROPN
ejpam-3003	81	17	et	et	PROPN
ejpam-3003	81	18	al	al	PROPN
ejpam-3003	81	19	.	.	PUNCT
ejpam-3003	82	1	then	then	ADV
ejpam-3003	82	2	,	,	PUNCT
ejpam-3003	82	3	they	they	PRON
ejpam-3003	82	4	established	establish	VERB
ejpam-3003	82	5	two	two	NUM
ejpam-3003	82	6	blow	blow	NOUN
ejpam-3003	82	7	up	up	ADP
ejpam-3003	82	8	results	result	NOUN
ejpam-3003	82	9	:	:	PUNCT
ejpam-3003	82	10	one	one	NUM
ejpam-3003	82	11	is	be	AUX
ejpam-3003	82	12	for	for	ADP
ejpam-3003	82	13	certain	certain	ADJ
ejpam-3003	82	14	solutions	solution	NOUN
ejpam-3003	82	15	with	with	ADP
ejpam-3003	82	16	nonpositive	nonpositive	ADJ
ejpam-3003	82	17	initial	initial	ADJ
ejpam-3003	82	18	energy	energy	NOUN
ejpam-3003	82	19	as	as	ADV
ejpam-3003	82	20	well	well	ADV
ejpam-3003	82	21	as	as	ADP
ejpam-3003	82	22	positive	positive	ADJ
ejpam-3003	82	23	initial	initial	ADJ
ejpam-3003	82	24	energy	energy	NOUN
ejpam-3003	82	25	in	in	ADP
ejpam-3003	82	26	the	the	DET
ejpam-3003	82	27	case	case	NOUN
ejpam-3003	82	28	m	m	VERB
ejpam-3003	82	29	≥	≥	NOUN
ejpam-3003	82	30	2	2	NUM
ejpam-3003	82	31	,	,	PUNCT
ejpam-3003	82	32	the	the	DET
ejpam-3003	82	33	other	other	ADJ
ejpam-3003	82	34	is	be	AUX
ejpam-3003	82	35	for	for	ADP
ejpam-3003	82	36	certain	certain	ADJ
ejpam-3003	82	37	solutions	solution	NOUN
ejpam-3003	82	38	with	with	ADP
ejpam-3003	82	39	arbitrary	arbitrary	ADJ
ejpam-3003	82	40	positive	positive	ADJ
ejpam-3003	82	41	initial	initial	ADJ
ejpam-3003	82	42	energy	energy	NOUN
ejpam-3003	82	43	in	in	ADP
ejpam-3003	82	44	the	the	DET
ejpam-3003	82	45	case	case	NOUN
ejpam-3003	82	46	m	m	NOUN
ejpam-3003	82	47	=	=	ADJ
ejpam-3003	82	48	2	2	X
ejpam-3003	82	49	.	.	NUM
ejpam-3003	82	50	motivated	motivate	VERB
ejpam-3003	82	51	by	by	ADP
ejpam-3003	82	52	the	the	DET
ejpam-3003	82	53	above	above	ADJ
ejpam-3003	82	54	researches	research	NOUN
ejpam-3003	82	55	,	,	PUNCT
ejpam-3003	82	56	in	in	ADP
ejpam-3003	82	57	the	the	DET
ejpam-3003	82	58	present	present	ADJ
ejpam-3003	82	59	work	work	NOUN
ejpam-3003	82	60	we	we	PRON
ejpam-3003	82	61	consider	consider	VERB
ejpam-3003	82	62	the	the	DET
ejpam-3003	82	63	viscoelastic	viscoelastic	ADJ
ejpam-3003	82	64	wave	wave	NOUN
ejpam-3003	82	65	equation	equation	NOUN
ejpam-3003	82	66	with	with	ADP
ejpam-3003	82	67	internal	internal	ADJ
ejpam-3003	82	68	nonlinear	nonlinear	ADJ
ejpam-3003	82	69	terms	term	NOUN
ejpam-3003	82	70	|ut|ρ−1utt	|ut|ρ−1utt	PROPN
ejpam-3003	82	71	,	,	PUNCT
ejpam-3003	82	72	|u|p−1u	|u|p−1u	NOUN
ejpam-3003	82	73	and	and	CCONJ
ejpam-3003	82	74	boundary	boundary	ADJ
ejpam-3003	82	75	nonlinear	nonlinear	ADJ
ejpam-3003	82	76	damping	damp	VERB
ejpam-3003	82	77	term	term	NOUN
ejpam-3003	82	78	|ut|q−1ut	|ut|q−1ut	PROPN
ejpam-3003	82	79	.	.	PUNCT
ejpam-3003	83	1	first	first	ADV
ejpam-3003	83	2	of	of	ADP
ejpam-3003	83	3	all	all	PRON
ejpam-3003	83	4	,	,	PUNCT
ejpam-3003	83	5	we	we	PRON
ejpam-3003	83	6	prove	prove	VERB
ejpam-3003	83	7	the	the	DET
ejpam-3003	83	8	existence	existence	NOUN
ejpam-3003	83	9	of	of	ADP
ejpam-3003	83	10	global	global	ADJ
ejpam-3003	83	11	weak	weak	ADJ
ejpam-3003	83	12	solutions	solution	NOUN
ejpam-3003	83	13	by	by	ADP
ejpam-3003	83	14	the	the	DET
ejpam-3003	83	15	combination	combination	NOUN
ejpam-3003	83	16	of	of	ADP
ejpam-3003	83	17	galerkin	galerkin	ADJ
ejpam-3003	83	18	approximation	approximation	NOUN
ejpam-3003	83	19	,	,	PUNCT
ejpam-3003	83	20	potential	potential	ADJ
ejpam-3003	83	21	well	well	ADV
ejpam-3003	83	22	and	and	CCONJ
ejpam-3003	83	23	monotonicity	monotonicity	NOUN
ejpam-3003	83	24	-	-	PUNCT
ejpam-3003	83	25	compactness	compactness	NOUN
ejpam-3003	83	26	methods	method	NOUN
ejpam-3003	83	27	.	.	PUNCT
ejpam-3003	84	1	then	then	ADV
ejpam-3003	84	2	,	,	PUNCT
ejpam-3003	84	3	we	we	PRON
ejpam-3003	84	4	give	give	VERB
ejpam-3003	84	5	an	an	DET
ejpam-3003	84	6	explicit	explicit	ADJ
ejpam-3003	84	7	decay	decay	NOUN
ejpam-3003	84	8	rate	rate	NOUN
ejpam-3003	84	9	estimate	estimate	NOUN
ejpam-3003	84	10	of	of	ADP
ejpam-3003	84	11	the	the	DET
ejpam-3003	84	12	energy	energy	NOUN
ejpam-3003	84	13	by	by	ADP
ejpam-3003	84	14	making	make	VERB
ejpam-3003	84	15	use	use	NOUN
ejpam-3003	84	16	of	of	ADP
ejpam-3003	84	17	the	the	DET
ejpam-3003	84	18	perturbed	perturb	VERB
ejpam-3003	84	19	energy	energy	NOUN
ejpam-3003	84	20	method	method	NOUN
ejpam-3003	84	21	introduced	introduce	VERB
ejpam-3003	84	22	by	by	ADP
ejpam-3003	84	23	cavalcanti	cavalcanti	PROPN
ejpam-3003	84	24	et	et	PROPN
ejpam-3003	84	25	al.[16,18,23	al.[16,18,23	PROPN
ejpam-3003	84	26	]	]	PUNCT
ejpam-3003	84	27	,	,	PUNCT
ejpam-3003	84	28	messaoudi	messaoudi	NOUN
ejpam-3003	84	29	and	and	CCONJ
ejpam-3003	84	30	tatar	tatar	NOUN
ejpam-3003	84	31	[	[	X
ejpam-3003	84	32	14,24	14,24	X
ejpam-3003	84	33	]	]	X
ejpam-3003	84	34	and	and	CCONJ
ejpam-3003	84	35	liu	liu	PROPN
ejpam-3003	85	1	[	[	X
ejpam-3003	85	2	22	22	NUM
ejpam-3003	85	3	]	]	PUNCT
ejpam-3003	85	4	coupled	couple	VERB
ejpam-3003	85	5	with	with	ADP
ejpam-3003	85	6	some	some	DET
ejpam-3003	85	7	technical	technical	ADJ
ejpam-3003	85	8	lemmas	lemma	NOUN
ejpam-3003	85	9	.	.	PUNCT
ejpam-3003	86	1	finally	finally	ADV
ejpam-3003	86	2	,	,	PUNCT
ejpam-3003	86	3	the	the	DET
ejpam-3003	86	4	finite	finite	ADJ
ejpam-3003	86	5	time	time	NOUN
ejpam-3003	86	6	blow	blow	VERB
ejpam-3003	86	7	up	up	ADP
ejpam-3003	86	8	result	result	NOUN
ejpam-3003	86	9	of	of	ADP
ejpam-3003	86	10	the	the	DET
ejpam-3003	86	11	solutions	solution	NOUN
ejpam-3003	86	12	is	be	AUX
ejpam-3003	86	13	investigated	investigate	VERB
ejpam-3003	86	14	under	under	ADP
ejpam-3003	86	15	certain	certain	ADJ
ejpam-3003	86	16	assumptions	assumption	NOUN
ejpam-3003	86	17	on	on	ADP
ejpam-3003	86	18	the	the	DET
ejpam-3003	86	19	relaxation	relaxation	NOUN
ejpam-3003	86	20	function	function	NOUN
ejpam-3003	86	21	g	g	NOUN
ejpam-3003	86	22	and	and	CCONJ
ejpam-3003	86	23	initial	initial	ADJ
ejpam-3003	86	24	data	datum	NOUN
ejpam-3003	86	25	.	.	PUNCT
ejpam-3003	87	1	the	the	DET
ejpam-3003	87	2	rest	rest	NOUN
ejpam-3003	87	3	of	of	ADP
ejpam-3003	87	4	this	this	DET
ejpam-3003	87	5	paper	paper	NOUN
ejpam-3003	87	6	is	be	AUX
ejpam-3003	87	7	organized	organize	VERB
ejpam-3003	87	8	as	as	SCONJ
ejpam-3003	87	9	follows	follow	VERB
ejpam-3003	87	10	:	:	PUNCT
ejpam-3003	87	11	in	in	ADP
ejpam-3003	87	12	section	section	NOUN
ejpam-3003	87	13	2	2	NUM
ejpam-3003	87	14	,	,	PUNCT
ejpam-3003	87	15	we	we	PRON
ejpam-3003	87	16	give	give	VERB
ejpam-3003	87	17	some	some	DET
ejpam-3003	87	18	preliminaries	preliminary	NOUN
ejpam-3003	87	19	and	and	CCONJ
ejpam-3003	87	20	state	state	VERB
ejpam-3003	87	21	our	our	PRON
ejpam-3003	87	22	main	main	ADJ
ejpam-3003	87	23	results	result	NOUN
ejpam-3003	87	24	.	.	PUNCT
ejpam-3003	88	1	the	the	DET
ejpam-3003	88	2	proof	proof	NOUN
ejpam-3003	88	3	of	of	ADP
ejpam-3003	88	4	the	the	DET
ejpam-3003	88	5	existence	existence	NOUN
ejpam-3003	88	6	of	of	ADP
ejpam-3003	88	7	global	global	ADJ
ejpam-3003	88	8	weak	weak	ADJ
ejpam-3003	88	9	solutions	solution	NOUN
ejpam-3003	88	10	and	and	CCONJ
ejpam-3003	88	11	an	an	DET
ejpam-3003	88	12	exponential	exponential	ADJ
ejpam-3003	88	13	decay	decay	NOUN
ejpam-3003	88	14	result	result	NOUN
ejpam-3003	88	15	will	will	AUX
ejpam-3003	88	16	be	be	AUX
ejpam-3003	88	17	given	give	VERB
ejpam-3003	88	18	in	in	ADP
ejpam-3003	88	19	sections	section	NOUN
ejpam-3003	88	20	3	3	NUM
ejpam-3003	88	21	and	and	CCONJ
ejpam-3003	88	22	4	4	NUM
ejpam-3003	88	23	.	.	X
ejpam-3003	89	1	in	in	ADP
ejpam-3003	89	2	the	the	DET
ejpam-3003	89	3	last	last	ADJ
ejpam-3003	89	4	section	section	NOUN
ejpam-3003	89	5	,	,	PUNCT
ejpam-3003	89	6	we	we	PRON
ejpam-3003	89	7	investigate	investigate	VERB
ejpam-3003	89	8	the	the	DET
ejpam-3003	89	9	finite	finite	ADJ
ejpam-3003	89	10	time	time	NOUN
ejpam-3003	89	11	blow	blow	VERB
ejpam-3003	89	12	up	up	ADP
ejpam-3003	89	13	result	result	NOUN
ejpam-3003	89	14	of	of	ADP
ejpam-3003	89	15	solutions	solution	NOUN
ejpam-3003	89	16	under	under	ADP
ejpam-3003	89	17	certain	certain	ADJ
ejpam-3003	89	18	conditions	condition	NOUN
ejpam-3003	89	19	.	.	PUNCT
ejpam-3003	90	1	h.f	h.f	PROPN
ejpam-3003	90	2	.	.	PROPN
ejpam-3003	90	3	di	di	PROPN
ejpam-3003	90	4	,	,	PUNCT
ejpam-3003	90	5	y.d	y.d	PROPN
ejpam-3003	90	6	.	.	PROPN
ejpam-3003	90	7	shang	shang	PROPN
ejpam-3003	90	8	/	/	SYM
ejpam-3003	90	9	eur	eur	PROPN
ejpam-3003	90	10	.	.	PUNCT
ejpam-3003	91	1	j.	j.	PROPN
ejpam-3003	91	2	pure	pure	PROPN
ejpam-3003	91	3	appl	appl	PROPN
ejpam-3003	91	4	.	.	PROPN
ejpam-3003	91	5	math	math	PROPN
ejpam-3003	91	6	,	,	PUNCT
ejpam-3003	91	7	10	10	NUM
ejpam-3003	91	8	(	(	PUNCT
ejpam-3003	91	9	4	4	NUM
ejpam-3003	91	10	)	)	PUNCT
ejpam-3003	91	11	(	(	PUNCT
ejpam-3003	91	12	2017	2017	NUM
ejpam-3003	91	13	)	)	PUNCT
ejpam-3003	91	14	,	,	PUNCT
ejpam-3003	91	15	668	668	NUM
ejpam-3003	91	16	-	-	SYM
ejpam-3003	91	17	701	701	NUM
ejpam-3003	91	18	672	672	NUM
ejpam-3003	91	19	2	2	NUM
ejpam-3003	91	20	.	.	PUNCT
ejpam-3003	91	21	preliminaries	preliminary	NOUN
ejpam-3003	91	22	in	in	ADP
ejpam-3003	91	23	order	order	NOUN
ejpam-3003	91	24	to	to	PART
ejpam-3003	91	25	state	state	VERB
ejpam-3003	91	26	our	our	PRON
ejpam-3003	91	27	results	result	NOUN
ejpam-3003	91	28	precisely	precisely	ADV
ejpam-3003	91	29	,	,	PUNCT
ejpam-3003	91	30	we	we	PRON
ejpam-3003	91	31	first	first	ADV
ejpam-3003	91	32	give	give	VERB
ejpam-3003	91	33	some	some	DET
ejpam-3003	91	34	notations	notation	NOUN
ejpam-3003	91	35	,	,	PUNCT
ejpam-3003	91	36	basic	basic	ADJ
ejpam-3003	91	37	definitions	definition	NOUN
ejpam-3003	91	38	and	and	CCONJ
ejpam-3003	91	39	important	important	ADJ
ejpam-3003	91	40	lemmas	lemma	NOUN
ejpam-3003	91	41	which	which	PRON
ejpam-3003	91	42	will	will	AUX
ejpam-3003	91	43	be	be	AUX
ejpam-3003	91	44	needed	need	VERB
ejpam-3003	91	45	in	in	ADP
ejpam-3003	91	46	the	the	DET
ejpam-3003	91	47	course	course	NOUN
ejpam-3003	91	48	of	of	ADP
ejpam-3003	91	49	this	this	DET
ejpam-3003	91	50	paper	paper	NOUN
ejpam-3003	91	51	.	.	PUNCT
ejpam-3003	92	1	let	let	VERB
ejpam-3003	92	2	ω	ω	PRON
ejpam-3003	92	3	be	be	AUX
ejpam-3003	92	4	a	a	DET
ejpam-3003	92	5	bounded	bounded	ADJ
ejpam-3003	92	6	open	open	ADJ
ejpam-3003	92	7	domain	domain	NOUN
ejpam-3003	92	8	of	of	ADP
ejpam-3003	92	9	rn	rn	PROPN
ejpam-3003	92	10	with	with	ADP
ejpam-3003	92	11	a	a	DET
ejpam-3003	92	12	smooth	smooth	ADJ
ejpam-3003	92	13	boundary	boundary	ADJ
ejpam-3003	92	14	γ	γ	X
ejpam-3003	92	15	.	.	PUNCT
ejpam-3003	93	1	we	we	PRON
ejpam-3003	93	2	consider	consider	VERB
ejpam-3003	93	3	m(x	m(x	X
ejpam-3003	93	4	)	)	PUNCT
ejpam-3003	94	1	=	=	PUNCT
ejpam-3003	95	1	x	x	PUNCT
ejpam-3003	95	2	−	−	NOUN
ejpam-3003	96	1	x0	x0	PROPN
ejpam-3003	96	2	(	(	PUNCT
ejpam-3003	96	3	x0	x0	PROPN
ejpam-3003	96	4	is	be	AUX
ejpam-3003	96	5	a	a	DET
ejpam-3003	96	6	fixed	fix	VERB
ejpam-3003	96	7	point	point	NOUN
ejpam-3003	96	8	of	of	ADP
ejpam-3003	96	9	rn	rn	PROPN
ejpam-3003	96	10	)	)	PUNCT
ejpam-3003	96	11	,	,	PUNCT
ejpam-3003	96	12	and	and	CCONJ
ejpam-3003	96	13	introduce	introduce	VERB
ejpam-3003	96	14	a	a	DET
ejpam-3003	96	15	partition	partition	NOUN
ejpam-3003	96	16	of	of	ADP
ejpam-3003	96	17	the	the	DET
ejpam-3003	96	18	boundary	boundary	ADJ
ejpam-3003	96	19	γ	γ	NOUN
ejpam-3003	96	20	such	such	ADJ
ejpam-3003	96	21	that	that	DET
ejpam-3003	96	22	γ0	γ0	NOUN
ejpam-3003	96	23	=	=	SYM
ejpam-3003	96	24	{	{	PUNCT
ejpam-3003	96	25	x	x	PROPN
ejpam-3003	96	26	∈	∈	PROPN
ejpam-3003	96	27	γ	γ	X
ejpam-3003	96	28	:	:	PUNCT
ejpam-3003	96	29	m(x	m(x	PROPN
ejpam-3003	96	30	)	)	PUNCT
ejpam-3003	96	31	·	·	PUNCT
ejpam-3003	97	1	ν(x	ν(x	PROPN
ejpam-3003	97	2	)	)	PUNCT
ejpam-3003	97	3	≤	≤	NOUN
ejpam-3003	97	4	0	0	NUM
ejpam-3003	97	5	}	}	PUNCT
ejpam-3003	97	6	,	,	PUNCT
ejpam-3003	97	7	γ1	γ1	NOUN
ejpam-3003	97	8	=	=	SYM
ejpam-3003	97	9	{	{	PUNCT
ejpam-3003	97	10	x	x	PROPN
ejpam-3003	97	11	∈	∈	PROPN
ejpam-3003	97	12	γ	γ	X
ejpam-3003	97	13	:	:	PUNCT
ejpam-3003	97	14	m(x	m(x	PROPN
ejpam-3003	97	15	)	)	PUNCT
ejpam-3003	97	16	·	·	PUNCT
ejpam-3003	98	1	ν(x	ν(x	X
ejpam-3003	98	2	)	)	PUNCT
ejpam-3003	98	3	>	>	X
ejpam-3003	98	4	0	0	NUM
ejpam-3003	98	5	}	}	PUNCT
ejpam-3003	98	6	.	.	PUNCT
ejpam-3003	99	1	we	we	PRON
ejpam-3003	99	2	define	define	VERB
ejpam-3003	99	3	some	some	DET
ejpam-3003	99	4	inner	inner	ADJ
ejpam-3003	99	5	products	product	NOUN
ejpam-3003	99	6	and	and	CCONJ
ejpam-3003	99	7	norms	norm	NOUN
ejpam-3003	99	8	(	(	PUNCT
ejpam-3003	99	9	u	u	NOUN
ejpam-3003	99	10	,	,	PUNCT
ejpam-3003	99	11	v	v	NOUN
ejpam-3003	99	12	)	)	PUNCT
ejpam-3003	99	13	=	=	SYM
ejpam-3003	99	14	∫	∫	PROPN
ejpam-3003	99	15	ω	ω	PROPN
ejpam-3003	99	16	u(x)v(x)dx	u(x)v(x)dx	PROPN
ejpam-3003	99	17	,	,	PUNCT
ejpam-3003	99	18	(	(	PUNCT
ejpam-3003	99	19	u	u	NOUN
ejpam-3003	99	20	,	,	PUNCT
ejpam-3003	99	21	v)γ1	v)γ1	ADV
ejpam-3003	99	22	=	=	SYM
ejpam-3003	99	23	∫	∫	PROPN
ejpam-3003	99	24	γ1	γ1	PROPN
ejpam-3003	99	25	u(x)v(x)dγ	u(x)v(x)dγ	PROPN
ejpam-3003	99	26	,	,	PUNCT
ejpam-3003	99	27	‖u‖pp	‖u‖pp	ADJ
ejpam-3003	99	28	=	=	SYM
ejpam-3003	99	29	∫	∫	PROPN
ejpam-3003	99	30	ω	ω	NUM
ejpam-3003	99	31	|u(x)|pdx	|u(x)|pdx	PROPN
ejpam-3003	99	32	,	,	PUNCT
ejpam-3003	99	33	‖u‖pγ1,p	‖u‖pγ1,p	PROPN
ejpam-3003	99	34	=	=	SYM
ejpam-3003	99	35	∫	∫	PROPN
ejpam-3003	99	36	γ1	γ1	PROPN
ejpam-3003	99	37	|u(x)|pdγ	|u(x)|pdγ	NOUN
ejpam-3003	99	38	,	,	PUNCT
ejpam-3003	99	39	‖u‖∞	‖u‖∞	PROPN
ejpam-3003	99	40	=	=	SYM
ejpam-3003	99	41	ess	ess	PROPN
ejpam-3003	99	42	sup	sup	PROPN
ejpam-3003	99	43	x∈ω	x∈ω	NOUN
ejpam-3003	99	44	|u(x)|	|u(x)|	PROPN
ejpam-3003	99	45	and	and	CCONJ
ejpam-3003	99	46	the	the	DET
ejpam-3003	99	47	hilbert	hilbert	PROPN
ejpam-3003	99	48	space	space	PROPN
ejpam-3003	99	49	h1	h1	PROPN
ejpam-3003	99	50	γ0	γ0	PROPN
ejpam-3003	99	51	(	(	PUNCT
ejpam-3003	99	52	ω	ω	NOUN
ejpam-3003	99	53	)	)	PUNCT
ejpam-3003	99	54	=	=	PRON
ejpam-3003	99	55	{	{	PUNCT
ejpam-3003	100	1	u	u	NOUN
ejpam-3003	100	2	∈	∈	PROPN
ejpam-3003	100	3	h1(ω	h1(ω	PROPN
ejpam-3003	100	4	)	)	PUNCT
ejpam-3003	100	5	∣∣	∣∣	NUM
ejpam-3003	100	6	u	u	NOUN
ejpam-3003	100	7	=	=	NOUN
ejpam-3003	100	8	0	0	NUM
ejpam-3003	100	9	on	on	ADP
ejpam-3003	100	10	γ0	γ0	NOUN
ejpam-3003	100	11	}	}	PUNCT
ejpam-3003	100	12	.	.	PUNCT
ejpam-3003	101	1	since	since	SCONJ
ejpam-3003	101	2	γ0	γ0	PROPN
ejpam-3003	101	3	has	have	VERB
ejpam-3003	101	4	positive	positive	ADJ
ejpam-3003	101	5	(	(	PUNCT
ejpam-3003	101	6	n	n	CCONJ
ejpam-3003	101	7	−	−	PROPN
ejpam-3003	101	8	1	1	X
ejpam-3003	101	9	)	)	PUNCT
ejpam-3003	101	10	dimensional	dimensional	ADJ
ejpam-3003	101	11	lebesgue	lebesgue	NOUN
ejpam-3003	101	12	measure	measure	NOUN
ejpam-3003	101	13	,	,	PUNCT
ejpam-3003	101	14	by	by	ADP
ejpam-3003	101	15	poincaré	poincaré	ADJ
ejpam-3003	101	16	inequality	inequality	NOUN
ejpam-3003	101	17	,	,	PUNCT
ejpam-3003	101	18	we	we	PRON
ejpam-3003	101	19	can	can	AUX
ejpam-3003	101	20	endow	endow	VERB
ejpam-3003	101	21	h1	h1	PROPN
ejpam-3003	101	22	γ0	γ0	PROPN
ejpam-3003	101	23	(	(	PUNCT
ejpam-3003	101	24	ω	ω	NOUN
ejpam-3003	101	25	)	)	PUNCT
ejpam-3003	101	26	with	with	ADP
ejpam-3003	101	27	the	the	DET
ejpam-3003	101	28	equivalent	equivalent	ADJ
ejpam-3003	101	29	norm	norm	NOUN
ejpam-3003	101	30	‖u‖h1	‖u‖h1	PROPN
ejpam-3003	101	31	γ0	γ0	NOUN
ejpam-3003	101	32	=	=	SYM
ejpam-3003	101	33	‖∇u‖2	‖∇u‖2	PROPN
ejpam-3003	101	34	(	(	PUNCT
ejpam-3003	101	35	see	see	VERB
ejpam-3003	101	36	[	[	X
ejpam-3003	101	37	25	25	NUM
ejpam-3003	101	38	]	]	PUNCT
ejpam-3003	101	39	for	for	ADP
ejpam-3003	101	40	details	detail	NOUN
ejpam-3003	101	41	)	)	PUNCT
ejpam-3003	101	42	.	.	PUNCT
ejpam-3003	102	1	now	now	ADV
ejpam-3003	102	2	,	,	PUNCT
ejpam-3003	102	3	we	we	PRON
ejpam-3003	102	4	state	state	VERB
ejpam-3003	102	5	the	the	DET
ejpam-3003	102	6	general	general	ADJ
ejpam-3003	102	7	hypotheses	hypothesis	NOUN
ejpam-3003	102	8	.	.	PUNCT
ejpam-3003	103	1	(	(	PUNCT
ejpam-3003	103	2	a1	a1	PROPN
ejpam-3003	103	3	)	)	PUNCT
ejpam-3003	103	4	the	the	DET
ejpam-3003	103	5	relaxation	relaxation	NOUN
ejpam-3003	103	6	function	function	VERB
ejpam-3003	103	7	g	g	NOUN
ejpam-3003	103	8	:	:	PUNCT
ejpam-3003	104	1	[	[	X
ejpam-3003	104	2	0,∞)→	0,∞)→	NOUN
ejpam-3003	104	3	(	(	PUNCT
ejpam-3003	104	4	0,∞	0,∞	NOUN
ejpam-3003	104	5	)	)	PUNCT
ejpam-3003	104	6	is	be	AUX
ejpam-3003	104	7	a	a	DET
ejpam-3003	104	8	c1	c1	NOUN
ejpam-3003	104	9	function	function	NOUN
ejpam-3003	104	10	satisfying	satisfy	VERB
ejpam-3003	104	11	g′(t	g′(t	PROPN
ejpam-3003	104	12	)	)	PUNCT
ejpam-3003	104	13	≤	≤	NOUN
ejpam-3003	104	14	0	0	NUM
ejpam-3003	104	15	,	,	PUNCT
ejpam-3003	104	16	b	b	X
ejpam-3003	104	17	=	=	SYM
ejpam-3003	104	18	1−	1−	NUM
ejpam-3003	104	19	∫	∫	NOUN
ejpam-3003	104	20	∞	∞	NOUN
ejpam-3003	104	21	0	0	NUM
ejpam-3003	104	22	g(s)ds	g(s)ds	PROPN
ejpam-3003	104	23	≤	≤	NOUN
ejpam-3003	105	1	1−	1−	NUM
ejpam-3003	105	2	∫	∫	PROPN
ejpam-3003	105	3	t	t	PROPN
ejpam-3003	105	4	0	0	NUM
ejpam-3003	105	5	g(s)ds	g(s)ds	PROPN
ejpam-3003	105	6	=	=	PUNCT
ejpam-3003	105	7	l(t	l(t	PROPN
ejpam-3003	105	8	)	)	PUNCT
ejpam-3003	105	9	.	.	PUNCT
ejpam-3003	106	1	(	(	PUNCT
ejpam-3003	106	2	a2	a2	PROPN
ejpam-3003	106	3	)	)	PUNCT
ejpam-3003	106	4	there	there	PRON
ejpam-3003	106	5	exists	exist	VERB
ejpam-3003	106	6	a	a	DET
ejpam-3003	106	7	positive	positive	ADJ
ejpam-3003	106	8	differentiable	differentiable	ADJ
ejpam-3003	106	9	function	function	NOUN
ejpam-3003	106	10	ξ(t	ξ(t	NOUN
ejpam-3003	106	11	)	)	PUNCT
ejpam-3003	106	12	such	such	ADJ
ejpam-3003	106	13	that	that	SCONJ
ejpam-3003	106	14	g′(t	g′(t	PROPN
ejpam-3003	106	15	)	)	PUNCT
ejpam-3003	106	16	≤	≤	NOUN
ejpam-3003	106	17	−ξ(t)g(t	−ξ(t)g(t	NOUN
ejpam-3003	106	18	)	)	PUNCT
ejpam-3003	106	19	,	,	PUNCT
ejpam-3003	106	20	t	t	PROPN
ejpam-3003	106	21	≥	≥	NUM
ejpam-3003	106	22	0	0	NUM
ejpam-3003	106	23	,	,	PUNCT
ejpam-3003	106	24	and	and	CCONJ
ejpam-3003	106	25	for	for	ADP
ejpam-3003	106	26	some	some	DET
ejpam-3003	106	27	positive	positive	ADJ
ejpam-3003	106	28	constant	constant	ADJ
ejpam-3003	106	29	k	k	PROPN
ejpam-3003	106	30	,	,	PUNCT
ejpam-3003	106	31	ξ(t	ξ(t	NOUN
ejpam-3003	106	32	)	)	PUNCT
ejpam-3003	106	33	satisfies∣∣∣∣ξ′(t)ξ(t	satisfies∣∣∣∣ξ′(t)ξ(t	NOUN
ejpam-3003	106	34	)	)	PUNCT
ejpam-3003	106	35	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3003	106	36	≤	≤	NUM
ejpam-3003	106	37	k	k	PROPN
ejpam-3003	106	38	,	,	PUNCT
ejpam-3003	106	39	ξ′(t	ξ′(t	NOUN
ejpam-3003	106	40	)	)	PUNCT
ejpam-3003	106	41	≤	≤	NOUN
ejpam-3003	106	42	0	0	NUM
ejpam-3003	106	43	,	,	PUNCT
ejpam-3003	106	44	∀	∀	X
ejpam-3003	106	45	t	t	NOUN
ejpam-3003	106	46	>	>	X
ejpam-3003	106	47	0	0	NUM
ejpam-3003	106	48	.	.	PUNCT
ejpam-3003	107	1	(	(	PUNCT
ejpam-3003	107	2	a3	a3	NOUN
ejpam-3003	107	3	)	)	PUNCT
ejpam-3003	107	4	we	we	PRON
ejpam-3003	107	5	also	also	ADV
ejpam-3003	107	6	assume	assume	VERB
ejpam-3003	107	7	that	that	SCONJ
ejpam-3003	107	8	1	1	X
ejpam-3003	107	9	<	<	X
ejpam-3003	107	10	p	p	X
ejpam-3003	107	11	<	<	X
ejpam-3003	107	12	∞	∞	PROPN
ejpam-3003	107	13	if	if	SCONJ
ejpam-3003	107	14	n	n	NOUN
ejpam-3003	107	15	≤	≤	ADV
ejpam-3003	107	16	2	2	NUM
ejpam-3003	107	17	,	,	PUNCT
ejpam-3003	107	18	1	1	NUM
ejpam-3003	107	19	<	<	X
ejpam-3003	107	20	p	p	PROPN
ejpam-3003	107	21	≤	≤	NUM
ejpam-3003	107	22	n+	n+	PUNCT
ejpam-3003	107	23	2	2	NUM
ejpam-3003	107	24	n−	n−	NOUN
ejpam-3003	107	25	2	2	NUM
ejpam-3003	107	26	if	if	SCONJ
ejpam-3003	107	27	n	n	PRON
ejpam-3003	107	28	≥	≥	NOUN
ejpam-3003	107	29	3	3	NUM
ejpam-3003	107	30	,	,	PUNCT
ejpam-3003	107	31	1	1	NUM
ejpam-3003	107	32	<	<	X
ejpam-3003	107	33	q	q	X
ejpam-3003	107	34	<	<	X
ejpam-3003	107	35	∞	∞	PROPN
ejpam-3003	107	36	if	if	SCONJ
ejpam-3003	107	37	n	n	NOUN
ejpam-3003	107	38	≤	≤	ADV
ejpam-3003	107	39	2	2	NUM
ejpam-3003	107	40	,	,	PUNCT
ejpam-3003	107	41	1	1	NUM
ejpam-3003	107	42	<	<	X
ejpam-3003	107	43	q	q	X
ejpam-3003	107	44	≤	≤	PROPN
ejpam-3003	107	45	n	n	PRON
ejpam-3003	107	46	n−	n−	NOUN
ejpam-3003	107	47	2	2	NUM
ejpam-3003	107	48	if	if	SCONJ
ejpam-3003	107	49	n	n	PRON
ejpam-3003	107	50	≥	≥	NOUN
ejpam-3003	107	51	3	3	NUM
ejpam-3003	107	52	.	.	PUNCT
ejpam-3003	108	1	h.f	h.f	PROPN
ejpam-3003	108	2	.	.	PROPN
ejpam-3003	108	3	di	di	PROPN
ejpam-3003	108	4	,	,	PUNCT
ejpam-3003	108	5	y.d	y.d	PROPN
ejpam-3003	108	6	.	.	PROPN
ejpam-3003	108	7	shang	shang	PROPN
ejpam-3003	108	8	/	/	SYM
ejpam-3003	108	9	eur	eur	PROPN
ejpam-3003	108	10	.	.	PUNCT
ejpam-3003	109	1	j.	j.	PROPN
ejpam-3003	109	2	pure	pure	PROPN
ejpam-3003	109	3	appl	appl	PROPN
ejpam-3003	109	4	.	.	PROPN
ejpam-3003	109	5	math	math	PROPN
ejpam-3003	109	6	,	,	PUNCT
ejpam-3003	109	7	10	10	NUM
ejpam-3003	109	8	(	(	PUNCT
ejpam-3003	109	9	4	4	NUM
ejpam-3003	109	10	)	)	PUNCT
ejpam-3003	109	11	(	(	PUNCT
ejpam-3003	109	12	2017	2017	NUM
ejpam-3003	109	13	)	)	PUNCT
ejpam-3003	109	14	,	,	PUNCT
ejpam-3003	109	15	668	668	NUM
ejpam-3003	109	16	-	-	SYM
ejpam-3003	109	17	701	701	NUM
ejpam-3003	109	18	673	673	NUM
ejpam-3003	109	19	next	next	ADV
ejpam-3003	109	20	,	,	PUNCT
ejpam-3003	109	21	we	we	PRON
ejpam-3003	109	22	shall	shall	AUX
ejpam-3003	109	23	define	define	VERB
ejpam-3003	109	24	some	some	DET
ejpam-3003	109	25	functionals	functional	NOUN
ejpam-3003	109	26	and	and	CCONJ
ejpam-3003	109	27	study	study	VERB
ejpam-3003	109	28	their	their	PRON
ejpam-3003	109	29	some	some	DET
ejpam-3003	109	30	basic	basic	ADJ
ejpam-3003	109	31	properties	property	NOUN
ejpam-3003	109	32	which	which	PRON
ejpam-3003	109	33	are	be	AUX
ejpam-3003	109	34	related	relate	VERB
ejpam-3003	109	35	with	with	ADP
ejpam-3003	109	36	potential	potential	ADJ
ejpam-3003	109	37	well	well	ADV
ejpam-3003	109	38	.	.	PUNCT
ejpam-3003	110	1	firstly	firstly	ADV
ejpam-3003	110	2	,	,	PUNCT
ejpam-3003	110	3	let	let	VERB
ejpam-3003	110	4	us	we	PRON
ejpam-3003	110	5	consider	consider	VERB
ejpam-3003	110	6	the	the	DET
ejpam-3003	110	7	functionals	functional	NOUN
ejpam-3003	110	8	e(t	e(t	NOUN
ejpam-3003	110	9	)	)	PUNCT
ejpam-3003	110	10	=	=	SYM
ejpam-3003	110	11	1	1	NUM
ejpam-3003	110	12	ρ+	ρ+	NUM
ejpam-3003	110	13	1	1	NUM
ejpam-3003	110	14	‖ut‖ρ+1	‖ut‖ρ+1	SYM
ejpam-3003	110	15	ρ+1	ρ+1	NUM
ejpam-3003	110	16	+	+	CCONJ
ejpam-3003	110	17	1	1	NUM
ejpam-3003	110	18	2	2	NUM
ejpam-3003	110	19	(	(	PUNCT
ejpam-3003	110	20	1−	1−	NUM
ejpam-3003	110	21	∫	∫	NOUN
ejpam-3003	110	22	t	t	PROPN
ejpam-3003	110	23	0	0	NUM
ejpam-3003	110	24	g(s)ds	g(s)ds	PROPN
ejpam-3003	110	25	)	)	PUNCT
ejpam-3003	110	26	‖∇u‖22	‖∇u‖22	NOUN
ejpam-3003	111	1	+	+	CCONJ
ejpam-3003	111	2	1	1	NUM
ejpam-3003	111	3	2	2	NUM
ejpam-3003	111	4	(	(	PUNCT
ejpam-3003	111	5	g	g	NOUN
ejpam-3003	111	6	◦	◦	NOUN
ejpam-3003	111	7	∇u)(t)−	∇u)(t)−	PROPN
ejpam-3003	111	8	1	1	NUM
ejpam-3003	111	9	p+	p+	NOUN
ejpam-3003	111	10	1	1	NUM
ejpam-3003	111	11	‖u‖p+1	‖u‖p+1	NOUN
ejpam-3003	111	12	p+1	p+1	NOUN
ejpam-3003	111	13	,	,	PUNCT
ejpam-3003	111	14	(	(	PUNCT
ejpam-3003	111	15	2.1	2.1	NUM
ejpam-3003	111	16	)	)	PUNCT
ejpam-3003	111	17	j(u	j(u	PROPN
ejpam-3003	111	18	)	)	PUNCT
ejpam-3003	111	19	=	=	SYM
ejpam-3003	111	20	1	1	NUM
ejpam-3003	111	21	2	2	NUM
ejpam-3003	111	22	(	(	PUNCT
ejpam-3003	111	23	1−	1−	NUM
ejpam-3003	111	24	∫	∫	NOUN
ejpam-3003	111	25	t	t	PROPN
ejpam-3003	111	26	0	0	NUM
ejpam-3003	111	27	g(s)ds	g(s)ds	PROPN
ejpam-3003	111	28	)	)	PUNCT
ejpam-3003	111	29	‖∇u‖22	‖∇u‖22	NOUN
ejpam-3003	112	1	+	+	CCONJ
ejpam-3003	112	2	1	1	NUM
ejpam-3003	112	3	2	2	NUM
ejpam-3003	112	4	(	(	PUNCT
ejpam-3003	112	5	g	g	NOUN
ejpam-3003	112	6	◦	◦	NOUN
ejpam-3003	112	7	∇u)(t)−	∇u)(t)−	PROPN
ejpam-3003	112	8	1	1	NUM
ejpam-3003	112	9	p+	p+	NOUN
ejpam-3003	112	10	1	1	NUM
ejpam-3003	112	11	‖u‖p+1	‖u‖p+1	NOUN
ejpam-3003	112	12	p+1	p+1	NOUN
ejpam-3003	112	13	,	,	PUNCT
ejpam-3003	112	14	(	(	PUNCT
ejpam-3003	112	15	2.2	2.2	NUM
ejpam-3003	112	16	)	)	PUNCT
ejpam-3003	112	17	i(u	i(u	NOUN
ejpam-3003	112	18	)	)	PUNCT
ejpam-3003	112	19	=	=	PRON
ejpam-3003	113	1	(	(	PUNCT
ejpam-3003	113	2	1−	1−	NUM
ejpam-3003	113	3	∫	∫	NOUN
ejpam-3003	113	4	t	t	PROPN
ejpam-3003	113	5	0	0	NUM
ejpam-3003	113	6	g(s)ds	g(s)ds	PROPN
ejpam-3003	113	7	)	)	PUNCT
ejpam-3003	113	8	‖∇u‖22	‖∇u‖22	NOUN
ejpam-3003	114	1	+	+	CCONJ
ejpam-3003	114	2	(	(	PUNCT
ejpam-3003	114	3	g	g	NOUN
ejpam-3003	114	4	◦	◦	NOUN
ejpam-3003	114	5	∇u)(t)−	∇u)(t)−	PROPN
ejpam-3003	114	6	‖u‖p+1	‖u‖p+1	PROPN
ejpam-3003	114	7	p+1	p+1	NOUN
ejpam-3003	114	8	,	,	PUNCT
ejpam-3003	114	9	(	(	PUNCT
ejpam-3003	114	10	2.3	2.3	NUM
ejpam-3003	114	11	)	)	PUNCT
ejpam-3003	114	12	where	where	SCONJ
ejpam-3003	114	13	(	(	PUNCT
ejpam-3003	114	14	g	g	PROPN
ejpam-3003	114	15	◦	◦	PROPN
ejpam-3003	114	16	∇u)(t	∇u)(t	PROPN
ejpam-3003	114	17	)	)	PUNCT
ejpam-3003	114	18	=	=	SYM
ejpam-3003	115	1	∫	∫	PROPN
ejpam-3003	115	2	t	t	PROPN
ejpam-3003	115	3	0	0	NUM
ejpam-3003	115	4	g(t−	g(t−	PROPN
ejpam-3003	115	5	s)‖∇u(t)−∇u(s)‖22ds	s)‖∇u(t)−∇u(s)‖22ds	NOUN
ejpam-3003	115	6	,	,	PUNCT
ejpam-3003	115	7	∀	∀	X
ejpam-3003	115	8	u	u	NOUN
ejpam-3003	115	9	∈	∈	PROPN
ejpam-3003	115	10	h1	h1	PROPN
ejpam-3003	115	11	γ0	γ0	PROPN
ejpam-3003	115	12	(	(	PUNCT
ejpam-3003	115	13	ω	ω	NOUN
ejpam-3003	115	14	)	)	PUNCT
ejpam-3003	115	15	.	.	PUNCT
ejpam-3003	116	1	lemma	lemma	PROPN
ejpam-3003	116	2	1	1	X
ejpam-3003	116	3	.	.	PUNCT
ejpam-3003	117	1	let	let	VERB
ejpam-3003	117	2	the	the	DET
ejpam-3003	117	3	assumptions	assumption	NOUN
ejpam-3003	117	4	(	(	PUNCT
ejpam-3003	117	5	a1	a1	NOUN
ejpam-3003	117	6	)	)	PUNCT
ejpam-3003	117	7	,	,	PUNCT
ejpam-3003	117	8	(	(	PUNCT
ejpam-3003	117	9	a3	a3	NOUN
ejpam-3003	117	10	)	)	PUNCT
ejpam-3003	117	11	hold	hold	VERB
ejpam-3003	117	12	,	,	PUNCT
ejpam-3003	117	13	then	then	ADV
ejpam-3003	117	14	for	for	ADP
ejpam-3003	117	15	any	any	DET
ejpam-3003	117	16	u	u	PROPN
ejpam-3003	117	17	∈	∈	PROPN
ejpam-3003	117	18	h1	h1	PROPN
ejpam-3003	117	19	γ0	γ0	PROPN
ejpam-3003	117	20	(	(	PUNCT
ejpam-3003	117	21	ω	ω	NOUN
ejpam-3003	117	22	)	)	PUNCT
ejpam-3003	117	23	,	,	PUNCT
ejpam-3003	117	24	‖u‖h1	‖u‖h1	PROPN
ejpam-3003	117	25	γ0	γ0	PROPN
ejpam-3003	117	26	6=	6=	ADP
ejpam-3003	117	27	0	0	NUM
ejpam-3003	117	28	,	,	PUNCT
ejpam-3003	117	29	it	it	PRON
ejpam-3003	117	30	follows	follow	VERB
ejpam-3003	117	31	that	that	SCONJ
ejpam-3003	117	32	(	(	PUNCT
ejpam-3003	117	33	1	1	X
ejpam-3003	117	34	)	)	PUNCT
ejpam-3003	117	35	limλ→0	limλ→0	PROPN
ejpam-3003	117	36	+	+	CCONJ
ejpam-3003	117	37	j(λu	j(λu	NUM
ejpam-3003	117	38	)	)	PUNCT
ejpam-3003	117	39	=	=	SYM
ejpam-3003	117	40	0	0	NUM
ejpam-3003	117	41	,	,	PUNCT
ejpam-3003	117	42	limλ→+∞	limλ→+∞	X
ejpam-3003	117	43	j(λu	j(λu	PROPN
ejpam-3003	117	44	)	)	PUNCT
ejpam-3003	117	45	=	=	PUNCT
ejpam-3003	118	1	−∞	−∞	PROPN
ejpam-3003	118	2	;	;	PUNCT
ejpam-3003	118	3	(	(	PUNCT
ejpam-3003	118	4	2	2	X
ejpam-3003	118	5	)	)	PUNCT
ejpam-3003	118	6	on	on	ADP
ejpam-3003	118	7	the	the	DET
ejpam-3003	118	8	interval	interval	NOUN
ejpam-3003	118	9	0	0	PUNCT
ejpam-3003	118	10	<	<	X
ejpam-3003	118	11	λ	λ	X
ejpam-3003	118	12	<	<	X
ejpam-3003	118	13	∞	∞	PROPN
ejpam-3003	118	14	,	,	PUNCT
ejpam-3003	118	15	there	there	PRON
ejpam-3003	118	16	exists	exist	VERB
ejpam-3003	118	17	a	a	DET
ejpam-3003	118	18	unique	unique	ADJ
ejpam-3003	118	19	λ∗	λ∗	NOUN
ejpam-3003	118	20	=	=	SYM
ejpam-3003	118	21	λ∗(u	λ∗(u	NOUN
ejpam-3003	118	22	)	)	PUNCT
ejpam-3003	118	23	such	such	ADJ
ejpam-3003	118	24	that	that	SCONJ
ejpam-3003	118	25	d	d	NUM
ejpam-3003	118	26	dλ	dλ	NOUN
ejpam-3003	118	27	j(λu	j(λu	PROPN
ejpam-3003	118	28	)	)	PUNCT
ejpam-3003	118	29	∣∣	∣∣	NUM
ejpam-3003	118	30	λ	λ	X
ejpam-3003	118	31	=	=	NOUN
ejpam-3003	118	32	λ∗	λ∗	NOUN
ejpam-3003	118	33	=	=	SYM
ejpam-3003	118	34	0	0	NUM
ejpam-3003	118	35	;	;	PUNCT
ejpam-3003	118	36	(	(	PUNCT
ejpam-3003	118	37	3	3	X
ejpam-3003	118	38	)	)	PUNCT
ejpam-3003	118	39	j(λu	j(λu	PROPN
ejpam-3003	118	40	)	)	PUNCT
ejpam-3003	118	41	is	be	AUX
ejpam-3003	118	42	increasing	increase	VERB
ejpam-3003	118	43	on	on	ADP
ejpam-3003	118	44	0	0	NUM
ejpam-3003	118	45	≤	≤	NUM
ejpam-3003	118	46	λ	λ	PROPN
ejpam-3003	118	47	≤	≤	PROPN
ejpam-3003	118	48	λ∗	λ∗	PROPN
ejpam-3003	118	49	,	,	PUNCT
ejpam-3003	118	50	decreasing	decrease	VERB
ejpam-3003	118	51	on	on	ADP
ejpam-3003	118	52	λ∗	λ∗	NOUN
ejpam-3003	118	53	≤	≤	PROPN
ejpam-3003	118	54	λ	λ	X
ejpam-3003	118	55	<	<	X
ejpam-3003	118	56	∞	∞	PROPN
ejpam-3003	118	57	,	,	PUNCT
ejpam-3003	118	58	and	and	CCONJ
ejpam-3003	118	59	takes	take	VERB
ejpam-3003	118	60	the	the	DET
ejpam-3003	118	61	maximum	maximum	NOUN
ejpam-3003	118	62	at	at	ADP
ejpam-3003	118	63	λ	λ	PROPN
ejpam-3003	118	64	=	=	SYM
ejpam-3003	118	65	λ∗	λ∗	PROPN
ejpam-3003	118	66	;	;	PUNCT
ejpam-3003	118	67	(	(	PUNCT
ejpam-3003	118	68	4	4	X
ejpam-3003	118	69	)	)	PUNCT
ejpam-3003	118	70	i(λu	i(λu	PROPN
ejpam-3003	118	71	)	)	PUNCT
ejpam-3003	118	72	>	>	X
ejpam-3003	118	73	0	0	PUNCT
ejpam-3003	119	1	for	for	ADP
ejpam-3003	119	2	0	0	NUM
ejpam-3003	119	3	≤	≤	NUM
ejpam-3003	119	4	λ	λ	PROPN
ejpam-3003	119	5	<	<	X
ejpam-3003	119	6	λ∗	λ∗	PROPN
ejpam-3003	119	7	,	,	PUNCT
ejpam-3003	119	8	i(λu	i(λu	PROPN
ejpam-3003	119	9	)	)	PUNCT
ejpam-3003	119	10	<	<	X
ejpam-3003	119	11	0	0	NUM
ejpam-3003	119	12	for	for	ADP
ejpam-3003	119	13	λ∗	λ∗	PROPN
ejpam-3003	119	14	<	<	X
ejpam-3003	119	15	λ	λ	X
ejpam-3003	119	16	<	<	X
ejpam-3003	119	17	∞	∞	PROPN
ejpam-3003	119	18	,	,	PUNCT
ejpam-3003	119	19	and	and	CCONJ
ejpam-3003	119	20	i(λ∗u	i(λ∗u	NOUN
ejpam-3003	119	21	)	)	PUNCT
ejpam-3003	119	22	=	=	PUNCT
ejpam-3003	119	23	0	0	X
ejpam-3003	119	24	.	.	PUNCT
ejpam-3003	119	25	proof	proof	NOUN
ejpam-3003	119	26	.	.	PUNCT
ejpam-3003	120	1	(	(	PUNCT
ejpam-3003	120	2	1	1	NUM
ejpam-3003	120	3	)	)	PUNCT
ejpam-3003	120	4	from	from	ADP
ejpam-3003	120	5	the	the	DET
ejpam-3003	120	6	definition	definition	NOUN
ejpam-3003	120	7	of	of	ADP
ejpam-3003	120	8	the	the	DET
ejpam-3003	120	9	functional	functional	ADJ
ejpam-3003	120	10	(	(	PUNCT
ejpam-3003	120	11	2.2	2.2	NUM
ejpam-3003	120	12	)	)	PUNCT
ejpam-3003	120	13	,	,	PUNCT
ejpam-3003	120	14	we	we	PRON
ejpam-3003	120	15	have	have	VERB
ejpam-3003	120	16	j(λu	j(λu	NOUN
ejpam-3003	120	17	)	)	PUNCT
ejpam-3003	120	18	=	=	SYM
ejpam-3003	121	1	1	1	NUM
ejpam-3003	121	2	2	2	NUM
ejpam-3003	121	3	l(t)λ2‖∇u‖22	l(t)λ2‖∇u‖22	NOUN
ejpam-3003	122	1	+	+	NOUN
ejpam-3003	122	2	1	1	NUM
ejpam-3003	122	3	2	2	NUM
ejpam-3003	122	4	λ2(g	λ2(g	PUNCT
ejpam-3003	122	5	◦	◦	VERB
ejpam-3003	122	6	∇u)(t)−	∇u)(t)−	PROPN
ejpam-3003	122	7	λp+1	λp+1	PROPN
ejpam-3003	122	8	p+	p+	PROPN
ejpam-3003	122	9	1	1	NUM
ejpam-3003	122	10	‖u‖p+1	‖u‖p+1	PROPN
ejpam-3003	122	11	p+1	p+1	NOUN
ejpam-3003	122	12	.	.	PUNCT
ejpam-3003	123	1	hence	hence	ADV
ejpam-3003	123	2	,	,	PUNCT
ejpam-3003	123	3	the	the	DET
ejpam-3003	123	4	conclusion	conclusion	NOUN
ejpam-3003	123	5	holds	hold	VERB
ejpam-3003	123	6	.	.	PUNCT
ejpam-3003	124	1	(	(	PUNCT
ejpam-3003	124	2	2	2	X
ejpam-3003	124	3	)	)	PUNCT
ejpam-3003	124	4	the	the	DET
ejpam-3003	124	5	conclusion	conclusion	NOUN
ejpam-3003	124	6	follows	follow	VERB
ejpam-3003	124	7	from	from	ADP
ejpam-3003	124	8	d	d	PROPN
ejpam-3003	124	9	dλ	dλ	NOUN
ejpam-3003	124	10	j(λu	j(λu	PROPN
ejpam-3003	124	11	)	)	PUNCT
ejpam-3003	124	12	=	=	PUNCT
ejpam-3003	125	1	λl(t)‖∇u‖22	λl(t)‖∇u‖22	PUNCT
ejpam-3003	125	2	+	+	NUM
ejpam-3003	125	3	λ(g	λ(g	PROPN
ejpam-3003	126	1	◦	◦	NOUN
ejpam-3003	126	2	∇u)(t)−	∇u)(t)−	NUM
ejpam-3003	127	1	λp‖u‖p+1	λp‖u‖p+1	INTJ
ejpam-3003	127	2	p+1	p+1	NOUN
ejpam-3003	128	1	=	=	NOUN
ejpam-3003	128	2	0	0	X
ejpam-3003	128	3	.	.	PUNCT
ejpam-3003	129	1	(	(	PUNCT
ejpam-3003	129	2	2.4	2.4	NUM
ejpam-3003	129	3	)	)	PUNCT
ejpam-3003	129	4	(	(	PUNCT
ejpam-3003	129	5	3	3	X
ejpam-3003	129	6	)	)	PUNCT
ejpam-3003	129	7	from	from	ADP
ejpam-3003	129	8	the	the	DET
ejpam-3003	129	9	conclusion	conclusion	NOUN
ejpam-3003	129	10	of	of	ADP
ejpam-3003	129	11	(	(	PUNCT
ejpam-3003	129	12	2	2	NUM
ejpam-3003	129	13	)	)	PUNCT
ejpam-3003	129	14	,	,	PUNCT
ejpam-3003	129	15	we	we	PRON
ejpam-3003	129	16	can	can	AUX
ejpam-3003	129	17	easily	easily	ADV
ejpam-3003	129	18	get	get	VERB
ejpam-3003	129	19	d	d	PROPN
ejpam-3003	129	20	dλ	dλ	NOUN
ejpam-3003	129	21	j(λu	j(λu	PROPN
ejpam-3003	129	22	)	)	PUNCT
ejpam-3003	129	23	≥	≥	NOUN
ejpam-3003	129	24	0	0	NUM
ejpam-3003	129	25	,	,	PUNCT
ejpam-3003	129	26	for	for	ADP
ejpam-3003	129	27	0	0	NUM
ejpam-3003	129	28	≤	≤	NUM
ejpam-3003	129	29	λ	λ	PROPN
ejpam-3003	129	30	≤	≤	PROPN
ejpam-3003	129	31	λ∗	λ∗	PROPN
ejpam-3003	129	32	,	,	PUNCT
ejpam-3003	129	33	d	d	PROPN
ejpam-3003	129	34	dλ	dλ	NOUN
ejpam-3003	129	35	j(λu	j(λu	PROPN
ejpam-3003	129	36	)	)	PUNCT
ejpam-3003	129	37	≤	≤	NOUN
ejpam-3003	129	38	0	0	NUM
ejpam-3003	129	39	,	,	PUNCT
ejpam-3003	129	40	for	for	ADP
ejpam-3003	129	41	λ∗	λ∗	NOUN
ejpam-3003	130	1	≤	≤	PROPN
ejpam-3003	130	2	λ	λ	PROPN
ejpam-3003	130	3	<	<	X
ejpam-3003	130	4	∞.	∞.	PROPN
ejpam-3003	130	5	(	(	PUNCT
ejpam-3003	130	6	4	4	NUM
ejpam-3003	130	7	)	)	PUNCT
ejpam-3003	130	8	the	the	DET
ejpam-3003	130	9	conclusion	conclusion	NOUN
ejpam-3003	130	10	follows	follow	VERB
ejpam-3003	130	11	from	from	ADP
ejpam-3003	130	12	i(λu	i(λu	NOUN
ejpam-3003	130	13	)	)	PUNCT
ejpam-3003	130	14	=	=	PUNCT
ejpam-3003	130	15	λ2l(t)‖∇u‖22	λ2l(t)‖∇u‖22	PROPN
ejpam-3003	131	1	+	+	CCONJ
ejpam-3003	131	2	λ2(g	λ2(g	PUNCT
ejpam-3003	131	3	◦	◦	NOUN
ejpam-3003	131	4	∇u)(t)−	∇u)(t)−	NUM
ejpam-3003	131	5	λp‖u‖p+1	λp‖u‖p+1	INTJ
ejpam-3003	131	6	p+1	p+1	NOUN
ejpam-3003	132	1	=	=	PUNCT
ejpam-3003	132	2	λ	λ	X
ejpam-3003	132	3	d	d	X
ejpam-3003	132	4	dλ	dλ	NOUN
ejpam-3003	132	5	j(λu	j(λu	PROPN
ejpam-3003	132	6	)	)	PUNCT
ejpam-3003	132	7	.	.	PUNCT
ejpam-3003	133	1	(	(	PUNCT
ejpam-3003	133	2	2.5	2.5	X
ejpam-3003	133	3	)	)	PUNCT
ejpam-3003	133	4	h.f	h.f	PROPN
ejpam-3003	133	5	.	.	PROPN
ejpam-3003	133	6	di	di	PROPN
ejpam-3003	133	7	,	,	PUNCT
ejpam-3003	133	8	y.d	y.d	PROPN
ejpam-3003	133	9	.	.	PROPN
ejpam-3003	133	10	shang	shang	PROPN
ejpam-3003	133	11	/	/	SYM
ejpam-3003	133	12	eur	eur	PROPN
ejpam-3003	133	13	.	.	PUNCT
ejpam-3003	134	1	j.	j.	PROPN
ejpam-3003	134	2	pure	pure	PROPN
ejpam-3003	134	3	appl	appl	PROPN
ejpam-3003	134	4	.	.	PROPN
ejpam-3003	134	5	math	math	PROPN
ejpam-3003	134	6	,	,	PUNCT
ejpam-3003	134	7	10	10	NUM
ejpam-3003	134	8	(	(	PUNCT
ejpam-3003	134	9	4	4	NUM
ejpam-3003	134	10	)	)	PUNCT
ejpam-3003	134	11	(	(	PUNCT
ejpam-3003	134	12	2017	2017	NUM
ejpam-3003	134	13	)	)	PUNCT
ejpam-3003	134	14	,	,	PUNCT
ejpam-3003	134	15	668	668	NUM
ejpam-3003	134	16	-	-	SYM
ejpam-3003	134	17	701	701	NUM
ejpam-3003	134	18	674	674	NUM
ejpam-3003	134	19	then	then	ADV
ejpam-3003	134	20	,	,	PUNCT
ejpam-3003	134	21	for	for	ADP
ejpam-3003	134	22	t	t	PROPN
ejpam-3003	134	23	≥	≥	NOUN
ejpam-3003	134	24	0	0	NUM
ejpam-3003	134	25	,	,	PUNCT
ejpam-3003	134	26	we	we	PRON
ejpam-3003	134	27	define	define	VERB
ejpam-3003	134	28	d(t	d(t	PROPN
ejpam-3003	134	29	)	)	PUNCT
ejpam-3003	134	30	=	=	PROPN
ejpam-3003	134	31	inf	inf	PROPN
ejpam-3003	134	32	u∈h1	u∈h1	VERB
ejpam-3003	134	33	γ0	γ0	PROPN
ejpam-3003	134	34	(	(	PUNCT
ejpam-3003	134	35	ω)\{0	ω)\{0	NOUN
ejpam-3003	134	36	}	}	PUNCT
ejpam-3003	134	37	{	{	PUNCT
ejpam-3003	134	38	sup	sup	PROPN
ejpam-3003	134	39	λ>0	λ>0	NOUN
ejpam-3003	134	40	j(λu	j(λu	NOUN
ejpam-3003	134	41	)	)	PUNCT
ejpam-3003	134	42	}	}	PUNCT
ejpam-3003	134	43	.	.	PUNCT
ejpam-3003	135	1	(	(	PUNCT
ejpam-3003	135	2	2.6	2.6	NUM
ejpam-3003	135	3	)	)	PUNCT
ejpam-3003	135	4	in	in	ADP
ejpam-3003	135	5	fact	fact	NOUN
ejpam-3003	135	6	(	(	PUNCT
ejpam-3003	135	7	see	see	VERB
ejpam-3003	135	8	[	[	X
ejpam-3003	135	9	26,27	26,27	NUM
ejpam-3003	135	10	]	]	PUNCT
ejpam-3003	135	11	for	for	ADP
ejpam-3003	135	12	details	detail	NOUN
ejpam-3003	135	13	)	)	PUNCT
ejpam-3003	135	14	,	,	PUNCT
ejpam-3003	135	15	d(t	d(t	PROPN
ejpam-3003	135	16	)	)	PUNCT
ejpam-3003	135	17	is	be	AUX
ejpam-3003	135	18	positive	positive	ADJ
ejpam-3003	135	19	and	and	CCONJ
ejpam-3003	135	20	equal	equal	ADJ
ejpam-3003	135	21	to	to	ADP
ejpam-3003	135	22	inf	inf	PROPN
ejpam-3003	135	23	i(u)=0,u6=0	i(u)=0,u6=0	PROPN
ejpam-3003	135	24	j(u	j(u	PROPN
ejpam-3003	135	25	)	)	PUNCT
ejpam-3003	135	26	.	.	PUNCT
ejpam-3003	136	1	(	(	PUNCT
ejpam-3003	136	2	2.7	2.7	NUM
ejpam-3003	136	3	)	)	PUNCT
ejpam-3003	136	4	lemma	lemma	PROPN
ejpam-3003	136	5	2	2	X
ejpam-3003	136	6	.	.	PUNCT
ejpam-3003	137	1	let	let	VERB
ejpam-3003	137	2	the	the	DET
ejpam-3003	137	3	assumptions	assumption	NOUN
ejpam-3003	137	4	(	(	PUNCT
ejpam-3003	137	5	a1	a1	NOUN
ejpam-3003	137	6	)	)	PUNCT
ejpam-3003	137	7	,	,	PUNCT
ejpam-3003	137	8	(	(	PUNCT
ejpam-3003	137	9	a3	a3	NOUN
ejpam-3003	137	10	)	)	PUNCT
ejpam-3003	137	11	hold	hold	VERB
ejpam-3003	137	12	,	,	PUNCT
ejpam-3003	137	13	then	then	ADV
ejpam-3003	137	14	for	for	ADP
ejpam-3003	137	15	all	all	DET
ejpam-3003	137	16	t	t	NOUN
ejpam-3003	137	17	∈	∈	PROPN
ejpam-3003	138	1	[	[	X
ejpam-3003	138	2	0,∞	0,∞	NOUN
ejpam-3003	138	3	)	)	PUNCT
ejpam-3003	138	4	,	,	PUNCT
ejpam-3003	138	5	we	we	PRON
ejpam-3003	138	6	have	have	VERB
ejpam-3003	138	7	0	0	NUM
ejpam-3003	138	8	<	<	X
ejpam-3003	138	9	d̃	d̃	PROPN
ejpam-3003	138	10	≤	≤	PROPN
ejpam-3003	138	11	d(t	d(t	PROPN
ejpam-3003	138	12	)	)	PUNCT
ejpam-3003	138	13	≤	≤	NUM
ejpam-3003	138	14	˜̃	˜̃	NOUN
ejpam-3003	138	15	d(u	d(u	PROPN
ejpam-3003	138	16	)	)	PUNCT
ejpam-3003	138	17	=	=	SYM
ejpam-3003	139	1	sup	sup	NOUN
ejpam-3003	139	2	λ>0	λ>0	NOUN
ejpam-3003	139	3	j(λu	j(λu	NOUN
ejpam-3003	139	4	)	)	PUNCT
ejpam-3003	139	5	,	,	PUNCT
ejpam-3003	139	6	(	(	PUNCT
ejpam-3003	139	7	2.8	2.8	NUM
ejpam-3003	139	8	)	)	PUNCT
ejpam-3003	139	9	where	where	SCONJ
ejpam-3003	139	10	d̃	d̃	PROPN
ejpam-3003	139	11	=	=	SYM
ejpam-3003	139	12	p−1	p−1	PROPN
ejpam-3003	139	13	2(p+1	2(p+1	NUM
ejpam-3003	139	14	)	)	PUNCT
ejpam-3003	139	15	(	(	PUNCT
ejpam-3003	139	16	b	b	X
ejpam-3003	139	17	b2	b2	NOUN
ejpam-3003	139	18	p+1	p+1	NOUN
ejpam-3003	139	19	)	)	PUNCT
ejpam-3003	140	1	p+1	p+1	PROPN
ejpam-3003	140	2	p−1	p−1	PROPN
ejpam-3003	140	3	,	,	PUNCT
ejpam-3003	140	4	and	and	CCONJ
ejpam-3003	140	5	bp+1	bp+1	NUM
ejpam-3003	140	6	is	be	AUX
ejpam-3003	140	7	the	the	DET
ejpam-3003	140	8	optimal	optimal	ADJ
ejpam-3003	140	9	constant	constant	ADJ
ejpam-3003	140	10	satisfying	satisfy	VERB
ejpam-3003	140	11	the	the	DET
ejpam-3003	140	12	sobolev	sobolev	NOUN
ejpam-3003	140	13	inequality	inequality	PROPN
ejpam-3003	140	14	‖u‖p+1	‖u‖p+1	PROPN
ejpam-3003	140	15	≤	≤	PROPN
ejpam-3003	140	16	bp+1‖∇u‖2	bp+1‖∇u‖2	PROPN
ejpam-3003	140	17	.	.	PUNCT
ejpam-3003	141	1	proof	proof	NOUN
ejpam-3003	141	2	.	.	PUNCT
ejpam-3003	142	1	from	from	ADP
ejpam-3003	142	2	the	the	DET
ejpam-3003	142	3	definition	definition	NOUN
ejpam-3003	142	4	of	of	ADP
ejpam-3003	142	5	d(t	d(t	PROPN
ejpam-3003	142	6	)	)	PUNCT
ejpam-3003	142	7	,	,	PUNCT
ejpam-3003	142	8	we	we	PRON
ejpam-3003	142	9	get	get	VERB
ejpam-3003	142	10	d(t	d(t	PROPN
ejpam-3003	142	11	)	)	PUNCT
ejpam-3003	142	12	≤	≤	NUM
ejpam-3003	142	13	˜̃	˜̃	NOUN
ejpam-3003	142	14	d	d	NOUN
ejpam-3003	142	15	=	=	SYM
ejpam-3003	142	16	supλ>0	supλ>0	NOUN
ejpam-3003	142	17	j(λu	j(λu	PROPN
ejpam-3003	142	18	)	)	PUNCT
ejpam-3003	142	19	.	.	PUNCT
ejpam-3003	143	1	by	by	ADP
ejpam-3003	143	2	the	the	DET
ejpam-3003	143	3	sobolev	sobolev	NOUN
ejpam-3003	143	4	inequality	inequality	NOUN
ejpam-3003	143	5	,	,	PUNCT
ejpam-3003	143	6	it	it	PRON
ejpam-3003	143	7	follows	follow	VERB
ejpam-3003	143	8	that	that	SCONJ
ejpam-3003	143	9	j(λu	j(λu	NOUN
ejpam-3003	143	10	)	)	PUNCT
ejpam-3003	143	11	=	=	SYM
ejpam-3003	143	12	1	1	NUM
ejpam-3003	143	13	2	2	NUM
ejpam-3003	143	14	l(t)‖∇λu‖22	l(t)‖∇λu‖22	NOUN
ejpam-3003	143	15	+	+	CCONJ
ejpam-3003	143	16	1	1	NUM
ejpam-3003	143	17	2	2	NUM
ejpam-3003	143	18	(	(	PUNCT
ejpam-3003	143	19	g	g	NOUN
ejpam-3003	143	20	◦	◦	NOUN
ejpam-3003	143	21	∇λu)(t)−	∇λu)(t)−	NUM
ejpam-3003	143	22	1	1	NUM
ejpam-3003	143	23	p+	p+	NOUN
ejpam-3003	143	24	1	1	NUM
ejpam-3003	143	25	‖λu‖p+1	‖λu‖p+1	NOUN
ejpam-3003	143	26	p+1	p+1	NOUN
ejpam-3003	143	27	≥	≥	NUM
ejpam-3003	143	28	1	1	NUM
ejpam-3003	143	29	2	2	NUM
ejpam-3003	143	30	b‖∇λu‖22	b‖∇λu‖22	PROPN
ejpam-3003	143	31	−	−	PROPN
ejpam-3003	143	32	1	1	NUM
ejpam-3003	143	33	p+	p+	NOUN
ejpam-3003	143	34	1	1	NUM
ejpam-3003	143	35	bp+1	bp+1	NUM
ejpam-3003	143	36	p+1‖∇λu‖	p+1‖∇λu‖	PROPN
ejpam-3003	143	37	p+1	p+1	NOUN
ejpam-3003	143	38	2	2	NUM
ejpam-3003	143	39	.	.	PUNCT
ejpam-3003	144	1	(	(	PUNCT
ejpam-3003	144	2	2.9	2.9	NUM
ejpam-3003	144	3	)	)	PUNCT
ejpam-3003	144	4	here	here	ADV
ejpam-3003	144	5	,	,	PUNCT
ejpam-3003	144	6	we	we	PRON
ejpam-3003	144	7	define	define	VERB
ejpam-3003	144	8	the	the	DET
ejpam-3003	144	9	function	function	NOUN
ejpam-3003	144	10	h(λ	h(λ	PROPN
ejpam-3003	144	11	)	)	PUNCT
ejpam-3003	145	1	=	=	SYM
ejpam-3003	145	2	1	1	NUM
ejpam-3003	145	3	2bλ	2bλ	NOUN
ejpam-3003	145	4	2	2	NUM
ejpam-3003	145	5	−	−	NOUN
ejpam-3003	145	6	1	1	NUM
ejpam-3003	146	1	p+1b	p+1b	NOUN
ejpam-3003	146	2	p+1	p+1	PROPN
ejpam-3003	146	3	p+1λ	p+1λ	PROPN
ejpam-3003	146	4	p+1	p+1	NOUN
ejpam-3003	146	5	,	,	PUNCT
ejpam-3003	146	6	λ	λ	X
ejpam-3003	146	7	>	>	X
ejpam-3003	146	8	0	0	NUM
ejpam-3003	146	9	.	.	PUNCT
ejpam-3003	147	1	by	by	ADP
ejpam-3003	147	2	the	the	DET
ejpam-3003	147	3	direct	direct	ADJ
ejpam-3003	147	4	computation	computation	NOUN
ejpam-3003	147	5	,	,	PUNCT
ejpam-3003	147	6	we	we	PRON
ejpam-3003	147	7	deduce	deduce	VERB
ejpam-3003	147	8	that	that	SCONJ
ejpam-3003	147	9	h	h	NOUN
ejpam-3003	147	10	is	be	AUX
ejpam-3003	147	11	increasing	increase	VERB
ejpam-3003	147	12	for	for	ADP
ejpam-3003	147	13	0	0	NUM
ejpam-3003	147	14	<	<	X
ejpam-3003	147	15	λ	λ	X
ejpam-3003	147	16	<	<	X
ejpam-3003	147	17	λ1	λ1	PROPN
ejpam-3003	147	18	,	,	PUNCT
ejpam-3003	147	19	decreasing	decrease	VERB
ejpam-3003	147	20	for	for	ADP
ejpam-3003	147	21	λ	λ	PROPN
ejpam-3003	147	22	>	>	X
ejpam-3003	147	23	λ1	λ1	PROPN
ejpam-3003	147	24	and	and	CCONJ
ejpam-3003	147	25	λ1	λ1	PROPN
ejpam-3003	147	26	=	=	PUNCT
ejpam-3003	147	27	(	(	PUNCT
ejpam-3003	147	28	b	b	X
ejpam-3003	147	29	bp+1	bp+1	NOUN
ejpam-3003	147	30	p+1	p+1	NOUN
ejpam-3003	147	31	)	)	PUNCT
ejpam-3003	147	32	1	1	NUM
ejpam-3003	147	33	p−1	p−1	PROPN
ejpam-3003	147	34	is	be	AUX
ejpam-3003	147	35	the	the	DET
ejpam-3003	147	36	absolute	absolute	ADJ
ejpam-3003	147	37	maximum	maximum	ADJ
ejpam-3003	147	38	point	point	NOUN
ejpam-3003	147	39	of	of	ADP
ejpam-3003	147	40	h	h	NOUN
ejpam-3003	147	41	such	such	ADJ
ejpam-3003	147	42	that	that	SCONJ
ejpam-3003	147	43	d̃	d̃	PROPN
ejpam-3003	147	44	=	=	SYM
ejpam-3003	147	45	h(λ1	h(λ1	NOUN
ejpam-3003	147	46	)	)	PUNCT
ejpam-3003	148	1	=	=	PUNCT
ejpam-3003	148	2	p−	p−	NOUN
ejpam-3003	148	3	1	1	NUM
ejpam-3003	148	4	2(p+	2(p+	NUM
ejpam-3003	148	5	1	1	NUM
ejpam-3003	148	6	)	)	PUNCT
ejpam-3003	148	7	(	(	PUNCT
ejpam-3003	148	8	b	b	X
ejpam-3003	148	9	b2	b2	NOUN
ejpam-3003	148	10	p+1	p+1	NOUN
ejpam-3003	148	11	)	)	PUNCT
ejpam-3003	149	1	p+1	p+1	PROPN
ejpam-3003	149	2	p−1	p−1	PROPN
ejpam-3003	149	3	.	.	PUNCT
ejpam-3003	150	1	by	by	ADP
ejpam-3003	150	2	the	the	DET
ejpam-3003	150	3	combination	combination	NOUN
ejpam-3003	150	4	of	of	ADP
ejpam-3003	150	5	(	(	PUNCT
ejpam-3003	150	6	2.9	2.9	NUM
ejpam-3003	150	7	)	)	PUNCT
ejpam-3003	150	8	and	and	CCONJ
ejpam-3003	150	9	the	the	DET
ejpam-3003	150	10	definition	definition	NOUN
ejpam-3003	150	11	of	of	ADP
ejpam-3003	150	12	d̃	d̃	PROPN
ejpam-3003	150	13	,	,	PUNCT
ejpam-3003	150	14	it	it	PRON
ejpam-3003	150	15	follows	follow	VERB
ejpam-3003	150	16	that	that	SCONJ
ejpam-3003	150	17	d̃	d̃	PROPN
ejpam-3003	150	18	=	=	SYM
ejpam-3003	150	19	h(λ1	h(λ1	NOUN
ejpam-3003	150	20	)	)	PUNCT
ejpam-3003	150	21	≤	≤	NOUN
ejpam-3003	150	22	j(λu	j(λu	NOUN
ejpam-3003	150	23	)	)	PUNCT
ejpam-3003	150	24	.	.	PUNCT
ejpam-3003	151	1	moreover	moreover	ADV
ejpam-3003	151	2	,	,	PUNCT
ejpam-3003	151	3	from	from	ADP
ejpam-3003	151	4	the	the	DET
ejpam-3003	151	5	definition	definition	NOUN
ejpam-3003	151	6	of	of	ADP
ejpam-3003	151	7	d(t	d(t	PROPN
ejpam-3003	151	8	)	)	PUNCT
ejpam-3003	151	9	,	,	PUNCT
ejpam-3003	151	10	we	we	PRON
ejpam-3003	151	11	have	have	VERB
ejpam-3003	151	12	d̃	d̃	PROPN
ejpam-3003	151	13	≤	≤	NUM
ejpam-3003	151	14	infu∈h1	infu∈h1	PROPN
ejpam-3003	151	15	γ0	γ0	NOUN
ejpam-3003	151	16	(	(	PUNCT
ejpam-3003	151	17	ω)\{0	ω)\{0	NOUN
ejpam-3003	151	18	}	}	PUNCT
ejpam-3003	151	19	{	{	PUNCT
ejpam-3003	151	20	supλ>0	supλ>0	NOUN
ejpam-3003	151	21	j(λu	j(λu	PROPN
ejpam-3003	151	22	)	)	PUNCT
ejpam-3003	151	23	}	}	PUNCT
ejpam-3003	151	24	=	=	SYM
ejpam-3003	151	25	d(t	d(t	PROPN
ejpam-3003	151	26	)	)	PUNCT
ejpam-3003	151	27	.	.	PUNCT
ejpam-3003	152	1	the	the	DET
ejpam-3003	152	2	proof	proof	NOUN
ejpam-3003	152	3	is	be	AUX
ejpam-3003	152	4	completed	complete	VERB
ejpam-3003	152	5	.	.	PUNCT
ejpam-3003	153	1	to	to	PART
ejpam-3003	153	2	obtain	obtain	VERB
ejpam-3003	153	3	the	the	DET
ejpam-3003	153	4	results	result	NOUN
ejpam-3003	153	5	of	of	ADP
ejpam-3003	153	6	this	this	DET
ejpam-3003	153	7	paper	paper	NOUN
ejpam-3003	153	8	,	,	PUNCT
ejpam-3003	153	9	we	we	PRON
ejpam-3003	153	10	will	will	AUX
ejpam-3003	153	11	construct	construct	VERB
ejpam-3003	153	12	the	the	DET
ejpam-3003	153	13	potential	potential	ADJ
ejpam-3003	153	14	wells	well	NOUN
ejpam-3003	153	15	associated	associate	VERB
ejpam-3003	153	16	with	with	ADP
ejpam-3003	153	17	the	the	DET
ejpam-3003	153	18	functionals	functional	NOUN
ejpam-3003	153	19	j(u	j(u	PROPN
ejpam-3003	153	20	)	)	PUNCT
ejpam-3003	153	21	and	and	CCONJ
ejpam-3003	153	22	i(u	i(u	PROPN
ejpam-3003	153	23	)	)	PUNCT
ejpam-3003	153	24	.	.	PUNCT
ejpam-3003	154	1	next	next	ADV
ejpam-3003	154	2	,	,	PUNCT
ejpam-3003	154	3	let	let	VERB
ejpam-3003	154	4	us	we	PRON
ejpam-3003	154	5	introduce	introduce	VERB
ejpam-3003	154	6	the	the	DET
ejpam-3003	154	7	stable	stable	ADJ
ejpam-3003	154	8	and	and	CCONJ
ejpam-3003	154	9	unstable	unstable	ADJ
ejpam-3003	154	10	sets	set	NOUN
ejpam-3003	154	11	:	:	PUNCT
ejpam-3003	154	12	w	w	X
ejpam-3003	154	13	=	=	PUNCT
ejpam-3003	154	14	{	{	PUNCT
ejpam-3003	154	15	u	u	NOUN
ejpam-3003	154	16	∈	∈	PROPN
ejpam-3003	154	17	h1	h1	PROPN
ejpam-3003	154	18	γ0	γ0	PROPN
ejpam-3003	154	19	(	(	PUNCT
ejpam-3003	154	20	ω	ω	NOUN
ejpam-3003	154	21	)	)	PUNCT
ejpam-3003	154	22	∣∣	∣∣	PROPN
ejpam-3003	154	23	i(u	i(u	PROPN
ejpam-3003	154	24	)	)	PUNCT
ejpam-3003	154	25	>	>	X
ejpam-3003	154	26	0	0	NUM
ejpam-3003	154	27	,	,	PUNCT
ejpam-3003	154	28	j(u	j(u	PROPN
ejpam-3003	154	29	)	)	PUNCT
ejpam-3003	154	30	<	<	X
ejpam-3003	154	31	d̃	d̃	PROPN
ejpam-3003	154	32	}	}	PUNCT
ejpam-3003	154	33	∪	∪	X
ejpam-3003	154	34	{	{	PUNCT
ejpam-3003	154	35	0	0	NUM
ejpam-3003	154	36	}	}	PUNCT
ejpam-3003	154	37	,	,	PUNCT
ejpam-3003	154	38	(	(	PUNCT
ejpam-3003	154	39	2.10	2.10	NUM
ejpam-3003	154	40	)	)	PUNCT
ejpam-3003	154	41	and	and	CCONJ
ejpam-3003	154	42	v	v	X
ejpam-3003	154	43	=	=	PUNCT
ejpam-3003	154	44	{	{	PUNCT
ejpam-3003	154	45	u	u	NOUN
ejpam-3003	154	46	∈	∈	PROPN
ejpam-3003	154	47	h1	h1	PROPN
ejpam-3003	154	48	γ0	γ0	PROPN
ejpam-3003	154	49	(	(	PUNCT
ejpam-3003	154	50	ω	ω	NOUN
ejpam-3003	154	51	)	)	PUNCT
ejpam-3003	154	52	∣∣	∣∣	PROPN
ejpam-3003	155	1	i(u	i(u	PROPN
ejpam-3003	155	2	)	)	PUNCT
ejpam-3003	155	3	<	<	X
ejpam-3003	155	4	0	0	NUM
ejpam-3003	155	5	,	,	PUNCT
ejpam-3003	155	6	j(u	j(u	PROPN
ejpam-3003	155	7	)	)	PUNCT
ejpam-3003	155	8	<	<	X
ejpam-3003	155	9	d̃	d̃	PROPN
ejpam-3003	155	10	}	}	PUNCT
ejpam-3003	155	11	.	.	PUNCT
ejpam-3003	156	1	(	(	PUNCT
ejpam-3003	156	2	2.11	2.11	NUM
ejpam-3003	156	3	)	)	PUNCT
ejpam-3003	156	4	for	for	ADP
ejpam-3003	156	5	simplicity	simplicity	NOUN
ejpam-3003	156	6	,	,	PUNCT
ejpam-3003	156	7	we	we	PRON
ejpam-3003	156	8	define	define	VERB
ejpam-3003	156	9	the	the	DET
ejpam-3003	156	10	weak	weak	ADJ
ejpam-3003	156	11	solutions	solution	NOUN
ejpam-3003	156	12	of	of	ADP
ejpam-3003	156	13	(	(	PUNCT
ejpam-3003	156	14	1.1	1.1	NUM
ejpam-3003	156	15	)	)	PUNCT
ejpam-3003	156	16	over	over	ADP
ejpam-3003	156	17	the	the	DET
ejpam-3003	156	18	interval	interval	NOUN
ejpam-3003	156	19	ω×	ω×	PUNCT
ejpam-3003	157	1	[	[	X
ejpam-3003	157	2	0	0	NUM
ejpam-3003	157	3	,	,	PUNCT
ejpam-3003	157	4	t	t	NOUN
ejpam-3003	157	5	)	)	PUNCT
ejpam-3003	157	6	,	,	PUNCT
ejpam-3003	157	7	but	but	CCONJ
ejpam-3003	157	8	it	it	PRON
ejpam-3003	157	9	is	be	AUX
ejpam-3003	157	10	to	to	PART
ejpam-3003	157	11	be	be	AUX
ejpam-3003	157	12	understood	understand	VERB
ejpam-3003	157	13	that	that	SCONJ
ejpam-3003	157	14	t	t	PROPN
ejpam-3003	157	15	is	be	AUX
ejpam-3003	157	16	either	either	CCONJ
ejpam-3003	157	17	infinity	infinity	NOUN
ejpam-3003	157	18	or	or	CCONJ
ejpam-3003	157	19	the	the	DET
ejpam-3003	157	20	limit	limit	NOUN
ejpam-3003	157	21	of	of	ADP
ejpam-3003	157	22	the	the	DET
ejpam-3003	157	23	existence	existence	NOUN
ejpam-3003	157	24	interval	interval	NOUN
ejpam-3003	157	25	.	.	PUNCT
ejpam-3003	158	1	h.f	h.f	PROPN
ejpam-3003	158	2	.	.	PROPN
ejpam-3003	158	3	di	di	PROPN
ejpam-3003	158	4	,	,	PUNCT
ejpam-3003	158	5	y.d	y.d	PROPN
ejpam-3003	158	6	.	.	PROPN
ejpam-3003	158	7	shang	shang	PROPN
ejpam-3003	158	8	/	/	SYM
ejpam-3003	158	9	eur	eur	PROPN
ejpam-3003	158	10	.	.	PUNCT
ejpam-3003	159	1	j.	j.	PROPN
ejpam-3003	159	2	pure	pure	PROPN
ejpam-3003	159	3	appl	appl	PROPN
ejpam-3003	159	4	.	.	PROPN
ejpam-3003	159	5	math	math	PROPN
ejpam-3003	159	6	,	,	PUNCT
ejpam-3003	159	7	10	10	NUM
ejpam-3003	159	8	(	(	PUNCT
ejpam-3003	159	9	4	4	NUM
ejpam-3003	159	10	)	)	PUNCT
ejpam-3003	159	11	(	(	PUNCT
ejpam-3003	159	12	2017	2017	NUM
ejpam-3003	159	13	)	)	PUNCT
ejpam-3003	159	14	,	,	PUNCT
ejpam-3003	159	15	668	668	NUM
ejpam-3003	159	16	-	-	SYM
ejpam-3003	159	17	701	701	NUM
ejpam-3003	159	18	675	675	NUM
ejpam-3003	159	19	definition	definition	NOUN
ejpam-3003	159	20	1	1	NUM
ejpam-3003	159	21	.	.	PUNCT
ejpam-3003	160	1	we	we	PRON
ejpam-3003	160	2	say	say	VERB
ejpam-3003	160	3	that	that	SCONJ
ejpam-3003	160	4	u(x	u(x	PROPN
ejpam-3003	160	5	,	,	PUNCT
ejpam-3003	160	6	t	t	PROPN
ejpam-3003	160	7	)	)	PUNCT
ejpam-3003	160	8	is	be	AUX
ejpam-3003	160	9	called	call	VERB
ejpam-3003	160	10	a	a	DET
ejpam-3003	160	11	weak	weak	ADJ
ejpam-3003	160	12	solution	solution	NOUN
ejpam-3003	160	13	of	of	ADP
ejpam-3003	160	14	the	the	DET
ejpam-3003	160	15	problem	problem	NOUN
ejpam-3003	160	16	(	(	PUNCT
ejpam-3003	160	17	1.1	1.1	NUM
ejpam-3003	160	18	)	)	PUNCT
ejpam-3003	160	19	on	on	ADP
ejpam-3003	160	20	the	the	DET
ejpam-3003	160	21	interval	interval	NOUN
ejpam-3003	160	22	ω×[0	ω×[0	NOUN
ejpam-3003	160	23	,	,	PUNCT
ejpam-3003	160	24	t	t	NOUN
ejpam-3003	160	25	)	)	PUNCT
ejpam-3003	160	26	.	.	PUNCT
ejpam-3003	161	1	if	if	SCONJ
ejpam-3003	161	2	u	u	PROPN
ejpam-3003	161	3	∈	∈	PROPN
ejpam-3003	161	4	l∞(0	l∞(0	PRON
ejpam-3003	161	5	,	,	PUNCT
ejpam-3003	161	6	t	t	PROPN
ejpam-3003	161	7	;	;	PUNCT
ejpam-3003	161	8	h1	h1	PROPN
ejpam-3003	161	9	γ0	γ0	PROPN
ejpam-3003	161	10	(	(	PUNCT
ejpam-3003	161	11	ω	ω	NOUN
ejpam-3003	161	12	)	)	PUNCT
ejpam-3003	161	13	)	)	PUNCT
ejpam-3003	161	14	with	with	ADP
ejpam-3003	161	15	ut	ut	PROPN
ejpam-3003	161	16	∈	∈	PROPN
ejpam-3003	161	17	l∞(0	l∞(0	PROPN
ejpam-3003	161	18	,	,	PUNCT
ejpam-3003	161	19	t	t	PROPN
ejpam-3003	161	20	;	;	PUNCT
ejpam-3003	161	21	lρ+1(ω))∩lq+1(0	lρ+1(ω))∩lq+1(0	PROPN
ejpam-3003	161	22	,	,	PUNCT
ejpam-3003	161	23	t	t	PROPN
ejpam-3003	161	24	;	;	PUNCT
ejpam-3003	161	25	lq+1(γ1	lq+1(γ1	NOUN
ejpam-3003	161	26	)	)	PUNCT
ejpam-3003	161	27	)	)	PUNCT
ejpam-3003	161	28	satisfy	satisfy	VERB
ejpam-3003	161	29	the	the	DET
ejpam-3003	161	30	following	follow	VERB
ejpam-3003	161	31	conditions	condition	NOUN
ejpam-3003	161	32	(	(	PUNCT
ejpam-3003	161	33	i	i	NOUN
ejpam-3003	161	34	)	)	PUNCT
ejpam-3003	161	35	for	for	ADP
ejpam-3003	161	36	any	any	DET
ejpam-3003	161	37	v	v	PROPN
ejpam-3003	161	38	∈	∈	PROPN
ejpam-3003	161	39	h1	h1	PROPN
ejpam-3003	161	40	γ0	γ0	PROPN
ejpam-3003	161	41	(	(	PUNCT
ejpam-3003	161	42	ω	ω	NOUN
ejpam-3003	161	43	)	)	PUNCT
ejpam-3003	161	44	∩	∩	NOUN
ejpam-3003	161	45	lq+1(γ1	lq+1(γ1	NOUN
ejpam-3003	161	46	)	)	PUNCT
ejpam-3003	161	47	∩	∩	NOUN
ejpam-3003	161	48	lρ+1(ω	lρ+1(ω	X
ejpam-3003	161	49	)	)	PUNCT
ejpam-3003	161	50	and	and	CCONJ
ejpam-3003	161	51	a.e	a.e	PROPN
ejpam-3003	161	52	0	0	NUM
ejpam-3003	161	53	≤	≤	PROPN
ejpam-3003	161	54	t	t	PROPN
ejpam-3003	161	55	≤	≤	PROPN
ejpam-3003	161	56	t	t	PROPN
ejpam-3003	161	57	,	,	PUNCT
ejpam-3003	161	58	such	such	ADJ
ejpam-3003	161	59	that	that	SCONJ
ejpam-3003	161	60	1	1	NUM
ejpam-3003	161	61	ρ	ρ	NOUN
ejpam-3003	161	62	(	(	PUNCT
ejpam-3003	161	63	|ut|ρ−1ut	|ut|ρ−1ut	PROPN
ejpam-3003	161	64	,	,	PUNCT
ejpam-3003	161	65	v	v	NOUN
ejpam-3003	161	66	)	)	PUNCT
ejpam-3003	162	1	+	+	CCONJ
ejpam-3003	162	2	∫	∫	PROPN
ejpam-3003	162	3	t	t	NOUN
ejpam-3003	162	4	0	0	NUM
ejpam-3003	162	5	b1(u	b1(u	NOUN
ejpam-3003	162	6	,	,	PUNCT
ejpam-3003	162	7	v)ds+	v)ds+	ADJ
ejpam-3003	162	8	∫	∫	NOUN
ejpam-3003	162	9	t	t	PROPN
ejpam-3003	162	10	0	0	NUM
ejpam-3003	162	11	b2(u	b2(u	PROPN
ejpam-3003	162	12	,	,	PUNCT
ejpam-3003	163	1	v)ds	v)ds	PROPN
ejpam-3003	163	2	−	−	PROPN
ejpam-3003	163	3	∫	∫	PROPN
ejpam-3003	163	4	t	t	PROPN
ejpam-3003	163	5	0	0	NUM
ejpam-3003	163	6	(	(	PUNCT
ejpam-3003	163	7	|u|p−1u	|u|p−1u	INTJ
ejpam-3003	163	8	,	,	PUNCT
ejpam-3003	163	9	v)ds+	v)ds+	ADJ
ejpam-3003	163	10	∫	∫	NOUN
ejpam-3003	163	11	t	t	NOUN
ejpam-3003	163	12	0	0	NUM
ejpam-3003	163	13	(	(	PUNCT
ejpam-3003	163	14	|ut|q−1ut	|ut|q−1ut	PROPN
ejpam-3003	163	15	,	,	PUNCT
ejpam-3003	163	16	v)γ1ds	v)γ1ds	NOUN
ejpam-3003	163	17	=	=	SYM
ejpam-3003	163	18	1	1	NUM
ejpam-3003	163	19	ρ	ρ	NOUN
ejpam-3003	163	20	(	(	PUNCT
ejpam-3003	163	21	|u1|ρ−1u1	|u1|ρ−1u1	NOUN
ejpam-3003	163	22	,	,	PUNCT
ejpam-3003	163	23	v	v	NOUN
ejpam-3003	163	24	)	)	PUNCT
ejpam-3003	163	25	,	,	PUNCT
ejpam-3003	163	26	(	(	PUNCT
ejpam-3003	163	27	2.12	2.12	NUM
ejpam-3003	163	28	)	)	PUNCT
ejpam-3003	163	29	where	where	SCONJ
ejpam-3003	163	30	b1(u	b1(u	NOUN
ejpam-3003	163	31	,	,	PUNCT
ejpam-3003	163	32	v	v	NOUN
ejpam-3003	163	33	)	)	PUNCT
ejpam-3003	163	34	=	=	SYM
ejpam-3003	163	35	(	(	PUNCT
ejpam-3003	163	36	∇u,∇v	∇u,∇v	PROPN
ejpam-3003	163	37	)	)	PUNCT
ejpam-3003	163	38	,	,	PUNCT
ejpam-3003	163	39	b2(u	b2(u	PROPN
ejpam-3003	163	40	,	,	PUNCT
ejpam-3003	163	41	v	v	NOUN
ejpam-3003	163	42	)	)	PUNCT
ejpam-3003	163	43	=	=	SYM
ejpam-3003	164	1	−	−	PROPN
ejpam-3003	164	2	(	(	PUNCT
ejpam-3003	164	3	∫	∫	PROPN
ejpam-3003	164	4	s	s	PART
ejpam-3003	164	5	0	0	NUM
ejpam-3003	164	6	g(s−	g(s−	PROPN
ejpam-3003	164	7	τ)∇u(τ)dτ,∇v	τ)∇u(τ)dτ,∇v	PROPN
ejpam-3003	164	8	)	)	PUNCT
ejpam-3003	164	9	;	;	PUNCT
ejpam-3003	164	10	(	(	PUNCT
ejpam-3003	164	11	ii	ii	NOUN
ejpam-3003	164	12	)	)	PUNCT
ejpam-3003	164	13	u(x	u(x	NOUN
ejpam-3003	164	14	,	,	PUNCT
ejpam-3003	164	15	0	0	NUM
ejpam-3003	164	16	)	)	PUNCT
ejpam-3003	164	17	=	=	SYM
ejpam-3003	164	18	u0(x	u0(x	NOUN
ejpam-3003	164	19	)	)	PUNCT
ejpam-3003	164	20	in	in	ADP
ejpam-3003	164	21	h1	h1	PROPN
ejpam-3003	164	22	γ0	γ0	PROPN
ejpam-3003	164	23	(	(	PUNCT
ejpam-3003	164	24	ω	ω	NOUN
ejpam-3003	164	25	)	)	PUNCT
ejpam-3003	164	26	,	,	PUNCT
ejpam-3003	164	27	ut(x	ut(x	NOUN
ejpam-3003	164	28	,	,	PUNCT
ejpam-3003	164	29	0	0	NUM
ejpam-3003	164	30	)	)	PUNCT
ejpam-3003	164	31	=	=	SYM
ejpam-3003	165	1	u1(x	u1(x	NOUN
ejpam-3003	165	2	)	)	PUNCT
ejpam-3003	165	3	in	in	ADP
ejpam-3003	165	4	lρ+1(ω	lρ+1(ω	ADJ
ejpam-3003	165	5	)	)	PUNCT
ejpam-3003	165	6	∩	∩	NOUN
ejpam-3003	165	7	lq+1(γ1	lq+1(γ1	NOUN
ejpam-3003	165	8	)	)	PUNCT
ejpam-3003	165	9	.	.	PUNCT
ejpam-3003	166	1	(	(	PUNCT
ejpam-3003	166	2	iii	iii	X
ejpam-3003	166	3	)	)	PUNCT
ejpam-3003	166	4	the	the	DET
ejpam-3003	166	5	following	follow	VERB
ejpam-3003	166	6	energy	energy	NOUN
ejpam-3003	166	7	inequality	inequality	NOUN
ejpam-3003	166	8	holds	hold	VERB
ejpam-3003	166	9	e(t	e(t	NOUN
ejpam-3003	166	10	)	)	PUNCT
ejpam-3003	166	11	≤	≤	NOUN
ejpam-3003	166	12	e(0	e(0	NOUN
ejpam-3003	166	13	)	)	PUNCT
ejpam-3003	166	14	,	,	PUNCT
ejpam-3003	166	15	(	(	PUNCT
ejpam-3003	166	16	2.13	2.13	NUM
ejpam-3003	166	17	)	)	PUNCT
ejpam-3003	166	18	for	for	ADP
ejpam-3003	166	19	any	any	DET
ejpam-3003	166	20	0	0	NUM
ejpam-3003	166	21	≤	≤	NOUN
ejpam-3003	166	22	t	t	PROPN
ejpam-3003	166	23	<	<	X
ejpam-3003	166	24	t	t	PROPN
ejpam-3003	166	25	.	.	PUNCT
ejpam-3003	167	1	the	the	DET
ejpam-3003	167	2	following	follow	VERB
ejpam-3003	167	3	lemma	lemma	PROPN
ejpam-3003	167	4	is	be	AUX
ejpam-3003	167	5	similar	similar	ADJ
ejpam-3003	167	6	to	to	ADP
ejpam-3003	167	7	the	the	DET
ejpam-3003	167	8	lemmas	lemma	NOUN
ejpam-3003	167	9	of	of	ADP
ejpam-3003	167	10	[	[	X
ejpam-3003	167	11	28,29	28,29	X
ejpam-3003	167	12	]	]	PUNCT
ejpam-3003	167	13	with	with	ADP
ejpam-3003	167	14	slight	slight	ADJ
ejpam-3003	167	15	modification	modification	NOUN
ejpam-3003	167	16	.	.	PUNCT
ejpam-3003	168	1	lemma	lemma	PROPN
ejpam-3003	168	2	3	3	X
ejpam-3003	168	3	.	.	PUNCT
ejpam-3003	169	1	let	let	VERB
ejpam-3003	169	2	the	the	DET
ejpam-3003	169	3	assumptions	assumption	NOUN
ejpam-3003	169	4	(	(	PUNCT
ejpam-3003	169	5	a1	a1	NOUN
ejpam-3003	169	6	)	)	PUNCT
ejpam-3003	169	7	,	,	PUNCT
ejpam-3003	169	8	(	(	PUNCT
ejpam-3003	169	9	a3	a3	NOUN
ejpam-3003	169	10	)	)	PUNCT
ejpam-3003	169	11	hold	hold	VERB
ejpam-3003	169	12	and	and	CCONJ
ejpam-3003	169	13	u	u	PRON
ejpam-3003	169	14	be	be	VERB
ejpam-3003	169	15	a	a	DET
ejpam-3003	169	16	solution	solution	NOUN
ejpam-3003	169	17	of	of	ADP
ejpam-3003	169	18	problem	problem	NOUN
ejpam-3003	169	19	(	(	PUNCT
ejpam-3003	169	20	1.1	1.1	NUM
ejpam-3003	169	21	)	)	PUNCT
ejpam-3003	169	22	.	.	PUNCT
ejpam-3003	170	1	further	far	ADV
ejpam-3003	170	2	assume	assume	VERB
ejpam-3003	170	3	that	that	SCONJ
ejpam-3003	170	4	u0(x	u0(x	NOUN
ejpam-3003	170	5	)	)	PUNCT
ejpam-3003	170	6	∈	∈	PROPN
ejpam-3003	170	7	h1	h1	PROPN
ejpam-3003	170	8	γ0	γ0	PROPN
ejpam-3003	170	9	(	(	PUNCT
ejpam-3003	170	10	ω	ω	NOUN
ejpam-3003	170	11	)	)	PUNCT
ejpam-3003	170	12	,	,	PUNCT
ejpam-3003	170	13	u1(x	u1(x	NOUN
ejpam-3003	170	14	)	)	PUNCT
ejpam-3003	170	15	∈	∈	PROPN
ejpam-3003	170	16	lρ+1(ω	lρ+1(ω	X
ejpam-3003	170	17	)	)	PUNCT
ejpam-3003	170	18	∩	∩	NOUN
ejpam-3003	170	19	lq+1(γ1	lq+1(γ1	NOUN
ejpam-3003	170	20	)	)	PUNCT
ejpam-3003	170	21	,	,	PUNCT
ejpam-3003	170	22	we	we	PRON
ejpam-3003	170	23	have	have	VERB
ejpam-3003	170	24	(	(	PUNCT
ejpam-3003	170	25	1	1	X
ejpam-3003	170	26	)	)	PUNCT
ejpam-3003	170	27	if	if	SCONJ
ejpam-3003	170	28	e(0	e(0	NOUN
ejpam-3003	170	29	)	)	PUNCT
ejpam-3003	171	1	<	<	X
ejpam-3003	171	2	d̃	d̃	PROPN
ejpam-3003	171	3	,	,	PUNCT
ejpam-3003	171	4	i(u0	i(u0	PROPN
ejpam-3003	171	5	)	)	PUNCT
ejpam-3003	171	6	>	>	X
ejpam-3003	171	7	0	0	PUNCT
ejpam-3003	171	8	or	or	CCONJ
ejpam-3003	171	9	‖u0‖h1	‖u0‖h1	PROPN
ejpam-3003	171	10	γ0	γ0	NOUN
ejpam-3003	171	11	=	=	SYM
ejpam-3003	171	12	0	0	NUM
ejpam-3003	171	13	,	,	PUNCT
ejpam-3003	171	14	then	then	ADV
ejpam-3003	171	15	the	the	DET
ejpam-3003	171	16	solution	solution	NOUN
ejpam-3003	171	17	u(t	u(t	NOUN
ejpam-3003	171	18	)	)	PUNCT
ejpam-3003	171	19	∈w	∈w	NOUN
ejpam-3003	171	20	for	for	ADP
ejpam-3003	171	21	all	all	DET
ejpam-3003	171	22	t	t	NOUN
ejpam-3003	171	23	∈	∈	PROPN
ejpam-3003	172	1	[	[	X
ejpam-3003	172	2	0	0	NUM
ejpam-3003	172	3	,	,	PUNCT
ejpam-3003	172	4	t	t	PROPN
ejpam-3003	172	5	)	)	PUNCT
ejpam-3003	172	6	;	;	PUNCT
ejpam-3003	172	7	(	(	PUNCT
ejpam-3003	172	8	2	2	X
ejpam-3003	172	9	)	)	PUNCT
ejpam-3003	172	10	if	if	SCONJ
ejpam-3003	172	11	e(0	e(0	NOUN
ejpam-3003	172	12	)	)	PUNCT
ejpam-3003	172	13	<	<	X
ejpam-3003	172	14	d̃	d̃	PROPN
ejpam-3003	172	15	,	,	PUNCT
ejpam-3003	172	16	i(u0	i(u0	PROPN
ejpam-3003	172	17	)	)	PUNCT
ejpam-3003	172	18	<	<	X
ejpam-3003	172	19	0	0	NUM
ejpam-3003	172	20	,	,	PUNCT
ejpam-3003	172	21	then	then	ADV
ejpam-3003	172	22	the	the	DET
ejpam-3003	172	23	solution	solution	NOUN
ejpam-3003	172	24	u(t	u(t	NOUN
ejpam-3003	172	25	)	)	PUNCT
ejpam-3003	172	26	∈	∈	NOUN
ejpam-3003	172	27	v	v	NOUN
ejpam-3003	172	28	for	for	ADP
ejpam-3003	172	29	all	all	DET
ejpam-3003	172	30	t	t	NOUN
ejpam-3003	172	31	∈	∈	PROPN
ejpam-3003	173	1	[	[	X
ejpam-3003	173	2	0	0	NUM
ejpam-3003	173	3	,	,	PUNCT
ejpam-3003	173	4	t	t	NOUN
ejpam-3003	173	5	)	)	PUNCT
ejpam-3003	173	6	.	.	PUNCT
ejpam-3003	174	1	proof	proof	NOUN
ejpam-3003	174	2	.	.	PUNCT
ejpam-3003	175	1	(	(	PUNCT
ejpam-3003	175	2	1	1	X
ejpam-3003	175	3	)	)	PUNCT
ejpam-3003	175	4	let	let	VERB
ejpam-3003	175	5	u	u	PRON
ejpam-3003	175	6	be	be	AUX
ejpam-3003	175	7	any	any	DET
ejpam-3003	175	8	solution	solution	NOUN
ejpam-3003	175	9	of	of	ADP
ejpam-3003	175	10	problem	problem	NOUN
ejpam-3003	175	11	(	(	PUNCT
ejpam-3003	175	12	1.1	1.1	NUM
ejpam-3003	175	13	)	)	PUNCT
ejpam-3003	175	14	with	with	ADP
ejpam-3003	175	15	e(0	e(0	NOUN
ejpam-3003	175	16	)	)	PUNCT
ejpam-3003	175	17	<	<	X
ejpam-3003	175	18	d̃	d̃	PROPN
ejpam-3003	175	19	and	and	CCONJ
ejpam-3003	175	20	i(u0	i(u0	PROPN
ejpam-3003	175	21	)	)	PUNCT
ejpam-3003	175	22	>	>	X
ejpam-3003	175	23	0	0	PUNCT
ejpam-3003	176	1	or	or	CCONJ
ejpam-3003	176	2	‖u0‖h1	‖u0‖h1	PROPN
ejpam-3003	176	3	γ0	γ0	NOUN
ejpam-3003	176	4	=	=	SYM
ejpam-3003	176	5	0	0	X
ejpam-3003	176	6	.	.	PUNCT
ejpam-3003	177	1	if	if	SCONJ
ejpam-3003	177	2	‖u0‖h1	‖u0‖h1	PROPN
ejpam-3003	177	3	γ0	γ0	PROPN
ejpam-3003	177	4	=	=	SYM
ejpam-3003	177	5	0	0	NUM
ejpam-3003	177	6	,	,	PUNCT
ejpam-3003	177	7	then	then	ADV
ejpam-3003	177	8	u0(x	u0(x	NOUN
ejpam-3003	177	9	)	)	PUNCT
ejpam-3003	177	10	∈w	∈w	NOUN
ejpam-3003	177	11	.	.	PUNCT
ejpam-3003	178	1	if	if	SCONJ
ejpam-3003	178	2	i(u0	i(u0	PROPN
ejpam-3003	178	3	)	)	PUNCT
ejpam-3003	178	4	>	>	X
ejpam-3003	178	5	0	0	NUM
ejpam-3003	178	6	,	,	PUNCT
ejpam-3003	178	7	from	from	ADP
ejpam-3003	178	8	the	the	DET
ejpam-3003	178	9	inequality	inequality	NOUN
ejpam-3003	178	10	1	1	NUM
ejpam-3003	178	11	ρ+	ρ+	NUM
ejpam-3003	178	12	1	1	NUM
ejpam-3003	178	13	‖u1‖ρ+1	‖u1‖ρ+1	SYM
ejpam-3003	178	14	ρ+1	ρ+1	NOUN
ejpam-3003	178	15	+	+	NOUN
ejpam-3003	178	16	j(u0	j(u0	NOUN
ejpam-3003	178	17	)	)	PUNCT
ejpam-3003	178	18	=	=	SYM
ejpam-3003	179	1	e(0	e(0	NOUN
ejpam-3003	179	2	)	)	PUNCT
ejpam-3003	179	3	<	<	X
ejpam-3003	179	4	d̃	d̃	PROPN
ejpam-3003	179	5	,	,	PUNCT
ejpam-3003	179	6	(	(	PUNCT
ejpam-3003	179	7	2.14	2.14	NUM
ejpam-3003	179	8	)	)	PUNCT
ejpam-3003	179	9	we	we	PRON
ejpam-3003	179	10	have	have	VERB
ejpam-3003	179	11	u0(x	u0(x	NUM
ejpam-3003	179	12	)	)	PUNCT
ejpam-3003	179	13	∈w	∈w	NOUN
ejpam-3003	179	14	.	.	PUNCT
ejpam-3003	180	1	we	we	PRON
ejpam-3003	180	2	prove	prove	VERB
ejpam-3003	180	3	u(t	u(t	NOUN
ejpam-3003	180	4	)	)	PUNCT
ejpam-3003	180	5	∈w	∈w	NOUN
ejpam-3003	180	6	for	for	ADP
ejpam-3003	180	7	0	0	NUM
ejpam-3003	180	8	<	<	X
ejpam-3003	180	9	t	t	X
ejpam-3003	180	10	<	<	X
ejpam-3003	180	11	t	t	PROPN
ejpam-3003	180	12	.	.	PUNCT
ejpam-3003	181	1	arguing	argue	VERB
ejpam-3003	181	2	by	by	ADP
ejpam-3003	181	3	contradiction	contradiction	NOUN
ejpam-3003	181	4	and	and	CCONJ
ejpam-3003	181	5	considering	consider	VERB
ejpam-3003	181	6	the	the	DET
ejpam-3003	181	7	time	time	NOUN
ejpam-3003	181	8	continuity	continuity	NOUN
ejpam-3003	181	9	of	of	ADP
ejpam-3003	181	10	i(u	i(u	PROPN
ejpam-3003	181	11	)	)	PUNCT
ejpam-3003	181	12	,	,	PUNCT
ejpam-3003	181	13	we	we	PRON
ejpam-3003	181	14	suppose	suppose	VERB
ejpam-3003	181	15	that	that	SCONJ
ejpam-3003	181	16	there	there	PRON
ejpam-3003	181	17	exists	exist	VERB
ejpam-3003	181	18	a	a	DET
ejpam-3003	181	19	time	time	NOUN
ejpam-3003	181	20	t0	t0	X
ejpam-3003	181	21	∈	∈	PROPN
ejpam-3003	181	22	(	(	PUNCT
ejpam-3003	181	23	0	0	NUM
ejpam-3003	181	24	,	,	PUNCT
ejpam-3003	181	25	t	t	NOUN
ejpam-3003	181	26	)	)	PUNCT
ejpam-3003	181	27	such	such	ADJ
ejpam-3003	181	28	that	that	DET
ejpam-3003	181	29	u(t0	u(t0	NOUN
ejpam-3003	181	30	)	)	PUNCT
ejpam-3003	181	31	∈	∈	PROPN
ejpam-3003	181	32	∂w	∂w	PROPN
ejpam-3003	181	33	,	,	PUNCT
ejpam-3003	181	34	which	which	PRON
ejpam-3003	181	35	means	mean	VERB
ejpam-3003	181	36	that	that	SCONJ
ejpam-3003	181	37	i(u(t0	i(u(t0	NOUN
ejpam-3003	181	38	)	)	PUNCT
ejpam-3003	181	39	)	)	PUNCT
ejpam-3003	182	1	=	=	SYM
ejpam-3003	182	2	0	0	NUM
ejpam-3003	182	3	,	,	PUNCT
ejpam-3003	182	4	‖u(t0)‖h1	‖u(t0)‖h1	PROPN
ejpam-3003	182	5	γ0	γ0	PROPN
ejpam-3003	182	6	6=	6=	PRON
ejpam-3003	182	7	0	0	NUM
ejpam-3003	182	8	or	or	CCONJ
ejpam-3003	182	9	j(u(t0	j(u(t0	PROPN
ejpam-3003	182	10	)	)	PUNCT
ejpam-3003	182	11	)	)	PUNCT
ejpam-3003	183	1	=	=	PUNCT
ejpam-3003	183	2	d̃.	d̃.	VERB
ejpam-3003	183	3	from	from	ADP
ejpam-3003	183	4	(	(	PUNCT
ejpam-3003	183	5	2.13	2.13	NUM
ejpam-3003	183	6	)	)	PUNCT
ejpam-3003	183	7	,	,	PUNCT
ejpam-3003	183	8	it	it	PRON
ejpam-3003	183	9	follows	follow	VERB
ejpam-3003	183	10	that	that	SCONJ
ejpam-3003	183	11	1	1	NUM
ejpam-3003	183	12	ρ+	ρ+	NUM
ejpam-3003	183	13	1	1	NUM
ejpam-3003	183	14	‖ut‖ρ+1	‖ut‖ρ+1	SYM
ejpam-3003	183	15	ρ+1	ρ+1	ADJ
ejpam-3003	183	16	+	+	CCONJ
ejpam-3003	183	17	j(u	j(u	NOUN
ejpam-3003	183	18	)	)	PUNCT
ejpam-3003	183	19	≤	≤	NOUN
ejpam-3003	183	20	e(0	e(0	NOUN
ejpam-3003	183	21	)	)	PUNCT
ejpam-3003	183	22	<	<	X
ejpam-3003	183	23	d̃	d̃	PROPN
ejpam-3003	183	24	,	,	PUNCT
ejpam-3003	183	25	0	0	NUM
ejpam-3003	183	26	<	<	X
ejpam-3003	183	27	t	t	X
ejpam-3003	183	28	<	<	X
ejpam-3003	183	29	t.	t.	PROPN
ejpam-3003	183	30	(	(	PUNCT
ejpam-3003	183	31	2.15	2.15	NUM
ejpam-3003	183	32	)	)	PUNCT
ejpam-3003	183	33	h.f	h.f	PROPN
ejpam-3003	183	34	.	.	PROPN
ejpam-3003	183	35	di	di	PROPN
ejpam-3003	183	36	,	,	PUNCT
ejpam-3003	183	37	y.d	y.d	PROPN
ejpam-3003	183	38	.	.	PROPN
ejpam-3003	183	39	shang	shang	PROPN
ejpam-3003	183	40	/	/	SYM
ejpam-3003	183	41	eur	eur	PROPN
ejpam-3003	183	42	.	.	PUNCT
ejpam-3003	184	1	j.	j.	PROPN
ejpam-3003	184	2	pure	pure	PROPN
ejpam-3003	184	3	appl	appl	PROPN
ejpam-3003	184	4	.	.	PROPN
ejpam-3003	184	5	math	math	PROPN
ejpam-3003	184	6	,	,	PUNCT
ejpam-3003	184	7	10	10	NUM
ejpam-3003	184	8	(	(	PUNCT
ejpam-3003	184	9	4	4	NUM
ejpam-3003	184	10	)	)	PUNCT
ejpam-3003	184	11	(	(	PUNCT
ejpam-3003	184	12	2017	2017	NUM
ejpam-3003	184	13	)	)	PUNCT
ejpam-3003	184	14	,	,	PUNCT
ejpam-3003	184	15	668	668	NUM
ejpam-3003	184	16	-	-	SYM
ejpam-3003	184	17	701	701	NUM
ejpam-3003	184	18	676	676	NUM
ejpam-3003	184	19	thus	thus	ADV
ejpam-3003	184	20	,	,	PUNCT
ejpam-3003	184	21	we	we	PRON
ejpam-3003	184	22	see	see	VERB
ejpam-3003	184	23	that	that	SCONJ
ejpam-3003	184	24	j(u(t0	j(u(t0	PROPN
ejpam-3003	184	25	)	)	PUNCT
ejpam-3003	184	26	)	)	PUNCT
ejpam-3003	185	1	6=	6=	NUM
ejpam-3003	185	2	d̃.	d̃.	VERB
ejpam-3003	185	3	if	if	SCONJ
ejpam-3003	185	4	i(u(t0	i(u(t0	NOUN
ejpam-3003	185	5	)	)	PUNCT
ejpam-3003	185	6	)	)	PUNCT
ejpam-3003	186	1	=	=	SYM
ejpam-3003	186	2	0	0	NUM
ejpam-3003	186	3	,	,	PUNCT
ejpam-3003	186	4	‖u(t0)‖h1	‖u(t0)‖h1	PROPN
ejpam-3003	186	5	γ0	γ0	PROPN
ejpam-3003	186	6	6=	6=	ADP
ejpam-3003	186	7	0	0	NUM
ejpam-3003	186	8	,	,	PUNCT
ejpam-3003	186	9	then	then	ADV
ejpam-3003	186	10	by	by	ADP
ejpam-3003	186	11	the	the	DET
ejpam-3003	186	12	definition	definition	NOUN
ejpam-3003	186	13	of	of	ADP
ejpam-3003	186	14	d	d	X
ejpam-3003	186	15	we	we	PRON
ejpam-3003	186	16	have	have	VERB
ejpam-3003	186	17	j(u(t0	j(u(t0	PROPN
ejpam-3003	186	18	)	)	PUNCT
ejpam-3003	186	19	)	)	PUNCT
ejpam-3003	187	1	≥	≥	X
ejpam-3003	188	1	d	d	X
ejpam-3003	188	2	which	which	PRON
ejpam-3003	188	3	contradicts	contradict	VERB
ejpam-3003	188	4	(	(	PUNCT
ejpam-3003	188	5	2.15	2.15	NUM
ejpam-3003	188	6	)	)	PUNCT
ejpam-3003	188	7	.	.	PUNCT
ejpam-3003	189	1	the	the	DET
ejpam-3003	189	2	proof	proof	NOUN
ejpam-3003	189	3	of	of	ADP
ejpam-3003	189	4	(	(	PUNCT
ejpam-3003	189	5	1	1	X
ejpam-3003	189	6	)	)	PUNCT
ejpam-3003	189	7	is	be	AUX
ejpam-3003	189	8	completed	complete	VERB
ejpam-3003	189	9	.	.	PUNCT
ejpam-3003	190	1	(	(	PUNCT
ejpam-3003	190	2	2	2	X
ejpam-3003	190	3	)	)	PUNCT
ejpam-3003	190	4	let	let	AUX
ejpam-3003	190	5	u(t	u(t	NOUN
ejpam-3003	190	6	)	)	PUNCT
ejpam-3003	190	7	be	be	VERB
ejpam-3003	190	8	any	any	DET
ejpam-3003	190	9	solution	solution	NOUN
ejpam-3003	190	10	of	of	ADP
ejpam-3003	190	11	problem	problem	NOUN
ejpam-3003	190	12	(	(	PUNCT
ejpam-3003	190	13	1.1	1.1	NUM
ejpam-3003	190	14	)	)	PUNCT
ejpam-3003	190	15	with	with	ADP
ejpam-3003	190	16	e(0	e(0	NOUN
ejpam-3003	190	17	)	)	PUNCT
ejpam-3003	190	18	<	<	X
ejpam-3003	191	1	d̃	d̃	PROPN
ejpam-3003	191	2	and	and	CCONJ
ejpam-3003	191	3	i(u0	i(u0	PROPN
ejpam-3003	191	4	)	)	PUNCT
ejpam-3003	191	5	<	<	X
ejpam-3003	191	6	0	0	X
ejpam-3003	191	7	.	.	PUNCT
ejpam-3003	191	8	from	from	ADP
ejpam-3003	191	9	(	(	PUNCT
ejpam-3003	191	10	2.11	2.11	NUM
ejpam-3003	191	11	)	)	PUNCT
ejpam-3003	191	12	we	we	PRON
ejpam-3003	191	13	get	get	VERB
ejpam-3003	191	14	that	that	PRON
ejpam-3003	191	15	u0(x	u0(x	NOUN
ejpam-3003	191	16	)	)	PUNCT
ejpam-3003	191	17	∈	∈	NOUN
ejpam-3003	191	18	v	v	NOUN
ejpam-3003	191	19	.	.	PUNCT
ejpam-3003	192	1	we	we	PRON
ejpam-3003	192	2	prove	prove	VERB
ejpam-3003	192	3	u(t	u(t	NOUN
ejpam-3003	192	4	)	)	PUNCT
ejpam-3003	192	5	∈	∈	NOUN
ejpam-3003	192	6	v	v	NOUN
ejpam-3003	192	7	for	for	ADP
ejpam-3003	192	8	0	0	NUM
ejpam-3003	192	9	<	<	X
ejpam-3003	192	10	t	t	X
ejpam-3003	192	11	<	<	X
ejpam-3003	192	12	t	t	PROPN
ejpam-3003	192	13	.	.	PUNCT
ejpam-3003	193	1	arguing	argue	VERB
ejpam-3003	193	2	by	by	ADP
ejpam-3003	193	3	contradiction	contradiction	NOUN
ejpam-3003	193	4	,	,	PUNCT
ejpam-3003	193	5	we	we	PRON
ejpam-3003	193	6	suppose	suppose	VERB
ejpam-3003	193	7	that	that	SCONJ
ejpam-3003	193	8	there	there	PRON
ejpam-3003	193	9	exists	exist	VERB
ejpam-3003	193	10	a	a	DET
ejpam-3003	193	11	time	time	NOUN
ejpam-3003	193	12	t0	t0	X
ejpam-3003	193	13	∈	∈	PROPN
ejpam-3003	193	14	(	(	PUNCT
ejpam-3003	193	15	0	0	NUM
ejpam-3003	193	16	,	,	PUNCT
ejpam-3003	193	17	t	t	NOUN
ejpam-3003	193	18	)	)	PUNCT
ejpam-3003	193	19	such	such	ADJ
ejpam-3003	193	20	that	that	DET
ejpam-3003	193	21	u(t0	u(t0	NOUN
ejpam-3003	193	22	)	)	PUNCT
ejpam-3003	193	23	∈	∈	PROPN
ejpam-3003	193	24	∂v	∂v	PROPN
ejpam-3003	193	25	which	which	PRON
ejpam-3003	193	26	means	mean	VERB
ejpam-3003	193	27	that	that	SCONJ
ejpam-3003	193	28	i(u(t0	i(u(t0	NOUN
ejpam-3003	193	29	)	)	PUNCT
ejpam-3003	193	30	)	)	PUNCT
ejpam-3003	194	1	=	=	SYM
ejpam-3003	194	2	0	0	NUM
ejpam-3003	194	3	or	or	CCONJ
ejpam-3003	194	4	j(u(t0	j(u(t0	PROPN
ejpam-3003	194	5	)	)	PUNCT
ejpam-3003	194	6	)	)	PUNCT
ejpam-3003	195	1	=	=	PUNCT
ejpam-3003	195	2	d̃.	d̃.	VERB
ejpam-3003	195	3	again	again	ADV
ejpam-3003	195	4	(	(	PUNCT
ejpam-3003	195	5	2.15	2.15	NUM
ejpam-3003	195	6	)	)	PUNCT
ejpam-3003	195	7	shows	show	VERB
ejpam-3003	195	8	that	that	SCONJ
ejpam-3003	195	9	j(u(t0	j(u(t0	PROPN
ejpam-3003	195	10	)	)	PUNCT
ejpam-3003	195	11	)	)	PUNCT
ejpam-3003	196	1	6=	6=	NUM
ejpam-3003	196	2	d̃.	d̃.	VERB
ejpam-3003	196	3	if	if	SCONJ
ejpam-3003	196	4	i(u(t0	i(u(t0	NOUN
ejpam-3003	196	5	)	)	PUNCT
ejpam-3003	196	6	)	)	PUNCT
ejpam-3003	197	1	=	=	PUNCT
ejpam-3003	197	2	0	0	NUM
ejpam-3003	197	3	,	,	PUNCT
ejpam-3003	197	4	then	then	ADV
ejpam-3003	197	5	by	by	ADP
ejpam-3003	197	6	the	the	DET
ejpam-3003	197	7	definition	definition	NOUN
ejpam-3003	197	8	of	of	ADP
ejpam-3003	197	9	d	d	X
ejpam-3003	197	10	we	we	PRON
ejpam-3003	197	11	have	have	VERB
ejpam-3003	197	12	j(u(t0	j(u(t0	PROPN
ejpam-3003	197	13	)	)	PUNCT
ejpam-3003	197	14	)	)	PUNCT
ejpam-3003	198	1	≥	≥	X
ejpam-3003	199	1	d	d	X
ejpam-3003	199	2	which	which	PRON
ejpam-3003	199	3	contradicts	contradict	VERB
ejpam-3003	199	4	(	(	PUNCT
ejpam-3003	199	5	2.15	2.15	NUM
ejpam-3003	199	6	)	)	PUNCT
ejpam-3003	199	7	.	.	PUNCT
ejpam-3003	200	1	lemma	lemma	PROPN
ejpam-3003	200	2	4	4	X
ejpam-3003	200	3	.	.	PUNCT
ejpam-3003	201	1	let	let	VERB
ejpam-3003	201	2	the	the	DET
ejpam-3003	201	3	assumptions	assumption	NOUN
ejpam-3003	201	4	(	(	PUNCT
ejpam-3003	201	5	a1	a1	NOUN
ejpam-3003	201	6	)	)	PUNCT
ejpam-3003	201	7	,	,	PUNCT
ejpam-3003	201	8	(	(	PUNCT
ejpam-3003	201	9	a3	a3	NOUN
ejpam-3003	201	10	)	)	PUNCT
ejpam-3003	201	11	hold	hold	VERB
ejpam-3003	201	12	.	.	PUNCT
ejpam-3003	202	1	for	for	ADP
ejpam-3003	202	2	any	any	DET
ejpam-3003	202	3	fixed	fix	VERB
ejpam-3003	202	4	positive	positive	ADJ
ejpam-3003	202	5	number	number	NOUN
ejpam-3003	202	6	β	β	X
ejpam-3003	202	7	<	<	X
ejpam-3003	202	8	1	1	NUM
ejpam-3003	202	9	,	,	PUNCT
ejpam-3003	202	10	assume	assume	VERB
ejpam-3003	202	11	that	that	SCONJ
ejpam-3003	202	12	i(u0	i(u0	NOUN
ejpam-3003	202	13	)	)	PUNCT
ejpam-3003	202	14	<	<	X
ejpam-3003	202	15	0	0	NUM
ejpam-3003	202	16	,	,	PUNCT
ejpam-3003	202	17	e(0	e(0	NOUN
ejpam-3003	202	18	)	)	PUNCT
ejpam-3003	202	19	<	<	X
ejpam-3003	202	20	βd̃	βd̃	PROPN
ejpam-3003	202	21	,	,	PUNCT
ejpam-3003	202	22	then	then	ADV
ejpam-3003	202	23	we	we	PRON
ejpam-3003	202	24	have	have	AUX
ejpam-3003	202	25	i(u(t	i(u(t	VERB
ejpam-3003	202	26	)	)	PUNCT
ejpam-3003	202	27	)	)	PUNCT
ejpam-3003	203	1	<	<	X
ejpam-3003	203	2	0	0	PUNCT
ejpam-3003	204	1	for	for	ADP
ejpam-3003	204	2	all	all	DET
ejpam-3003	204	3	t	t	NOUN
ejpam-3003	204	4	∈	∈	PROPN
ejpam-3003	205	1	[	[	X
ejpam-3003	205	2	0	0	NUM
ejpam-3003	205	3	,	,	PUNCT
ejpam-3003	205	4	t	t	NOUN
ejpam-3003	205	5	)	)	PUNCT
ejpam-3003	205	6	and	and	CCONJ
ejpam-3003	205	7	d̃	d̃	PROPN
ejpam-3003	205	8	<	<	X
ejpam-3003	205	9	p−	p−	NOUN
ejpam-3003	205	10	1	1	NUM
ejpam-3003	205	11	2(p+	2(p+	NUM
ejpam-3003	205	12	1	1	NUM
ejpam-3003	205	13	)	)	PUNCT
ejpam-3003	206	1	[	[	X
ejpam-3003	206	2	l(t)‖∇u‖22	l(t)‖∇u‖22	X
ejpam-3003	206	3	+	+	CCONJ
ejpam-3003	206	4	(	(	PUNCT
ejpam-3003	206	5	g	g	PROPN
ejpam-3003	206	6	◦	◦	PROPN
ejpam-3003	206	7	∇u)(t	∇u)(t	PROPN
ejpam-3003	206	8	)	)	PUNCT
ejpam-3003	206	9	]	]	PUNCT
ejpam-3003	207	1	<	<	X
ejpam-3003	207	2	p−	p−	PROPN
ejpam-3003	207	3	1	1	NUM
ejpam-3003	207	4	2(p+	2(p+	NUM
ejpam-3003	207	5	1	1	NUM
ejpam-3003	207	6	)	)	PUNCT
ejpam-3003	207	7	‖u‖p+1	‖u‖p+1	PROPN
ejpam-3003	207	8	p+1	p+1	NOUN
ejpam-3003	207	9	.	.	PUNCT
ejpam-3003	208	1	(	(	PUNCT
ejpam-3003	208	2	2.16	2.16	NUM
ejpam-3003	208	3	)	)	PUNCT
ejpam-3003	208	4	proof	proof	NOUN
ejpam-3003	208	5	.	.	PUNCT
ejpam-3003	209	1	arguing	argue	VERB
ejpam-3003	209	2	by	by	ADP
ejpam-3003	209	3	contradiction	contradiction	NOUN
ejpam-3003	209	4	,	,	PUNCT
ejpam-3003	209	5	we	we	PRON
ejpam-3003	209	6	can	can	AUX
ejpam-3003	209	7	get	get	VERB
ejpam-3003	209	8	i(u(t	i(u(t	NOUN
ejpam-3003	209	9	)	)	PUNCT
ejpam-3003	209	10	)	)	PUNCT
ejpam-3003	210	1	<	<	X
ejpam-3003	210	2	0	0	PUNCT
ejpam-3003	211	1	for	for	ADP
ejpam-3003	211	2	all	all	DET
ejpam-3003	211	3	t	t	NOUN
ejpam-3003	211	4	∈	∈	PROPN
ejpam-3003	212	1	[	[	X
ejpam-3003	212	2	0	0	NUM
ejpam-3003	212	3	,	,	PUNCT
ejpam-3003	212	4	t	t	NOUN
ejpam-3003	212	5	)	)	PUNCT
ejpam-3003	212	6	.	.	PUNCT
ejpam-3003	213	1	in	in	ADP
ejpam-3003	213	2	fact	fact	NOUN
ejpam-3003	213	3	,	,	PUNCT
ejpam-3003	213	4	suppose	suppose	VERB
ejpam-3003	213	5	this	this	PRON
ejpam-3003	213	6	is	be	AUX
ejpam-3003	213	7	not	not	PART
ejpam-3003	213	8	true	true	ADJ
ejpam-3003	213	9	,	,	PUNCT
ejpam-3003	213	10	then	then	ADV
ejpam-3003	213	11	there	there	PRON
ejpam-3003	213	12	exist	exist	VERB
ejpam-3003	213	13	some	some	DET
ejpam-3003	213	14	t0	t0	PROPN
ejpam-3003	213	15	∈	∈	PROPN
ejpam-3003	214	1	[	[	X
ejpam-3003	214	2	0	0	NUM
ejpam-3003	214	3	,	,	PUNCT
ejpam-3003	214	4	t	t	NOUN
ejpam-3003	214	5	)	)	PUNCT
ejpam-3003	214	6	such	such	ADJ
ejpam-3003	214	7	that	that	DET
ejpam-3003	214	8	i(u(t0	i(u(t0	NOUN
ejpam-3003	214	9	)	)	PUNCT
ejpam-3003	214	10	)	)	PUNCT
ejpam-3003	215	1	=	=	SYM
ejpam-3003	215	2	0	0	NUM
ejpam-3003	215	3	and	and	CCONJ
ejpam-3003	215	4	i(u(t	i(u(t	NOUN
ejpam-3003	215	5	)	)	PUNCT
ejpam-3003	215	6	)	)	PUNCT
ejpam-3003	216	1	<	<	X
ejpam-3003	216	2	0	0	PUNCT
ejpam-3003	217	1	for	for	ADP
ejpam-3003	217	2	0	0	NUM
ejpam-3003	217	3	≤	≤	NOUN
ejpam-3003	217	4	t	t	PROPN
ejpam-3003	217	5	<	<	X
ejpam-3003	217	6	t0	t0	PROPN
ejpam-3003	217	7	.	.	PUNCT
ejpam-3003	218	1	hence	hence	ADV
ejpam-3003	218	2	,	,	PUNCT
ejpam-3003	218	3	l(t)‖∇u‖22	l(t)‖∇u‖22	PUNCT
ejpam-3003	219	1	+	+	CCONJ
ejpam-3003	219	2	(	(	PUNCT
ejpam-3003	219	3	g	g	PROPN
ejpam-3003	219	4	◦	◦	PROPN
ejpam-3003	219	5	∇u)(t	∇u)(t	PROPN
ejpam-3003	219	6	)	)	PUNCT
ejpam-3003	220	1	<	<	X
ejpam-3003	220	2	‖u‖p+1	‖u‖p+1	PROPN
ejpam-3003	220	3	p+1	p+1	NOUN
ejpam-3003	220	4	,	,	PUNCT
ejpam-3003	220	5	0	0	NUM
ejpam-3003	220	6	≤	≤	NUM
ejpam-3003	220	7	t	t	X
ejpam-3003	220	8	<	<	X
ejpam-3003	220	9	t0	t0	PROPN
ejpam-3003	220	10	.	.	PUNCT
ejpam-3003	221	1	(	(	PUNCT
ejpam-3003	221	2	2.17	2.17	NUM
ejpam-3003	221	3	)	)	PUNCT
ejpam-3003	221	4	from	from	ADP
ejpam-3003	221	5	the	the	DET
ejpam-3003	221	6	definition	definition	NOUN
ejpam-3003	221	7	of	of	ADP
ejpam-3003	221	8	d̃	d̃	PROPN
ejpam-3003	221	9	,	,	PUNCT
ejpam-3003	221	10	it	it	PRON
ejpam-3003	221	11	follows	follow	VERB
ejpam-3003	221	12	that	that	SCONJ
ejpam-3003	221	13	d̃	d̃	PROPN
ejpam-3003	221	14	=	=	PUNCT
ejpam-3003	222	1	p−	p−	NOUN
ejpam-3003	222	2	1	1	NUM
ejpam-3003	222	3	2(p+	2(p+	NUM
ejpam-3003	222	4	1	1	NUM
ejpam-3003	222	5	)	)	PUNCT
ejpam-3003	222	6	(	(	PUNCT
ejpam-3003	222	7	b	b	X
ejpam-3003	222	8	b2	b2	NOUN
ejpam-3003	222	9	p+1	p+1	NOUN
ejpam-3003	222	10	)	)	PUNCT
ejpam-3003	223	1	p+1	p+1	PROPN
ejpam-3003	223	2	p−1	p−1	NOUN
ejpam-3003	223	3	≤	≤	NUM
ejpam-3003	223	4	p−	p−	NOUN
ejpam-3003	223	5	1	1	NUM
ejpam-3003	223	6	2(p+	2(p+	NUM
ejpam-3003	223	7	1	1	NUM
ejpam-3003	223	8	)	)	PUNCT
ejpam-3003	223	9	{	{	PUNCT
ejpam-3003	223	10	l(t)‖∇u‖22	l(t)‖∇u‖22	PUNCT
ejpam-3003	224	1	+	+	CCONJ
ejpam-3003	224	2	(	(	PUNCT
ejpam-3003	224	3	g	g	PROPN
ejpam-3003	224	4	◦	◦	PROPN
ejpam-3003	224	5	∇u)(t	∇u)(t	PROPN
ejpam-3003	224	6	)	)	PUNCT
ejpam-3003	224	7	‖u‖2p+1	‖u‖2p+1	NUM
ejpam-3003	224	8	}	}	PUNCT
ejpam-3003	225	1	p+1	p+1	NOUN
ejpam-3003	226	1	p−1	p−1	NOUN
ejpam-3003	226	2	<	<	X
ejpam-3003	226	3	p−	p−	PROPN
ejpam-3003	226	4	1	1	NUM
ejpam-3003	226	5	2(p+	2(p+	NUM
ejpam-3003	226	6	1	1	NUM
ejpam-3003	226	7	)	)	PUNCT
ejpam-3003	226	8	{	{	PUNCT
ejpam-3003	226	9	l(t)‖∇u‖22	l(t)‖∇u‖22	PUNCT
ejpam-3003	227	1	+	+	CCONJ
ejpam-3003	227	2	(	(	PUNCT
ejpam-3003	227	3	g	g	PROPN
ejpam-3003	227	4	◦	◦	PROPN
ejpam-3003	227	5	∇u)(t	∇u)(t	PROPN
ejpam-3003	227	6	)	)	PUNCT
ejpam-3003	227	7	(	(	PUNCT
ejpam-3003	227	8	l(t)‖∇u‖22	l(t)‖∇u‖22	X
ejpam-3003	227	9	+	+	CCONJ
ejpam-3003	227	10	(	(	PUNCT
ejpam-3003	227	11	g	g	PROPN
ejpam-3003	227	12	◦	◦	PROPN
ejpam-3003	227	13	∇u)(t	∇u)(t	PROPN
ejpam-3003	227	14	)	)	PUNCT
ejpam-3003	227	15	)	)	PUNCT
ejpam-3003	227	16	2	2	NUM
ejpam-3003	227	17	p+1	p+1	NOUN
ejpam-3003	227	18	}	}	PUNCT
ejpam-3003	227	19	p+1	p+1	NOUN
ejpam-3003	227	20	p−1	p−1	NOUN
ejpam-3003	227	21	=	=	PUNCT
ejpam-3003	228	1	p−	p−	NOUN
ejpam-3003	228	2	1	1	NUM
ejpam-3003	228	3	2(p+	2(p+	NUM
ejpam-3003	228	4	1	1	NUM
ejpam-3003	228	5	)	)	PUNCT
ejpam-3003	229	1	[	[	X
ejpam-3003	229	2	l(t)‖∇u‖22	l(t)‖∇u‖22	X
ejpam-3003	229	3	+	+	CCONJ
ejpam-3003	229	4	(	(	PUNCT
ejpam-3003	229	5	g	g	PROPN
ejpam-3003	229	6	◦	◦	PROPN
ejpam-3003	229	7	∇u)(t	∇u)(t	PROPN
ejpam-3003	229	8	)	)	PUNCT
ejpam-3003	229	9	]	]	PUNCT
ejpam-3003	229	10	,	,	PUNCT
ejpam-3003	229	11	0	0	NUM
ejpam-3003	229	12	≤	≤	NUM
ejpam-3003	229	13	t	t	X
ejpam-3003	229	14	<	<	X
ejpam-3003	229	15	t0	t0	PROPN
ejpam-3003	229	16	.	.	PUNCT
ejpam-3003	230	1	(	(	PUNCT
ejpam-3003	230	2	2.18	2.18	NUM
ejpam-3003	230	3	)	)	PUNCT
ejpam-3003	230	4	we	we	PRON
ejpam-3003	230	5	deduce	deduce	VERB
ejpam-3003	230	6	from	from	ADP
ejpam-3003	230	7	(	(	PUNCT
ejpam-3003	230	8	2.17	2.17	NUM
ejpam-3003	230	9	)	)	PUNCT
ejpam-3003	230	10	and	and	CCONJ
ejpam-3003	230	11	(	(	PUNCT
ejpam-3003	230	12	2.18	2.18	NUM
ejpam-3003	230	13	)	)	PUNCT
ejpam-3003	230	14	that	that	PRON
ejpam-3003	230	15	‖u‖p+1	‖u‖p+1	VERB
ejpam-3003	231	1	p+1	p+1	NOUN
ejpam-3003	231	2	>	>	X
ejpam-3003	232	1	2(p+	2(p+	NUM
ejpam-3003	232	2	1	1	NUM
ejpam-3003	232	3	)	)	PUNCT
ejpam-3003	232	4	p−	p−	NOUN
ejpam-3003	232	5	1	1	NUM
ejpam-3003	232	6	d̃	d̃	PROPN
ejpam-3003	232	7	>	>	PUNCT
ejpam-3003	232	8	0	0	NUM
ejpam-3003	232	9	,	,	PUNCT
ejpam-3003	232	10	0	0	NUM
ejpam-3003	232	11	≤	≤	NUM
ejpam-3003	232	12	t	t	X
ejpam-3003	232	13	<	<	X
ejpam-3003	232	14	t0	t0	PROPN
ejpam-3003	232	15	.	.	PUNCT
ejpam-3003	233	1	(	(	PUNCT
ejpam-3003	233	2	2.19	2.19	NUM
ejpam-3003	233	3	)	)	PUNCT
ejpam-3003	233	4	since	since	SCONJ
ejpam-3003	233	5	t→	t→	X
ejpam-3003	233	6	‖u(t)‖p+1	‖u(t)‖p+1	PROPN
ejpam-3003	233	7	p+1	p+1	NOUN
ejpam-3003	233	8	is	be	AUX
ejpam-3003	233	9	continuous	continuous	ADJ
ejpam-3003	233	10	,	,	PUNCT
ejpam-3003	233	11	from	from	ADP
ejpam-3003	233	12	(	(	PUNCT
ejpam-3003	233	13	2.19	2.19	NUM
ejpam-3003	233	14	)	)	PUNCT
ejpam-3003	233	15	we	we	PRON
ejpam-3003	233	16	have	have	VERB
ejpam-3003	233	17	d̃	d̃	PROPN
ejpam-3003	233	18	≤	≤	NUM
ejpam-3003	233	19	p−	p−	NOUN
ejpam-3003	233	20	1	1	NUM
ejpam-3003	233	21	2(p+	2(p+	NUM
ejpam-3003	233	22	1	1	NUM
ejpam-3003	233	23	)	)	PUNCT
ejpam-3003	233	24	‖u(t0)‖p+1	‖u(t0)‖p+1	NOUN
ejpam-3003	233	25	p+1	p+1	NOUN
ejpam-3003	233	26	=	=	PUNCT
ejpam-3003	233	27	j(u(t0	j(u(t0	PROPN
ejpam-3003	233	28	)	)	PUNCT
ejpam-3003	233	29	)	)	PUNCT
ejpam-3003	233	30	.	.	PUNCT
ejpam-3003	234	1	(	(	PUNCT
ejpam-3003	234	2	2.20	2.20	NUM
ejpam-3003	234	3	)	)	PUNCT
ejpam-3003	234	4	this	this	PRON
ejpam-3003	234	5	is	be	AUX
ejpam-3003	234	6	impossible	impossible	ADJ
ejpam-3003	234	7	since	since	SCONJ
ejpam-3003	234	8	j(u(t0	j(u(t0	PROPN
ejpam-3003	234	9	)	)	PUNCT
ejpam-3003	234	10	)	)	PUNCT
ejpam-3003	235	1	≤	≤	NUM
ejpam-3003	235	2	e(t0	e(t0	NOUN
ejpam-3003	235	3	)	)	PUNCT
ejpam-3003	235	4	≤	≤	NOUN
ejpam-3003	235	5	e(0	e(0	NOUN
ejpam-3003	235	6	)	)	PUNCT
ejpam-3003	235	7	<	<	X
ejpam-3003	236	1	d̃.	d̃.	PROPN
ejpam-3003	236	2	hence	hence	ADV
ejpam-3003	236	3	,	,	PUNCT
ejpam-3003	236	4	we	we	PRON
ejpam-3003	236	5	obtain	obtain	VERB
ejpam-3003	236	6	i(u(t	i(u(t	NOUN
ejpam-3003	236	7	)	)	PUNCT
ejpam-3003	236	8	)	)	PUNCT
ejpam-3003	237	1	<	<	X
ejpam-3003	237	2	0	0	PUNCT
ejpam-3003	238	1	for	for	ADP
ejpam-3003	238	2	all	all	DET
ejpam-3003	238	3	t	t	NOUN
ejpam-3003	238	4	∈	∈	PROPN
ejpam-3003	239	1	[	[	X
ejpam-3003	239	2	0	0	NUM
ejpam-3003	239	3	,	,	PUNCT
ejpam-3003	239	4	t	t	NOUN
ejpam-3003	239	5	)	)	PUNCT
ejpam-3003	239	6	.	.	PUNCT
ejpam-3003	240	1	furthermore	furthermore	ADV
ejpam-3003	240	2	,	,	PUNCT
ejpam-3003	240	3	from	from	ADP
ejpam-3003	240	4	(	(	PUNCT
ejpam-3003	240	5	2.18	2.18	NUM
ejpam-3003	240	6	)	)	PUNCT
ejpam-3003	240	7	again	again	ADV
ejpam-3003	240	8	,	,	PUNCT
ejpam-3003	240	9	we	we	PRON
ejpam-3003	240	10	have	have	VERB
ejpam-3003	240	11	d̃	d̃	PROPN
ejpam-3003	240	12	<	<	X
ejpam-3003	240	13	p−	p−	PROPN
ejpam-3003	240	14	1	1	NUM
ejpam-3003	240	15	2(p+	2(p+	NUM
ejpam-3003	240	16	1	1	NUM
ejpam-3003	240	17	)	)	PUNCT
ejpam-3003	241	1	[	[	X
ejpam-3003	241	2	l(t)‖∇u‖22	l(t)‖∇u‖22	X
ejpam-3003	241	3	+	+	CCONJ
ejpam-3003	241	4	(	(	PUNCT
ejpam-3003	241	5	g	g	PROPN
ejpam-3003	241	6	◦	◦	PROPN
ejpam-3003	241	7	∇u)(t	∇u)(t	PROPN
ejpam-3003	241	8	)	)	PUNCT
ejpam-3003	241	9	]	]	PUNCT
ejpam-3003	241	10	h.f	h.f	PROPN
ejpam-3003	241	11	.	.	PROPN
ejpam-3003	241	12	di	di	PROPN
ejpam-3003	241	13	,	,	PUNCT
ejpam-3003	241	14	y.d	y.d	PROPN
ejpam-3003	241	15	.	.	PROPN
ejpam-3003	241	16	shang	shang	PROPN
ejpam-3003	241	17	/	/	SYM
ejpam-3003	241	18	eur	eur	PROPN
ejpam-3003	241	19	.	.	PUNCT
ejpam-3003	242	1	j.	j.	PROPN
ejpam-3003	242	2	pure	pure	PROPN
ejpam-3003	242	3	appl	appl	PROPN
ejpam-3003	242	4	.	.	PROPN
ejpam-3003	242	5	math	math	PROPN
ejpam-3003	242	6	,	,	PUNCT
ejpam-3003	242	7	10	10	NUM
ejpam-3003	242	8	(	(	PUNCT
ejpam-3003	242	9	4	4	NUM
ejpam-3003	242	10	)	)	PUNCT
ejpam-3003	242	11	(	(	PUNCT
ejpam-3003	242	12	2017	2017	NUM
ejpam-3003	242	13	)	)	PUNCT
ejpam-3003	242	14	,	,	PUNCT
ejpam-3003	242	15	668	668	NUM
ejpam-3003	242	16	-	-	SYM
ejpam-3003	242	17	701	701	NUM
ejpam-3003	242	18	677	677	NUM
ejpam-3003	242	19	<	<	X
ejpam-3003	242	20	(	(	PUNCT
ejpam-3003	242	21	p−	p−	NOUN
ejpam-3003	242	22	1	1	NUM
ejpam-3003	242	23	)	)	PUNCT
ejpam-3003	242	24	2(p+	2(p+	NUM
ejpam-3003	242	25	1	1	NUM
ejpam-3003	242	26	)	)	PUNCT
ejpam-3003	242	27	‖u‖p+1	‖u‖p+1	PROPN
ejpam-3003	242	28	p+1	p+1	NOUN
ejpam-3003	242	29	,	,	PUNCT
ejpam-3003	242	30	0	0	NUM
ejpam-3003	242	31	≤	≤	NUM
ejpam-3003	242	32	t	t	X
ejpam-3003	242	33	<	<	X
ejpam-3003	242	34	t.	t.	PROPN
ejpam-3003	242	35	(	(	PUNCT
ejpam-3003	242	36	2.21	2.21	NUM
ejpam-3003	242	37	)	)	PUNCT
ejpam-3003	242	38	thus	thus	ADV
ejpam-3003	242	39	,	,	PUNCT
ejpam-3003	242	40	the	the	DET
ejpam-3003	242	41	proof	proof	NOUN
ejpam-3003	242	42	is	be	AUX
ejpam-3003	242	43	completed	complete	VERB
ejpam-3003	242	44	.	.	PUNCT
ejpam-3003	243	1	3	3	X
ejpam-3003	243	2	.	.	X
ejpam-3003	243	3	existence	existence	NOUN
ejpam-3003	243	4	of	of	ADP
ejpam-3003	243	5	global	global	ADJ
ejpam-3003	243	6	weak	weak	ADJ
ejpam-3003	243	7	solutions	solution	NOUN
ejpam-3003	243	8	in	in	ADP
ejpam-3003	243	9	this	this	DET
ejpam-3003	243	10	section	section	NOUN
ejpam-3003	243	11	,	,	PUNCT
ejpam-3003	243	12	we	we	PRON
ejpam-3003	243	13	are	be	AUX
ejpam-3003	243	14	going	go	VERB
ejpam-3003	243	15	to	to	PART
ejpam-3003	243	16	obtain	obtain	VERB
ejpam-3003	243	17	the	the	DET
ejpam-3003	243	18	existence	existence	NOUN
ejpam-3003	243	19	of	of	ADP
ejpam-3003	243	20	global	global	ADJ
ejpam-3003	243	21	weak	weak	ADJ
ejpam-3003	243	22	solutions	solution	NOUN
ejpam-3003	243	23	for	for	ADP
ejpam-3003	243	24	the	the	DET
ejpam-3003	243	25	problem	problem	NOUN
ejpam-3003	243	26	(	(	PUNCT
ejpam-3003	243	27	1.1	1.1	NUM
ejpam-3003	243	28	)	)	PUNCT
ejpam-3003	243	29	with	with	ADP
ejpam-3003	243	30	the	the	DET
ejpam-3003	243	31	initial	initial	ADJ
ejpam-3003	243	32	conditions	condition	NOUN
ejpam-3003	243	33	e(0	e(0	NOUN
ejpam-3003	243	34	)	)	PUNCT
ejpam-3003	243	35	<	<	X
ejpam-3003	243	36	d̃	d̃	PROPN
ejpam-3003	243	37	and	and	CCONJ
ejpam-3003	243	38	i(u0	i(u0	PROPN
ejpam-3003	243	39	)	)	PUNCT
ejpam-3003	243	40	>	>	X
ejpam-3003	243	41	0	0	PUNCT
ejpam-3003	244	1	or	or	CCONJ
ejpam-3003	244	2	‖u0‖h1	‖u0‖h1	PROPN
ejpam-3003	244	3	γ0	γ0	NOUN
ejpam-3003	244	4	=	=	SYM
ejpam-3003	244	5	0	0	NUM
ejpam-3003	244	6	by	by	ADP
ejpam-3003	244	7	the	the	DET
ejpam-3003	244	8	combination	combination	NOUN
ejpam-3003	244	9	of	of	ADP
ejpam-3003	244	10	galerkin	galerkin	ADJ
ejpam-3003	244	11	approximation	approximation	NOUN
ejpam-3003	244	12	,	,	PUNCT
ejpam-3003	244	13	potential	potential	ADJ
ejpam-3003	244	14	well	well	ADV
ejpam-3003	244	15	and	and	CCONJ
ejpam-3003	244	16	monotonicity	monotonicity	NOUN
ejpam-3003	244	17	-	-	PUNCT
ejpam-3003	244	18	compactness	compactness	NOUN
ejpam-3003	244	19	methods	method	NOUN
ejpam-3003	244	20	.	.	PUNCT
ejpam-3003	245	1	theorem	theorem	NOUN
ejpam-3003	245	2	5	5	NUM
ejpam-3003	245	3	.	.	PUNCT
ejpam-3003	246	1	let	let	VERB
ejpam-3003	246	2	the	the	DET
ejpam-3003	246	3	assumptions	assumption	NOUN
ejpam-3003	246	4	(	(	PUNCT
ejpam-3003	246	5	a1	a1	NOUN
ejpam-3003	246	6	)	)	PUNCT
ejpam-3003	246	7	,	,	PUNCT
ejpam-3003	246	8	(	(	PUNCT
ejpam-3003	246	9	a3	a3	NOUN
ejpam-3003	246	10	)	)	PUNCT
ejpam-3003	246	11	hold	hold	VERB
ejpam-3003	246	12	,	,	PUNCT
ejpam-3003	246	13	u0(x	u0(x	NOUN
ejpam-3003	246	14	)	)	PUNCT
ejpam-3003	246	15	∈	∈	PROPN
ejpam-3003	246	16	h1	h1	PROPN
ejpam-3003	246	17	γ0	γ0	PROPN
ejpam-3003	246	18	(	(	PUNCT
ejpam-3003	246	19	ω	ω	NOUN
ejpam-3003	246	20	)	)	PUNCT
ejpam-3003	246	21	,	,	PUNCT
ejpam-3003	246	22	u1(x	u1(x	NOUN
ejpam-3003	246	23	)	)	PUNCT
ejpam-3003	246	24	∈	∈	PROPN
ejpam-3003	246	25	lρ+1(ω	lρ+1(ω	X
ejpam-3003	246	26	)	)	PUNCT
ejpam-3003	246	27	∩	∩	NOUN
ejpam-3003	246	28	lq+1(γ1	lq+1(γ1	NOUN
ejpam-3003	246	29	)	)	PUNCT
ejpam-3003	246	30	.	.	PUNCT
ejpam-3003	247	1	further	far	ADV
ejpam-3003	247	2	assume	assume	VERB
ejpam-3003	247	3	that	that	SCONJ
ejpam-3003	247	4	e(0	e(0	NOUN
ejpam-3003	247	5	)	)	PUNCT
ejpam-3003	247	6	<	<	X
ejpam-3003	247	7	d̃	d̃	PROPN
ejpam-3003	247	8	and	and	CCONJ
ejpam-3003	247	9	i(u0	i(u0	PROPN
ejpam-3003	247	10	)	)	PUNCT
ejpam-3003	247	11	>	>	X
ejpam-3003	247	12	0	0	PUNCT
ejpam-3003	248	1	or	or	CCONJ
ejpam-3003	248	2	‖u0‖h1	‖u0‖h1	PROPN
ejpam-3003	248	3	γ0	γ0	NOUN
ejpam-3003	248	4	=	=	SYM
ejpam-3003	248	5	0	0	NUM
ejpam-3003	248	6	,	,	PUNCT
ejpam-3003	248	7	then	then	ADV
ejpam-3003	248	8	the	the	DET
ejpam-3003	248	9	problem	problem	NOUN
ejpam-3003	248	10	(	(	PUNCT
ejpam-3003	248	11	1.1	1.1	NUM
ejpam-3003	248	12	)	)	PUNCT
ejpam-3003	248	13	admits	admit	VERB
ejpam-3003	248	14	a	a	DET
ejpam-3003	248	15	global	global	ADJ
ejpam-3003	248	16	weak	weak	ADJ
ejpam-3003	248	17	solution	solution	NOUN
ejpam-3003	248	18	satisfying	satisfy	VERB
ejpam-3003	248	19	u	u	NOUN
ejpam-3003	248	20	∈	∈	PROPN
ejpam-3003	248	21	l∞(0,∞;h1	l∞(0,∞;h1	PROPN
ejpam-3003	248	22	γ0	γ0	PROPN
ejpam-3003	248	23	(	(	PUNCT
ejpam-3003	248	24	ω	ω	NOUN
ejpam-3003	248	25	)	)	PUNCT
ejpam-3003	248	26	)	)	PUNCT
ejpam-3003	248	27	,	,	PUNCT
ejpam-3003	248	28	ut	ut	PROPN
ejpam-3003	248	29	∈	∈	PROPN
ejpam-3003	248	30	l∞(0,∞;lρ+1(ω	l∞(0,∞;lρ+1(ω	NOUN
ejpam-3003	248	31	)	)	PUNCT
ejpam-3003	248	32	)	)	PUNCT
ejpam-3003	248	33	∩	∩	NOUN
ejpam-3003	248	34	lq+1(0,∞;lq+1(γ1	lq+1(0,∞;lq+1(γ1	NOUN
ejpam-3003	248	35	)	)	PUNCT
ejpam-3003	248	36	)	)	PUNCT
ejpam-3003	248	37	,	,	PUNCT
ejpam-3003	248	38	u(t	u(t	NOUN
ejpam-3003	248	39	)	)	PUNCT
ejpam-3003	248	40	∈w	∈w	NOUN
ejpam-3003	248	41	for	for	ADP
ejpam-3003	248	42	0	0	NUM
ejpam-3003	248	43	≤	≤	NOUN
ejpam-3003	248	44	t	t	NOUN
ejpam-3003	248	45	<	<	X
ejpam-3003	248	46	∞	∞	PROPN
ejpam-3003	248	47	,	,	PUNCT
ejpam-3003	248	48	and	and	CCONJ
ejpam-3003	248	49	the	the	DET
ejpam-3003	248	50	energy	energy	NOUN
ejpam-3003	248	51	identity	identity	NOUN
ejpam-3003	248	52	e(t	e(t	NOUN
ejpam-3003	248	53	)	)	PUNCT
ejpam-3003	249	1	+	+	CCONJ
ejpam-3003	250	1	∫	∫	PROPN
ejpam-3003	250	2	t	t	PROPN
ejpam-3003	250	3	0	0	NUM
ejpam-3003	250	4	‖ut(s)‖q+1	‖ut(s)‖q+1	PROPN
ejpam-3003	250	5	γ1,q+1ds−	γ1,q+1ds−	PROPN
ejpam-3003	250	6	1	1	NUM
ejpam-3003	250	7	2	2	NUM
ejpam-3003	250	8	∫	∫	NOUN
ejpam-3003	250	9	t	t	NOUN
ejpam-3003	250	10	0	0	NUM
ejpam-3003	251	1	(	(	PUNCT
ejpam-3003	251	2	g′	g′	NOUN
ejpam-3003	251	3	◦	◦	NOUN
ejpam-3003	251	4	∇u)(s)ds+	∇u)(s)ds+	PROPN
ejpam-3003	251	5	1	1	NUM
ejpam-3003	251	6	2	2	NUM
ejpam-3003	251	7	∫	∫	NOUN
ejpam-3003	251	8	t	t	NOUN
ejpam-3003	251	9	0	0	NUM
ejpam-3003	251	10	g(s)‖∇u(s)‖22ds	g(s)‖∇u(s)‖22ds	NOUN
ejpam-3003	251	11	=	=	PUNCT
ejpam-3003	251	12	e(0	e(0	NOUN
ejpam-3003	251	13	)	)	PUNCT
ejpam-3003	251	14	,	,	PUNCT
ejpam-3003	251	15	(	(	PUNCT
ejpam-3003	251	16	3.1	3.1	NUM
ejpam-3003	251	17	)	)	PUNCT
ejpam-3003	251	18	holds	hold	VERB
ejpam-3003	251	19	for	for	ADP
ejpam-3003	251	20	0	0	NUM
ejpam-3003	251	21	≤	≤	NOUN
ejpam-3003	251	22	t	t	PROPN
ejpam-3003	251	23	<	<	X
ejpam-3003	251	24	∞.	∞.	PROPN
ejpam-3003	251	25	remark	remark	NOUN
ejpam-3003	251	26	1	1	NUM
ejpam-3003	251	27	.	.	PUNCT
ejpam-3003	251	28	from	from	ADP
ejpam-3003	251	29	(	(	PUNCT
ejpam-3003	251	30	3.1	3.1	NUM
ejpam-3003	251	31	)	)	PUNCT
ejpam-3003	251	32	,	,	PUNCT
ejpam-3003	251	33	we	we	PRON
ejpam-3003	251	34	can	can	AUX
ejpam-3003	251	35	easily	easily	ADV
ejpam-3003	251	36	obtain	obtain	VERB
ejpam-3003	251	37	e′(t	e′(t	NOUN
ejpam-3003	251	38	)	)	PUNCT
ejpam-3003	251	39	=	=	PUNCT
ejpam-3003	252	1	−‖ut(t)‖q+1	−‖ut(t)‖q+1	PUNCT
ejpam-3003	252	2	γ1,q+1	γ1,q+1	PUNCT
ejpam-3003	253	1	+	+	CCONJ
ejpam-3003	253	2	1	1	NUM
ejpam-3003	253	3	2	2	NUM
ejpam-3003	253	4	(	(	PUNCT
ejpam-3003	253	5	g′	g′	NOUN
ejpam-3003	253	6	◦	◦	NOUN
ejpam-3003	253	7	∇u)(t)−	∇u)(t)−	NUM
ejpam-3003	253	8	1	1	NUM
ejpam-3003	253	9	2	2	NUM
ejpam-3003	253	10	g(t)‖∇u(t)‖22	g(t)‖∇u(t)‖22	NOUN
ejpam-3003	253	11	≤	≤	NOUN
ejpam-3003	253	12	0	0	NUM
ejpam-3003	253	13	.	.	PUNCT
ejpam-3003	254	1	(	(	PUNCT
ejpam-3003	254	2	3.2	3.2	NUM
ejpam-3003	254	3	)	)	PUNCT
ejpam-3003	254	4	proof	proof	NOUN
ejpam-3003	254	5	.	.	PUNCT
ejpam-3003	255	1	let	let	AUX
ejpam-3003	255	2	{	{	PUNCT
ejpam-3003	255	3	wj(x	wj(x	PROPN
ejpam-3003	255	4	)	)	PUNCT
ejpam-3003	255	5	}	}	PUNCT
ejpam-3003	255	6	be	be	AUX
ejpam-3003	255	7	a	a	DET
ejpam-3003	255	8	complete	complete	ADJ
ejpam-3003	255	9	orthogonal	orthogonal	ADJ
ejpam-3003	255	10	system	system	NOUN
ejpam-3003	255	11	in	in	ADP
ejpam-3003	255	12	h1	h1	PROPN
ejpam-3003	255	13	γ0	γ0	PROPN
ejpam-3003	255	14	(	(	PUNCT
ejpam-3003	255	15	ω)∩lq+1(γ1)∩lρ+1(ω	ω)∩lq+1(γ1)∩lρ+1(ω	NOUN
ejpam-3003	255	16	)	)	PUNCT
ejpam-3003	255	17	.	.	PUNCT
ejpam-3003	256	1	we	we	PRON
ejpam-3003	256	2	suppose	suppose	VERB
ejpam-3003	256	3	that	that	SCONJ
ejpam-3003	256	4	the	the	DET
ejpam-3003	256	5	approximate	approximate	ADJ
ejpam-3003	256	6	weak	weak	ADJ
ejpam-3003	256	7	solution	solution	NOUN
ejpam-3003	256	8	um	um	INTJ
ejpam-3003	256	9	of	of	ADP
ejpam-3003	256	10	the	the	DET
ejpam-3003	256	11	problem	problem	NOUN
ejpam-3003	256	12	(	(	PUNCT
ejpam-3003	256	13	1.1	1.1	NUM
ejpam-3003	256	14	)	)	PUNCT
ejpam-3003	256	15	can	can	AUX
ejpam-3003	256	16	be	be	AUX
ejpam-3003	256	17	written	write	VERB
ejpam-3003	256	18	um(t	um(t	ADP
ejpam-3003	256	19	)	)	PUNCT
ejpam-3003	256	20	=	=	PUNCT
ejpam-3003	257	1	m∑	m∑	CCONJ
ejpam-3003	257	2	j=1	j=1	PROPN
ejpam-3003	257	3	dmj(t)wj(x	dmj(t)wj(x	PROPN
ejpam-3003	257	4	)	)	PUNCT
ejpam-3003	257	5	,	,	PUNCT
ejpam-3003	257	6	m	m	VERB
ejpam-3003	257	7	=	=	NOUN
ejpam-3003	257	8	1	1	NUM
ejpam-3003	257	9	,	,	PUNCT
ejpam-3003	257	10	2	2	NUM
ejpam-3003	257	11	,	,	PUNCT
ejpam-3003	257	12	·	·	PUNCT
ejpam-3003	257	13	·	·	PUNCT
ejpam-3003	257	14	·	·	PUNCT
ejpam-3003	257	15	·	·	PUNCT
ejpam-3003	257	16	·	·	PUNCT
ejpam-3003	257	17	·	·	PUNCT
ejpam-3003	257	18	.	.	PUNCT
ejpam-3003	258	1	(	(	PUNCT
ejpam-3003	258	2	3.3	3.3	NUM
ejpam-3003	258	3	)	)	PUNCT
ejpam-3003	258	4	according	accord	VERB
ejpam-3003	258	5	to	to	ADP
ejpam-3003	258	6	galerkin	galerkin	PROPN
ejpam-3003	258	7	’s	’s	PART
ejpam-3003	258	8	method	method	NOUN
ejpam-3003	258	9	,	,	PUNCT
ejpam-3003	258	10	these	these	DET
ejpam-3003	258	11	coefficients	coefficient	NOUN
ejpam-3003	258	12	dmj	dmj	NOUN
ejpam-3003	258	13	need	need	VERB
ejpam-3003	258	14	to	to	PART
ejpam-3003	258	15	satisfy	satisfy	VERB
ejpam-3003	258	16	the	the	DET
ejpam-3003	258	17	following	following	ADJ
ejpam-3003	258	18	initial	initial	ADJ
ejpam-3003	258	19	value	value	NOUN
ejpam-3003	258	20	problem	problem	NOUN
ejpam-3003	258	21	of	of	ADP
ejpam-3003	258	22	nonlinear	nonlinear	ADJ
ejpam-3003	258	23	ordinary	ordinary	ADJ
ejpam-3003	258	24	integro	integro	ADJ
ejpam-3003	258	25	-	-	PUNCT
ejpam-3003	258	26	differential	differential	NOUN
ejpam-3003	258	27	equations	equation	NOUN
ejpam-3003	258	28	1	1	NUM
ejpam-3003	258	29	ρ	ρ	NOUN
ejpam-3003	258	30	(	(	PUNCT
ejpam-3003	258	31	|u′m|ρ−1u′m	|u′m|ρ−1u′m	PROPN
ejpam-3003	258	32	,	,	PUNCT
ejpam-3003	258	33	wj	wj	PROPN
ejpam-3003	258	34	)	)	PUNCT
ejpam-3003	259	1	+	+	CCONJ
ejpam-3003	260	1	∫	∫	PROPN
ejpam-3003	260	2	t	t	PROPN
ejpam-3003	260	3	0	0	NUM
ejpam-3003	260	4	b1(um	b1(um	NUM
ejpam-3003	260	5	,	,	PUNCT
ejpam-3003	260	6	wj)ds+	wj)ds+	NOUN
ejpam-3003	260	7	∫	∫	PROPN
ejpam-3003	260	8	t	t	PROPN
ejpam-3003	260	9	0	0	NUM
ejpam-3003	261	1	b2(um	b2(um	PROPN
ejpam-3003	261	2	,	,	PUNCT
ejpam-3003	261	3	wj)ds	wj)ds	PROPN
ejpam-3003	261	4	−	−	PROPN
ejpam-3003	261	5	∫	∫	PROPN
ejpam-3003	261	6	t	t	PROPN
ejpam-3003	261	7	0	0	NUM
ejpam-3003	261	8	(	(	PUNCT
ejpam-3003	261	9	|um|p−1um	|um|p−1um	PROPN
ejpam-3003	261	10	,	,	PUNCT
ejpam-3003	261	11	wj)ds+	wj)ds+	ADJ
ejpam-3003	261	12	∫	∫	PROPN
ejpam-3003	261	13	t	t	PROPN
ejpam-3003	261	14	0	0	NUM
ejpam-3003	261	15	(	(	PUNCT
ejpam-3003	261	16	|u′m|q−1u′m	|u′m|q−1u′m	NOUN
ejpam-3003	261	17	,	,	PUNCT
ejpam-3003	261	18	wj)γ1ds	wj)γ1ds	NOUN
ejpam-3003	261	19	=	=	PROPN
ejpam-3003	261	20	1	1	NUM
ejpam-3003	261	21	ρ	ρ	NOUN
ejpam-3003	261	22	(	(	PUNCT
ejpam-3003	261	23	|u′m(0)|ρ−1u′m(0	|u′m(0)|ρ−1u′m(0	NOUN
ejpam-3003	261	24	)	)	PUNCT
ejpam-3003	261	25	,	,	PUNCT
ejpam-3003	261	26	wj	wj	PROPN
ejpam-3003	261	27	)	)	PUNCT
ejpam-3003	261	28	,	,	PUNCT
ejpam-3003	261	29	j	j	PROPN
ejpam-3003	261	30	=	=	SYM
ejpam-3003	261	31	1	1	NUM
ejpam-3003	261	32	,	,	PUNCT
ejpam-3003	261	33	2	2	NUM
ejpam-3003	261	34	,	,	PUNCT
ejpam-3003	261	35	·	·	PUNCT
ejpam-3003	261	36	·	·	PUNCT
ejpam-3003	261	37	·	·	PUNCT
ejpam-3003	261	38	,	,	PUNCT
ejpam-3003	261	39	m	m	PROPN
ejpam-3003	261	40	,	,	PUNCT
ejpam-3003	261	41	(	(	PUNCT
ejpam-3003	261	42	3.4	3.4	NUM
ejpam-3003	261	43	)	)	PUNCT
ejpam-3003	261	44	h.f	h.f	PROPN
ejpam-3003	261	45	.	.	PROPN
ejpam-3003	261	46	di	di	PROPN
ejpam-3003	261	47	,	,	PUNCT
ejpam-3003	261	48	y.d	y.d	PROPN
ejpam-3003	261	49	.	.	PROPN
ejpam-3003	261	50	shang	shang	PROPN
ejpam-3003	261	51	/	/	SYM
ejpam-3003	261	52	eur	eur	PROPN
ejpam-3003	261	53	.	.	PUNCT
ejpam-3003	262	1	j.	j.	PROPN
ejpam-3003	262	2	pure	pure	PROPN
ejpam-3003	262	3	appl	appl	PROPN
ejpam-3003	262	4	.	.	PROPN
ejpam-3003	262	5	math	math	PROPN
ejpam-3003	262	6	,	,	PUNCT
ejpam-3003	262	7	10	10	NUM
ejpam-3003	262	8	(	(	PUNCT
ejpam-3003	262	9	4	4	NUM
ejpam-3003	262	10	)	)	PUNCT
ejpam-3003	262	11	(	(	PUNCT
ejpam-3003	262	12	2017	2017	NUM
ejpam-3003	262	13	)	)	PUNCT
ejpam-3003	262	14	,	,	PUNCT
ejpam-3003	262	15	668	668	NUM
ejpam-3003	262	16	-	-	SYM
ejpam-3003	262	17	701	701	NUM
ejpam-3003	262	18	678	678	NUM
ejpam-3003	262	19	um(x	um(x	NOUN
ejpam-3003	262	20	,	,	PUNCT
ejpam-3003	262	21	0	0	NUM
ejpam-3003	262	22	)	)	PUNCT
ejpam-3003	262	23	=	=	PUNCT
ejpam-3003	263	1	m∑	m∑	ADV
ejpam-3003	263	2	j=1	j=1	PROPN
ejpam-3003	263	3	dmj(0)ωj(x)→	dmj(0)ωj(x)→	PROPN
ejpam-3003	263	4	u0(x	u0(x	PROPN
ejpam-3003	263	5	)	)	PUNCT
ejpam-3003	263	6	,	,	PUNCT
ejpam-3003	263	7	in	in	ADP
ejpam-3003	263	8	h1	h1	PROPN
ejpam-3003	263	9	γ0	γ0	PROPN
ejpam-3003	263	10	(	(	PUNCT
ejpam-3003	263	11	ω	ω	NOUN
ejpam-3003	263	12	)	)	PUNCT
ejpam-3003	263	13	,	,	PUNCT
ejpam-3003	263	14	(	(	PUNCT
ejpam-3003	263	15	3.5	3.5	NUM
ejpam-3003	263	16	)	)	PUNCT
ejpam-3003	263	17	u′m(x	u′m(x	NOUN
ejpam-3003	263	18	,	,	PUNCT
ejpam-3003	263	19	0	0	NUM
ejpam-3003	263	20	)	)	PUNCT
ejpam-3003	263	21	=	=	PUNCT
ejpam-3003	264	1	m∑	m∑	ADV
ejpam-3003	264	2	j=1	j=1	NOUN
ejpam-3003	264	3	d′mj(0)ωj(x)→	d′mj(0)ωj(x)→	NOUN
ejpam-3003	264	4	u1(x	u1(x	NOUN
ejpam-3003	264	5	)	)	PUNCT
ejpam-3003	264	6	,	,	PUNCT
ejpam-3003	264	7	in	in	ADP
ejpam-3003	264	8	lρ+1(ω	lρ+1(ω	PROPN
ejpam-3003	264	9	)	)	PUNCT
ejpam-3003	264	10	∩	∩	NOUN
ejpam-3003	264	11	lq+1(γ1	lq+1(γ1	NOUN
ejpam-3003	264	12	)	)	PUNCT
ejpam-3003	264	13	,	,	PUNCT
ejpam-3003	264	14	(	(	PUNCT
ejpam-3003	264	15	3.6	3.6	NUM
ejpam-3003	264	16	)	)	PUNCT
ejpam-3003	265	1	where	where	SCONJ
ejpam-3003	265	2	b1(um	b1(um	NUM
ejpam-3003	265	3	,	,	PUNCT
ejpam-3003	265	4	wj	wj	NOUN
ejpam-3003	265	5	)	)	PUNCT
ejpam-3003	265	6	=	=	PRON
ejpam-3003	265	7	(	(	PUNCT
ejpam-3003	265	8	∇um,∇wj	∇um,∇wj	ADJ
ejpam-3003	265	9	)	)	PUNCT
ejpam-3003	265	10	,	,	PUNCT
ejpam-3003	265	11	b2(um	b2(um	PROPN
ejpam-3003	265	12	,	,	PUNCT
ejpam-3003	265	13	wj	wj	NOUN
ejpam-3003	265	14	)	)	PUNCT
ejpam-3003	266	1	=	=	SYM
ejpam-3003	266	2	−	−	PROPN
ejpam-3003	266	3	(	(	PUNCT
ejpam-3003	266	4	∫	∫	PROPN
ejpam-3003	266	5	s	s	PART
ejpam-3003	266	6	0	0	NUM
ejpam-3003	266	7	g(s−	g(s−	PROPN
ejpam-3003	266	8	τ)∇um(τ)dτ,∇wj	τ)∇um(τ)dτ,∇wj	PROPN
ejpam-3003	266	9	)	)	PUNCT
ejpam-3003	266	10	.	.	PUNCT
ejpam-3003	267	1	we	we	PRON
ejpam-3003	267	2	will	will	AUX
ejpam-3003	267	3	prove	prove	VERB
ejpam-3003	267	4	that	that	SCONJ
ejpam-3003	267	5	the	the	DET
ejpam-3003	267	6	initial	initial	ADJ
ejpam-3003	267	7	value	value	NOUN
ejpam-3003	267	8	problem	problem	NOUN
ejpam-3003	267	9	(	(	PUNCT
ejpam-3003	267	10	3.4)-(3.6	3.4)-(3.6	NUM
ejpam-3003	267	11	)	)	PUNCT
ejpam-3003	267	12	of	of	ADP
ejpam-3003	267	13	the	the	DET
ejpam-3003	267	14	nonlinear	nonlinear	ADJ
ejpam-3003	267	15	integro	integro	ADJ
ejpam-3003	267	16	-	-	PUNCT
ejpam-3003	267	17	differential	differential	NOUN
ejpam-3003	267	18	equations	equation	NOUN
ejpam-3003	267	19	have	have	VERB
ejpam-3003	267	20	global	global	ADJ
ejpam-3003	267	21	weak	weak	ADJ
ejpam-3003	267	22	solutions	solution	NOUN
ejpam-3003	267	23	in	in	ADP
ejpam-3003	267	24	the	the	DET
ejpam-3003	267	25	interval	interval	NOUN
ejpam-3003	267	26	[	[	X
ejpam-3003	267	27	0,∞	0,∞	NOUN
ejpam-3003	267	28	)	)	PUNCT
ejpam-3003	267	29	.	.	PUNCT
ejpam-3003	268	1	furthermore	furthermore	ADV
ejpam-3003	268	2	,	,	PUNCT
ejpam-3003	268	3	we	we	PRON
ejpam-3003	268	4	show	show	VERB
ejpam-3003	268	5	that	that	SCONJ
ejpam-3003	268	6	the	the	DET
ejpam-3003	268	7	solutions	solution	NOUN
ejpam-3003	268	8	of	of	ADP
ejpam-3003	268	9	the	the	DET
ejpam-3003	268	10	problem	problem	NOUN
ejpam-3003	268	11	(	(	PUNCT
ejpam-3003	268	12	1.1	1.1	NUM
ejpam-3003	268	13	)	)	PUNCT
ejpam-3003	268	14	can	can	AUX
ejpam-3003	268	15	be	be	AUX
ejpam-3003	268	16	approximated	approximate	VERB
ejpam-3003	268	17	by	by	ADP
ejpam-3003	268	18	the	the	DET
ejpam-3003	268	19	functions	function	NOUN
ejpam-3003	268	20	um	um	INTJ
ejpam-3003	268	21	.	.	PUNCT
ejpam-3003	269	1	now	now	ADV
ejpam-3003	269	2	,	,	PUNCT
ejpam-3003	269	3	differentiating	differentiate	VERB
ejpam-3003	269	4	(	(	PUNCT
ejpam-3003	269	5	3.4	3.4	NUM
ejpam-3003	269	6	)	)	PUNCT
ejpam-3003	269	7	with	with	ADP
ejpam-3003	269	8	respect	respect	NOUN
ejpam-3003	269	9	to	to	ADP
ejpam-3003	269	10	t	t	PROPN
ejpam-3003	269	11	,	,	PUNCT
ejpam-3003	269	12	and	and	CCONJ
ejpam-3003	269	13	multiplying	multiply	VERB
ejpam-3003	269	14	the	the	DET
ejpam-3003	269	15	obtained	obtain	VERB
ejpam-3003	269	16	equation	equation	NOUN
ejpam-3003	269	17	by	by	ADP
ejpam-3003	269	18	d′mj(t	d′mj(t	PROPN
ejpam-3003	269	19	)	)	PUNCT
ejpam-3003	269	20	,	,	PUNCT
ejpam-3003	269	21	summing	sum	VERB
ejpam-3003	269	22	for	for	ADP
ejpam-3003	269	23	j	j	PROPN
ejpam-3003	269	24	=	=	SYM
ejpam-3003	269	25	1	1	NUM
ejpam-3003	269	26	,	,	PUNCT
ejpam-3003	269	27	·	·	PUNCT
ejpam-3003	269	28	·	·	PUNCT
ejpam-3003	269	29	·	·	PUNCT
ejpam-3003	269	30	,	,	PUNCT
ejpam-3003	269	31	m	m	PROPN
ejpam-3003	269	32	,	,	PUNCT
ejpam-3003	269	33	then	then	ADV
ejpam-3003	269	34	we	we	PRON
ejpam-3003	269	35	have	have	VERB
ejpam-3003	269	36	(	(	PUNCT
ejpam-3003	269	37	|u′m|ρ−1u′′m	|u′m|ρ−1u′′m	NOUN
ejpam-3003	269	38	,	,	PUNCT
ejpam-3003	269	39	u	u	NOUN
ejpam-3003	269	40	′	′	NOUN
ejpam-3003	269	41	m	m	VERB
ejpam-3003	269	42	)	)	PUNCT
ejpam-3003	270	1	+	+	CCONJ
ejpam-3003	270	2	b1(um	b1(um	NUM
ejpam-3003	270	3	,	,	PUNCT
ejpam-3003	270	4	u	u	NOUN
ejpam-3003	270	5	′	′	NOUN
ejpam-3003	270	6	m	m	VERB
ejpam-3003	270	7	)	)	PUNCT
ejpam-3003	271	1	+	+	CCONJ
ejpam-3003	271	2	b2(um	b2(um	PROPN
ejpam-3003	271	3	,	,	PUNCT
ejpam-3003	271	4	u	u	NOUN
ejpam-3003	271	5	′	′	NOUN
ejpam-3003	271	6	m	m	VERB
ejpam-3003	271	7	)	)	PUNCT
ejpam-3003	272	1	+	+	CCONJ
ejpam-3003	272	2	(	(	PUNCT
ejpam-3003	272	3	|u′m|q−1u′m	|u′m|q−1u′m	NOUN
ejpam-3003	272	4	,	,	PUNCT
ejpam-3003	272	5	u	u	NOUN
ejpam-3003	272	6	′	′	NOUN
ejpam-3003	272	7	m)γ1	m)γ1	PROPN
ejpam-3003	272	8	=	=	SYM
ejpam-3003	272	9	(	(	PUNCT
ejpam-3003	272	10	|um|p−1um	|um|p−1um	PROPN
ejpam-3003	272	11	,	,	PUNCT
ejpam-3003	272	12	u	u	NOUN
ejpam-3003	272	13	′	′	NUM
ejpam-3003	272	14	m).(3.7	m).(3.7	NOUN
ejpam-3003	272	15	)	)	PUNCT
ejpam-3003	272	16	by	by	ADP
ejpam-3003	272	17	a	a	DET
ejpam-3003	272	18	direct	direct	ADJ
ejpam-3003	272	19	calculation	calculation	NOUN
ejpam-3003	272	20	,	,	PUNCT
ejpam-3003	272	21	it	it	PRON
ejpam-3003	272	22	follows	follow	VERB
ejpam-3003	272	23	that	that	SCONJ
ejpam-3003	272	24	(	(	PUNCT
ejpam-3003	272	25	|u′m|ρ−1u′′m	|u′m|ρ−1u′′m	PROPN
ejpam-3003	272	26	,	,	PUNCT
ejpam-3003	272	27	u	u	NOUN
ejpam-3003	272	28	′	′	NOUN
ejpam-3003	272	29	m	m	VERB
ejpam-3003	272	30	)	)	PUNCT
ejpam-3003	272	31	=	=	SYM
ejpam-3003	272	32	1	1	NUM
ejpam-3003	272	33	ρ+	ρ+	NUM
ejpam-3003	272	34	1	1	NUM
ejpam-3003	272	35	d	d	NOUN
ejpam-3003	272	36	dt	dt	ADP
ejpam-3003	272	37	‖u′m‖	‖u′m‖	NUM
ejpam-3003	272	38	ρ+1	ρ+1	NUM
ejpam-3003	272	39	ρ+1	ρ+1	PROPN
ejpam-3003	272	40	,	,	PUNCT
ejpam-3003	272	41	(	(	PUNCT
ejpam-3003	272	42	3.8	3.8	NUM
ejpam-3003	272	43	)	)	PUNCT
ejpam-3003	272	44	b1(um	b1(um	NUM
ejpam-3003	272	45	,	,	PUNCT
ejpam-3003	272	46	u	u	NOUN
ejpam-3003	272	47	′	′	NOUN
ejpam-3003	272	48	m	m	VERB
ejpam-3003	272	49	)	)	PUNCT
ejpam-3003	273	1	=	=	PRON
ejpam-3003	273	2	(	(	PUNCT
ejpam-3003	273	3	∇um,∇u′m	∇um,∇u′m	NUM
ejpam-3003	273	4	)	)	PUNCT
ejpam-3003	273	5	=	=	SYM
ejpam-3003	273	6	1	1	NUM
ejpam-3003	273	7	2	2	NUM
ejpam-3003	273	8	d	d	NOUN
ejpam-3003	273	9	dt	dt	NOUN
ejpam-3003	273	10	‖∇um‖22	‖∇um‖22	NOUN
ejpam-3003	273	11	,	,	PUNCT
ejpam-3003	273	12	(	(	PUNCT
ejpam-3003	273	13	3.9	3.9	NUM
ejpam-3003	273	14	)	)	PUNCT
ejpam-3003	273	15	(	(	PUNCT
ejpam-3003	273	16	|um|p−1um	|um|p−1um	PROPN
ejpam-3003	273	17	,	,	PUNCT
ejpam-3003	273	18	u	u	NOUN
ejpam-3003	273	19	′	′	NOUN
ejpam-3003	273	20	m	m	VERB
ejpam-3003	273	21	)	)	PUNCT
ejpam-3003	273	22	=	=	SYM
ejpam-3003	273	23	1	1	NUM
ejpam-3003	273	24	p+	p+	NOUN
ejpam-3003	273	25	1	1	NUM
ejpam-3003	273	26	d	d	NOUN
ejpam-3003	273	27	dt	dt	X
ejpam-3003	273	28	‖um‖p+1	‖um‖p+1	NOUN
ejpam-3003	273	29	p+1	p+1	NOUN
ejpam-3003	273	30	,	,	PUNCT
ejpam-3003	273	31	(	(	PUNCT
ejpam-3003	273	32	3.10	3.10	NUM
ejpam-3003	273	33	)	)	PUNCT
ejpam-3003	273	34	and	and	CCONJ
ejpam-3003	273	35	b2(um	b2(um	PROPN
ejpam-3003	273	36	,	,	PUNCT
ejpam-3003	273	37	u	u	NOUN
ejpam-3003	273	38	′	′	NOUN
ejpam-3003	273	39	m	m	VERB
ejpam-3003	273	40	)	)	PUNCT
ejpam-3003	274	1	=	=	SYM
ejpam-3003	275	1	−	−	PROPN
ejpam-3003	276	1	∫	∫	PROPN
ejpam-3003	276	2	ω	ω	NUM
ejpam-3003	276	3	∫	∫	PROPN
ejpam-3003	276	4	t	t	PROPN
ejpam-3003	276	5	0	0	NUM
ejpam-3003	276	6	g(t−	g(t−	PROPN
ejpam-3003	276	7	s)∇um(s)∇u′m(t)dsdx	s)∇um(s)∇u′m(t)dsdx	PROPN
ejpam-3003	276	8	=	=	PROPN
ejpam-3003	276	9	−	−	PROPN
ejpam-3003	276	10	∫	∫	PROPN
ejpam-3003	276	11	ω	ω	NUM
ejpam-3003	276	12	∫	∫	PROPN
ejpam-3003	276	13	t	t	PROPN
ejpam-3003	276	14	0	0	NUM
ejpam-3003	276	15	g(t−	g(t−	PROPN
ejpam-3003	276	16	s)[∇um(s)−∇um(t)]∇u′m(t)dsdx	s)[∇um(s)−∇um(t)]∇u′m(t)dsdx	PROPN
ejpam-3003	276	17	−	−	PROPN
ejpam-3003	276	18	∫	∫	PROPN
ejpam-3003	276	19	ω	ω	NUM
ejpam-3003	276	20	∫	∫	PROPN
ejpam-3003	276	21	t	t	PROPN
ejpam-3003	276	22	0	0	NUM
ejpam-3003	276	23	g(t−	g(t−	PROPN
ejpam-3003	276	24	s)∇um(t)∇u′m(t)dsdx	s)∇um(t)∇u′m(t)dsdx	NOUN
ejpam-3003	276	25	=	=	NOUN
ejpam-3003	276	26	1	1	NUM
ejpam-3003	276	27	2	2	NUM
ejpam-3003	276	28	∫	∫	PROPN
ejpam-3003	276	29	ω	ω	NUM
ejpam-3003	276	30	∫	∫	PROPN
ejpam-3003	276	31	t	t	PROPN
ejpam-3003	276	32	0	0	NUM
ejpam-3003	276	33	g(t−	g(t−	PROPN
ejpam-3003	276	34	s	s	PART
ejpam-3003	276	35	)	)	PUNCT
ejpam-3003	276	36	d	d	NOUN
ejpam-3003	276	37	dt	dt	X
ejpam-3003	277	1	[	[	X
ejpam-3003	277	2	∇um(s)−∇um(t)]2dsdx	∇um(s)−∇um(t)]2dsdx	PROPN
ejpam-3003	277	3	h.f	h.f	PROPN
ejpam-3003	277	4	.	.	PROPN
ejpam-3003	277	5	di	di	PROPN
ejpam-3003	277	6	,	,	PUNCT
ejpam-3003	277	7	y.d	y.d	PROPN
ejpam-3003	277	8	.	.	PROPN
ejpam-3003	277	9	shang	shang	PROPN
ejpam-3003	277	10	/	/	SYM
ejpam-3003	277	11	eur	eur	PROPN
ejpam-3003	277	12	.	.	PUNCT
ejpam-3003	278	1	j.	j.	PROPN
ejpam-3003	278	2	pure	pure	PROPN
ejpam-3003	278	3	appl	appl	PROPN
ejpam-3003	278	4	.	.	PROPN
ejpam-3003	278	5	math	math	PROPN
ejpam-3003	278	6	,	,	PUNCT
ejpam-3003	278	7	10	10	NUM
ejpam-3003	278	8	(	(	PUNCT
ejpam-3003	278	9	4	4	NUM
ejpam-3003	278	10	)	)	PUNCT
ejpam-3003	278	11	(	(	PUNCT
ejpam-3003	278	12	2017	2017	NUM
ejpam-3003	278	13	)	)	PUNCT
ejpam-3003	278	14	,	,	PUNCT
ejpam-3003	278	15	668	668	NUM
ejpam-3003	278	16	-	-	SYM
ejpam-3003	278	17	701	701	NUM
ejpam-3003	278	18	679	679	NUM
ejpam-3003	278	19	−	−	NOUN
ejpam-3003	278	20	1	1	NUM
ejpam-3003	278	21	2	2	NUM
ejpam-3003	278	22	∫	∫	PROPN
ejpam-3003	278	23	ω	ω	NUM
ejpam-3003	278	24	∫	∫	PROPN
ejpam-3003	278	25	t	t	PROPN
ejpam-3003	278	26	0	0	NUM
ejpam-3003	278	27	g(t−	g(t−	PROPN
ejpam-3003	278	28	s	s	PART
ejpam-3003	278	29	)	)	PUNCT
ejpam-3003	279	1	d	d	NOUN
ejpam-3003	279	2	dt	dt	X
ejpam-3003	280	1	[	[	X
ejpam-3003	280	2	∇um(t)]2dsdx	∇um(t)]2dsdx	X
ejpam-3003	280	3	=	=	SYM
ejpam-3003	280	4	1	1	NUM
ejpam-3003	280	5	2	2	NUM
ejpam-3003	280	6	d	d	NOUN
ejpam-3003	280	7	dt	dt	X
ejpam-3003	281	1	∫	∫	PROPN
ejpam-3003	281	2	ω	ω	PROPN
ejpam-3003	281	3	∫	∫	PROPN
ejpam-3003	281	4	t	t	PROPN
ejpam-3003	281	5	0	0	NUM
ejpam-3003	281	6	g(t−	g(t−	PROPN
ejpam-3003	281	7	s)[∇um(s)−∇um(t)]2dsdx	s)[∇um(s)−∇um(t)]2dsdx	PROPN
ejpam-3003	281	8	−	−	PROPN
ejpam-3003	281	9	1	1	NUM
ejpam-3003	281	10	2	2	NUM
ejpam-3003	281	11	∫	∫	PROPN
ejpam-3003	281	12	ω	ω	NUM
ejpam-3003	281	13	∫	∫	PROPN
ejpam-3003	281	14	t	t	PROPN
ejpam-3003	281	15	0	0	NUM
ejpam-3003	282	1	g′(t−	g′(t−	NOUN
ejpam-3003	282	2	s)[∇um(s)−∇um(t)]2dsdx	s)[∇um(s)−∇um(t)]2dsdx	NOUN
ejpam-3003	283	1	−	−	PROPN
ejpam-3003	283	2	1	1	NUM
ejpam-3003	283	3	2	2	NUM
ejpam-3003	283	4	d	d	NOUN
ejpam-3003	283	5	dt	dt	X
ejpam-3003	284	1	∫	∫	PROPN
ejpam-3003	284	2	t	t	PROPN
ejpam-3003	284	3	0	0	NUM
ejpam-3003	284	4	g(s)ds‖∇um(t)‖22	g(s)ds‖∇um(t)‖22	PROPN
ejpam-3003	284	5	+	+	CCONJ
ejpam-3003	284	6	1	1	NUM
ejpam-3003	284	7	2	2	NUM
ejpam-3003	284	8	g(t)‖∇um(t)‖22	g(t)‖∇um(t)‖22	NOUN
ejpam-3003	284	9	.	.	PUNCT
ejpam-3003	285	1	(	(	PUNCT
ejpam-3003	285	2	3.11	3.11	NUM
ejpam-3003	285	3	)	)	PUNCT
ejpam-3003	285	4	inserting	insert	VERB
ejpam-3003	285	5	(	(	PUNCT
ejpam-3003	285	6	3.8)-(3.11	3.8)-(3.11	NUM
ejpam-3003	285	7	)	)	PUNCT
ejpam-3003	285	8	into	into	ADP
ejpam-3003	285	9	(	(	PUNCT
ejpam-3003	285	10	3.7	3.7	NUM
ejpam-3003	285	11	)	)	PUNCT
ejpam-3003	285	12	,	,	PUNCT
ejpam-3003	285	13	we	we	PRON
ejpam-3003	285	14	have	have	VERB
ejpam-3003	285	15	1	1	NUM
ejpam-3003	285	16	ρ+	ρ+	NUM
ejpam-3003	285	17	1	1	NUM
ejpam-3003	285	18	d	d	NOUN
ejpam-3003	285	19	dt	dt	ADP
ejpam-3003	285	20	‖u′m‖	‖u′m‖	NUM
ejpam-3003	285	21	ρ+1	ρ+1	NOUN
ejpam-3003	285	22	ρ+1	ρ+1	NOUN
ejpam-3003	286	1	+	+	CCONJ
ejpam-3003	286	2	1	1	NUM
ejpam-3003	286	3	2	2	NUM
ejpam-3003	286	4	d	d	NOUN
ejpam-3003	286	5	dt	dt	X
ejpam-3003	287	1	[	[	X
ejpam-3003	287	2	(	(	PUNCT
ejpam-3003	287	3	1−	1−	NUM
ejpam-3003	287	4	∫	∫	PROPN
ejpam-3003	287	5	t	t	PROPN
ejpam-3003	287	6	0	0	NUM
ejpam-3003	287	7	g(s)ds)‖∇um(t)‖22	g(s)ds)‖∇um(t)‖22	NOUN
ejpam-3003	287	8	]	]	X
ejpam-3003	288	1	+	+	CCONJ
ejpam-3003	288	2	1	1	NUM
ejpam-3003	288	3	2	2	NUM
ejpam-3003	288	4	d	d	NOUN
ejpam-3003	288	5	dt	dt	X
ejpam-3003	288	6	(	(	PUNCT
ejpam-3003	288	7	g	g	PROPN
ejpam-3003	288	8	◦	◦	NOUN
ejpam-3003	288	9	∇um)(t)−	∇um)(t)−	PROPN
ejpam-3003	288	10	1	1	NUM
ejpam-3003	288	11	p+	p+	NOUN
ejpam-3003	288	12	1	1	NUM
ejpam-3003	288	13	d	d	NOUN
ejpam-3003	288	14	dt	dt	NOUN
ejpam-3003	289	1	‖um‖p+1	‖um‖p+1	NOUN
ejpam-3003	289	2	p+1	p+1	NOUN
ejpam-3003	289	3	=	=	NOUN
ejpam-3003	289	4	−	−	PROPN
ejpam-3003	289	5	‖u′m‖	‖u′m‖	PROPN
ejpam-3003	289	6	q+1	q+1	NUM
ejpam-3003	289	7	γ1,q+1	γ1,q+1	PROPN
ejpam-3003	290	1	+	+	CCONJ
ejpam-3003	290	2	1	1	NUM
ejpam-3003	290	3	2	2	NUM
ejpam-3003	290	4	(	(	PUNCT
ejpam-3003	290	5	g′	g′	NOUN
ejpam-3003	290	6	◦	◦	NOUN
ejpam-3003	290	7	∇um)(t)−	∇um)(t)−	NOUN
ejpam-3003	290	8	1	1	NUM
ejpam-3003	290	9	2	2	NUM
ejpam-3003	290	10	g(t)‖∇um(t)‖22	g(t)‖∇um(t)‖22	PROPN
ejpam-3003	290	11	≤	≤	NOUN
ejpam-3003	290	12	0	0	NUM
ejpam-3003	290	13	,	,	PUNCT
ejpam-3003	290	14	(	(	PUNCT
ejpam-3003	290	15	3.12	3.12	NUM
ejpam-3003	290	16	)	)	PUNCT
ejpam-3003	290	17	which	which	PRON
ejpam-3003	290	18	implies	imply	VERB
ejpam-3003	290	19	that	that	SCONJ
ejpam-3003	290	20	e′m(t	e′m(t	ADJ
ejpam-3003	290	21	)	)	PUNCT
ejpam-3003	290	22	=	=	SYM
ejpam-3003	291	1	−‖u′m‖	−‖u′m‖	NOUN
ejpam-3003	291	2	q+1	q+1	X
ejpam-3003	291	3	γ1,q+1	γ1,q+1	PROPN
ejpam-3003	292	1	+	+	CCONJ
ejpam-3003	292	2	1	1	NUM
ejpam-3003	292	3	2	2	NUM
ejpam-3003	292	4	(	(	PUNCT
ejpam-3003	292	5	g′	g′	NOUN
ejpam-3003	292	6	◦	◦	NOUN
ejpam-3003	292	7	∇um)(t)−	∇um)(t)−	NOUN
ejpam-3003	292	8	1	1	NUM
ejpam-3003	292	9	2	2	NUM
ejpam-3003	292	10	g(t)‖∇um(t)‖22	g(t)‖∇um(t)‖22	PROPN
ejpam-3003	292	11	≤	≤	NOUN
ejpam-3003	292	12	0	0	NUM
ejpam-3003	292	13	,	,	PUNCT
ejpam-3003	292	14	(	(	PUNCT
ejpam-3003	292	15	3.13	3.13	NUM
ejpam-3003	292	16	)	)	PUNCT
ejpam-3003	292	17	where	where	SCONJ
ejpam-3003	292	18	em(t	em(t	NOUN
ejpam-3003	292	19	)	)	PUNCT
ejpam-3003	292	20	=	=	SYM
ejpam-3003	292	21	1	1	NUM
ejpam-3003	292	22	ρ+	ρ+	NUM
ejpam-3003	292	23	1	1	NUM
ejpam-3003	292	24	‖u′m‖	‖u′m‖	NUM
ejpam-3003	292	25	ρ+1	ρ+1	NOUN
ejpam-3003	292	26	ρ+1	ρ+1	NOUN
ejpam-3003	292	27	+	+	CCONJ
ejpam-3003	292	28	1	1	NUM
ejpam-3003	292	29	2	2	NUM
ejpam-3003	292	30	(	(	PUNCT
ejpam-3003	292	31	1−	1−	NUM
ejpam-3003	292	32	∫	∫	PROPN
ejpam-3003	292	33	t	t	PROPN
ejpam-3003	292	34	0	0	NUM
ejpam-3003	292	35	g(s)ds)‖∇um(t)‖22	g(s)ds)‖∇um(t)‖22	PROPN
ejpam-3003	293	1	+	+	CCONJ
ejpam-3003	293	2	1	1	NUM
ejpam-3003	293	3	2	2	NUM
ejpam-3003	293	4	(	(	PUNCT
ejpam-3003	293	5	g	g	PROPN
ejpam-3003	293	6	◦	◦	NOUN
ejpam-3003	293	7	∇um)(t)−	∇um)(t)−	PROPN
ejpam-3003	293	8	1	1	NUM
ejpam-3003	293	9	p+	p+	NOUN
ejpam-3003	293	10	1	1	NUM
ejpam-3003	293	11	‖um‖p+1	‖um‖p+1	NOUN
ejpam-3003	293	12	p+1	p+1	NOUN
ejpam-3003	293	13	=	=	SYM
ejpam-3003	293	14	1	1	NUM
ejpam-3003	293	15	ρ+	ρ+	NUM
ejpam-3003	293	16	1	1	NUM
ejpam-3003	293	17	‖u′m‖	‖u′m‖	NUM
ejpam-3003	293	18	ρ+1	ρ+1	NOUN
ejpam-3003	293	19	ρ+1	ρ+1	NOUN
ejpam-3003	293	20	+	+	CCONJ
ejpam-3003	293	21	j(um	j(um	NOUN
ejpam-3003	293	22	)	)	PUNCT
ejpam-3003	293	23	,	,	PUNCT
ejpam-3003	293	24	0	0	NUM
ejpam-3003	293	25	≤	≤	NUM
ejpam-3003	293	26	t	t	PROPN
ejpam-3003	293	27	<	<	X
ejpam-3003	293	28	∞.	∞.	PROPN
ejpam-3003	293	29	(	(	PUNCT
ejpam-3003	293	30	3.14	3.14	NUM
ejpam-3003	293	31	)	)	PUNCT
ejpam-3003	293	32	from	from	ADP
ejpam-3003	293	33	e(0	e(0	NOUN
ejpam-3003	293	34	)	)	PUNCT
ejpam-3003	293	35	<	<	X
ejpam-3003	293	36	d̃	d̃	PROPN
ejpam-3003	293	37	and	and	CCONJ
ejpam-3003	293	38	i(u0	i(u0	PROPN
ejpam-3003	293	39	)	)	PUNCT
ejpam-3003	293	40	>	>	X
ejpam-3003	293	41	0	0	PUNCT
ejpam-3003	293	42	or	or	CCONJ
ejpam-3003	293	43	‖u0‖h1	‖u0‖h1	PROPN
ejpam-3003	293	44	γ0	γ0	NOUN
ejpam-3003	293	45	=	=	SYM
ejpam-3003	293	46	0	0	NUM
ejpam-3003	293	47	,	,	PUNCT
ejpam-3003	293	48	it	it	PRON
ejpam-3003	293	49	follows	follow	VERB
ejpam-3003	293	50	that	that	SCONJ
ejpam-3003	293	51	u0(x	u0(x	NOUN
ejpam-3003	293	52	)	)	PUNCT
ejpam-3003	293	53	∈	∈	PROPN
ejpam-3003	293	54	w	w	PROPN
ejpam-3003	293	55	.	.	PUNCT
ejpam-3003	294	1	hence	hence	ADV
ejpam-3003	294	2	,	,	PUNCT
ejpam-3003	294	3	we	we	PRON
ejpam-3003	294	4	obtain	obtain	VERB
ejpam-3003	294	5	from	from	ADP
ejpam-3003	294	6	(	(	PUNCT
ejpam-3003	294	7	3.5	3.5	NUM
ejpam-3003	294	8	)	)	PUNCT
ejpam-3003	294	9	and	and	CCONJ
ejpam-3003	294	10	(	(	PUNCT
ejpam-3003	294	11	3.6	3.6	NUM
ejpam-3003	294	12	)	)	PUNCT
ejpam-3003	294	13	that	that	SCONJ
ejpam-3003	294	14	em(0	em(0	VERB
ejpam-3003	294	15	)	)	PUNCT
ejpam-3003	294	16	<	<	X
ejpam-3003	294	17	d̃	d̃	PROPN
ejpam-3003	294	18	,	,	PUNCT
ejpam-3003	294	19	i(um(0	i(um(0	NOUN
ejpam-3003	294	20	)	)	PUNCT
ejpam-3003	294	21	)	)	PUNCT
ejpam-3003	294	22	>	>	X
ejpam-3003	294	23	0	0	PUNCT
ejpam-3003	295	1	and	and	CCONJ
ejpam-3003	295	2	um(0	um(0	NOUN
ejpam-3003	295	3	)	)	PUNCT
ejpam-3003	295	4	∈w	∈w	NOUN
ejpam-3003	295	5	for	for	ADP
ejpam-3003	295	6	sufficiently	sufficiently	ADV
ejpam-3003	295	7	large	large	ADJ
ejpam-3003	295	8	m.	m.	NOUN
ejpam-3003	295	9	in	in	ADP
ejpam-3003	295	10	what	what	PRON
ejpam-3003	295	11	follows	follow	VERB
ejpam-3003	295	12	,	,	PUNCT
ejpam-3003	295	13	from	from	ADP
ejpam-3003	295	14	the	the	DET
ejpam-3003	295	15	(	(	PUNCT
ejpam-3003	295	16	3.14	3.14	NUM
ejpam-3003	295	17	)	)	PUNCT
ejpam-3003	295	18	and	and	CCONJ
ejpam-3003	295	19	the	the	DET
ejpam-3003	295	20	arguments	argument	NOUN
ejpam-3003	295	21	in	in	ADP
ejpam-3003	295	22	the	the	DET
ejpam-3003	295	23	proof	proof	NOUN
ejpam-3003	295	24	of	of	ADP
ejpam-3003	295	25	lemma	lemma	PROPN
ejpam-3003	295	26	3	3	NUM
ejpam-3003	295	27	(	(	PUNCT
ejpam-3003	295	28	1	1	NUM
ejpam-3003	295	29	)	)	PUNCT
ejpam-3003	295	30	,	,	PUNCT
ejpam-3003	295	31	we	we	PRON
ejpam-3003	295	32	can	can	AUX
ejpam-3003	295	33	obtain	obtain	VERB
ejpam-3003	295	34	um(t	um(t	NOUN
ejpam-3003	295	35	)	)	PUNCT
ejpam-3003	295	36	∈w	∈w	NOUN
ejpam-3003	295	37	for	for	ADP
ejpam-3003	295	38	sufficiently	sufficiently	ADV
ejpam-3003	295	39	large	large	ADJ
ejpam-3003	295	40	m	m	NOUN
ejpam-3003	295	41	and	and	CCONJ
ejpam-3003	295	42	0	0	NUM
ejpam-3003	295	43	≤	≤	NUM
ejpam-3003	295	44	t	t	NOUN
ejpam-3003	295	45	<	<	X
ejpam-3003	295	46	∞	∞	NUM
ejpam-3003	295	47	such	such	ADJ
ejpam-3003	295	48	that	that	SCONJ
ejpam-3003	295	49	j(um	j(um	NOUN
ejpam-3003	295	50	)	)	PUNCT
ejpam-3003	295	51	=	=	SYM
ejpam-3003	296	1	1	1	NUM
ejpam-3003	296	2	2	2	NUM
ejpam-3003	296	3	l(t)‖∇um‖22	l(t)‖∇um‖22	NOUN
ejpam-3003	296	4	+	+	CCONJ
ejpam-3003	296	5	1	1	NUM
ejpam-3003	296	6	2	2	NUM
ejpam-3003	296	7	(	(	PUNCT
ejpam-3003	296	8	g	g	PROPN
ejpam-3003	296	9	◦	◦	NOUN
ejpam-3003	296	10	∇um)(t)−	∇um)(t)−	PROPN
ejpam-3003	296	11	1	1	NUM
ejpam-3003	296	12	p+	p+	NOUN
ejpam-3003	296	13	1	1	NUM
ejpam-3003	296	14	‖um‖p+1	‖um‖p+1	NOUN
ejpam-3003	296	15	p+1	p+1	NOUN
ejpam-3003	296	16	=	=	PUNCT
ejpam-3003	297	1	p−	p−	NOUN
ejpam-3003	297	2	1	1	NUM
ejpam-3003	297	3	2(p+	2(p+	NUM
ejpam-3003	297	4	1	1	NUM
ejpam-3003	297	5	)	)	PUNCT
ejpam-3003	298	1	[	[	X
ejpam-3003	298	2	l(t)‖∇um‖22	l(t)‖∇um‖22	X
ejpam-3003	298	3	+	+	CCONJ
ejpam-3003	298	4	(	(	PUNCT
ejpam-3003	298	5	g	g	PROPN
ejpam-3003	298	6	◦	◦	NOUN
ejpam-3003	298	7	∇um)(t	∇um)(t	PROPN
ejpam-3003	298	8	)	)	PUNCT
ejpam-3003	298	9	]	]	PUNCT
ejpam-3003	299	1	+	+	CCONJ
ejpam-3003	299	2	1	1	NUM
ejpam-3003	299	3	p+	p+	VERB
ejpam-3003	299	4	1	1	NUM
ejpam-3003	299	5	i(um	i(um	NOUN
ejpam-3003	299	6	)	)	PUNCT
ejpam-3003	299	7	≥	≥	NOUN
ejpam-3003	299	8	p−	p−	NOUN
ejpam-3003	299	9	1	1	NUM
ejpam-3003	299	10	2(p+	2(p+	NUM
ejpam-3003	299	11	1	1	NUM
ejpam-3003	299	12	)	)	PUNCT
ejpam-3003	300	1	[	[	X
ejpam-3003	300	2	l(t)‖∇um‖22	l(t)‖∇um‖22	X
ejpam-3003	300	3	+	+	CCONJ
ejpam-3003	300	4	(	(	PUNCT
ejpam-3003	300	5	g	g	PROPN
ejpam-3003	300	6	◦	◦	NOUN
ejpam-3003	300	7	∇um)(t	∇um)(t	PROPN
ejpam-3003	300	8	)	)	PUNCT
ejpam-3003	300	9	]	]	PUNCT
ejpam-3003	300	10	.	.	PUNCT
ejpam-3003	301	1	(	(	PUNCT
ejpam-3003	301	2	3.15	3.15	NUM
ejpam-3003	301	3	)	)	PUNCT
ejpam-3003	301	4	by	by	ADP
ejpam-3003	301	5	the	the	DET
ejpam-3003	301	6	combination	combination	NOUN
ejpam-3003	301	7	of	of	ADP
ejpam-3003	301	8	(	(	PUNCT
ejpam-3003	301	9	3.13	3.13	NUM
ejpam-3003	301	10	)	)	PUNCT
ejpam-3003	301	11	and	and	CCONJ
ejpam-3003	301	12	(	(	PUNCT
ejpam-3003	301	13	3.15	3.15	NUM
ejpam-3003	301	14	)	)	PUNCT
ejpam-3003	301	15	,	,	PUNCT
ejpam-3003	301	16	we	we	PRON
ejpam-3003	301	17	get	get	VERB
ejpam-3003	301	18	1	1	NUM
ejpam-3003	301	19	ρ+	ρ+	NOUN
ejpam-3003	301	20	1	1	NUM
ejpam-3003	301	21	‖u′m‖	‖u′m‖	NUM
ejpam-3003	301	22	ρ+1	ρ+1	NOUN
ejpam-3003	301	23	ρ+1	ρ+1	NOUN
ejpam-3003	301	24	+	+	CCONJ
ejpam-3003	301	25	p−	p−	NOUN
ejpam-3003	301	26	1	1	NUM
ejpam-3003	301	27	2(p+	2(p+	NUM
ejpam-3003	301	28	1	1	NUM
ejpam-3003	301	29	)	)	PUNCT
ejpam-3003	302	1	[	[	X
ejpam-3003	302	2	l(t)‖∇um‖22	l(t)‖∇um‖22	X
ejpam-3003	302	3	+	+	CCONJ
ejpam-3003	302	4	(	(	PUNCT
ejpam-3003	302	5	g	g	PROPN
ejpam-3003	302	6	◦	◦	NOUN
ejpam-3003	302	7	∇um)(t	∇um)(t	PROPN
ejpam-3003	302	8	)	)	PUNCT
ejpam-3003	302	9	]	]	PUNCT
ejpam-3003	302	10	≤	≤	NUM
ejpam-3003	302	11	em(t	em(t	NOUN
ejpam-3003	302	12	)	)	PUNCT
ejpam-3003	302	13	≤	≤	NOUN
ejpam-3003	302	14	em(0	em(0	X
ejpam-3003	302	15	)	)	PUNCT
ejpam-3003	302	16	<	<	X
ejpam-3003	302	17	d̃	d̃	PROPN
ejpam-3003	302	18	,	,	PUNCT
ejpam-3003	302	19	(	(	PUNCT
ejpam-3003	302	20	3.16	3.16	NUM
ejpam-3003	302	21	)	)	PUNCT
ejpam-3003	302	22	h.f	h.f	PROPN
ejpam-3003	302	23	.	.	PROPN
ejpam-3003	302	24	di	di	PROPN
ejpam-3003	302	25	,	,	PUNCT
ejpam-3003	302	26	y.d	y.d	PROPN
ejpam-3003	302	27	.	.	PROPN
ejpam-3003	302	28	shang	shang	PROPN
ejpam-3003	302	29	/	/	SYM
ejpam-3003	302	30	eur	eur	PROPN
ejpam-3003	302	31	.	.	PUNCT
ejpam-3003	303	1	j.	j.	PROPN
ejpam-3003	303	2	pure	pure	PROPN
ejpam-3003	303	3	appl	appl	PROPN
ejpam-3003	303	4	.	.	PROPN
ejpam-3003	303	5	math	math	PROPN
ejpam-3003	303	6	,	,	PUNCT
ejpam-3003	303	7	10	10	NUM
ejpam-3003	303	8	(	(	PUNCT
ejpam-3003	303	9	4	4	NUM
ejpam-3003	303	10	)	)	PUNCT
ejpam-3003	303	11	(	(	PUNCT
ejpam-3003	303	12	2017	2017	NUM
ejpam-3003	303	13	)	)	PUNCT
ejpam-3003	303	14	,	,	PUNCT
ejpam-3003	303	15	668	668	NUM
ejpam-3003	303	16	-	-	SYM
ejpam-3003	303	17	701	701	NUM
ejpam-3003	303	18	680	680	NUM
ejpam-3003	303	19	for	for	ADP
ejpam-3003	303	20	sufficiently	sufficiently	ADV
ejpam-3003	303	21	large	large	ADJ
ejpam-3003	303	22	m	m	NOUN
ejpam-3003	303	23	and	and	CCONJ
ejpam-3003	303	24	0	0	NUM
ejpam-3003	303	25	≤	≤	NUM
ejpam-3003	303	26	t	t	PROPN
ejpam-3003	303	27	<	<	AUX
ejpam-3003	303	28	∞.	∞.	PROPN
ejpam-3003	303	29	integrating	integrate	VERB
ejpam-3003	303	30	(	(	PUNCT
ejpam-3003	303	31	3.13	3.13	NUM
ejpam-3003	303	32	)	)	PUNCT
ejpam-3003	303	33	with	with	ADP
ejpam-3003	303	34	respect	respect	NOUN
ejpam-3003	303	35	to	to	ADP
ejpam-3003	303	36	t	t	PROPN
ejpam-3003	303	37	,	,	PUNCT
ejpam-3003	303	38	then	then	ADV
ejpam-3003	303	39	we	we	PRON
ejpam-3003	303	40	have	have	VERB
ejpam-3003	303	41	em(t	em(t	NOUN
ejpam-3003	303	42	)	)	PUNCT
ejpam-3003	304	1	+	+	CCONJ
ejpam-3003	304	2	∫	∫	PROPN
ejpam-3003	304	3	t	t	PROPN
ejpam-3003	304	4	0	0	NUM
ejpam-3003	304	5	‖u′m‖	‖u′m‖	PROPN
ejpam-3003	304	6	q+1	q+1	NUM
ejpam-3003	304	7	γ1,q+1ds	γ1,q+1ds	NOUN
ejpam-3003	304	8	=	=	SYM
ejpam-3003	304	9	1	1	NUM
ejpam-3003	304	10	2	2	NUM
ejpam-3003	304	11	∫	∫	NOUN
ejpam-3003	304	12	t	t	NOUN
ejpam-3003	304	13	0	0	NUM
ejpam-3003	304	14	(	(	PUNCT
ejpam-3003	304	15	g′	g′	NOUN
ejpam-3003	304	16	◦	◦	NOUN
ejpam-3003	304	17	∇um)(s)ds−	∇um)(s)ds−	PROPN
ejpam-3003	304	18	1	1	NUM
ejpam-3003	304	19	2	2	NUM
ejpam-3003	304	20	∫	∫	NOUN
ejpam-3003	304	21	t	t	NOUN
ejpam-3003	304	22	0	0	NUM
ejpam-3003	305	1	g(s)‖∇um(s)‖22ds+	g(s)‖∇um(s)‖22ds+	ADP
ejpam-3003	305	2	em(0	em(0	NOUN
ejpam-3003	305	3	)	)	PUNCT
ejpam-3003	305	4	.	.	PUNCT
ejpam-3003	306	1	(	(	PUNCT
ejpam-3003	306	2	3.17	3.17	NUM
ejpam-3003	306	3	)	)	PUNCT
ejpam-3003	306	4	combining	combine	VERB
ejpam-3003	306	5	(	(	PUNCT
ejpam-3003	306	6	3.16	3.16	NUM
ejpam-3003	306	7	)	)	PUNCT
ejpam-3003	306	8	and	and	CCONJ
ejpam-3003	306	9	(	(	PUNCT
ejpam-3003	306	10	3.17	3.17	NUM
ejpam-3003	306	11	)	)	PUNCT
ejpam-3003	306	12	,	,	PUNCT
ejpam-3003	306	13	we	we	PRON
ejpam-3003	306	14	obtain	obtain	VERB
ejpam-3003	306	15	1	1	NUM
ejpam-3003	306	16	ρ+	ρ+	NOUN
ejpam-3003	306	17	1	1	NUM
ejpam-3003	306	18	‖u′m‖	‖u′m‖	NUM
ejpam-3003	306	19	ρ+1	ρ+1	NOUN
ejpam-3003	306	20	ρ+1	ρ+1	NOUN
ejpam-3003	307	1	+	+	CCONJ
ejpam-3003	307	2	∫	∫	PROPN
ejpam-3003	307	3	t	t	PROPN
ejpam-3003	307	4	0	0	NUM
ejpam-3003	308	1	‖u′m‖	‖u′m‖	PROPN
ejpam-3003	308	2	q+1	q+1	NUM
ejpam-3003	308	3	γ1,q+1ds+	γ1,q+1ds+	ADV
ejpam-3003	308	4	p−	p−	NOUN
ejpam-3003	308	5	1	1	NUM
ejpam-3003	308	6	2(p+	2(p+	NUM
ejpam-3003	308	7	1	1	NUM
ejpam-3003	308	8	)	)	PUNCT
ejpam-3003	309	1	[	[	X
ejpam-3003	309	2	l(t)‖∇um‖22	l(t)‖∇um‖22	X
ejpam-3003	309	3	+	+	CCONJ
ejpam-3003	309	4	(	(	PUNCT
ejpam-3003	309	5	g	g	PROPN
ejpam-3003	309	6	◦	◦	NOUN
ejpam-3003	309	7	∇um	∇um	NUM
ejpam-3003	309	8	)	)	PUNCT
ejpam-3003	309	9	]	]	PUNCT
ejpam-3003	309	10	≤	≤	NUM
ejpam-3003	309	11	em(0	em(0	X
ejpam-3003	309	12	)	)	PUNCT
ejpam-3003	309	13	<	<	X
ejpam-3003	309	14	d̃,(3.18	d̃,(3.18	X
ejpam-3003	309	15	)	)	PUNCT
ejpam-3003	309	16	for	for	ADP
ejpam-3003	309	17	sufficiently	sufficiently	ADV
ejpam-3003	309	18	large	large	ADJ
ejpam-3003	309	19	m	m	NOUN
ejpam-3003	309	20	and	and	CCONJ
ejpam-3003	309	21	0	0	NUM
ejpam-3003	309	22	≤	≤	NUM
ejpam-3003	309	23	t	t	PROPN
ejpam-3003	309	24	<	<	X
ejpam-3003	309	25	∞.	∞.	PROPN
ejpam-3003	309	26	from	from	ADP
ejpam-3003	309	27	(	(	PUNCT
ejpam-3003	309	28	3.18	3.18	NUM
ejpam-3003	309	29	)	)	PUNCT
ejpam-3003	309	30	,	,	PUNCT
ejpam-3003	309	31	we	we	PRON
ejpam-3003	309	32	have	have	VERB
ejpam-3003	309	33	l(t)‖∇um‖22	l(t)‖∇um‖22	PROPN
ejpam-3003	310	1	+	+	CCONJ
ejpam-3003	310	2	(	(	PUNCT
ejpam-3003	310	3	g	g	PROPN
ejpam-3003	310	4	◦	◦	NOUN
ejpam-3003	310	5	∇um)(t	∇um)(t	PROPN
ejpam-3003	310	6	)	)	PUNCT
ejpam-3003	310	7	<	<	X
ejpam-3003	310	8	2(p+	2(p+	NUM
ejpam-3003	310	9	1	1	NUM
ejpam-3003	310	10	)	)	PUNCT
ejpam-3003	310	11	p−	p−	NOUN
ejpam-3003	310	12	1	1	NUM
ejpam-3003	310	13	d̃	d̃	PROPN
ejpam-3003	310	14	,	,	PUNCT
ejpam-3003	310	15	0	0	NUM
ejpam-3003	310	16	≤	≤	NUM
ejpam-3003	310	17	t	t	X
ejpam-3003	310	18	<	<	X
ejpam-3003	310	19	∞	∞	PROPN
ejpam-3003	310	20	,	,	PUNCT
ejpam-3003	310	21	(	(	PUNCT
ejpam-3003	310	22	3.19	3.19	NUM
ejpam-3003	310	23	)	)	PUNCT
ejpam-3003	310	24	‖u′m‖	‖u′m‖	VERB
ejpam-3003	311	1	ρ+1	ρ+1	NOUN
ejpam-3003	311	2	ρ+1	ρ+1	NOUN
ejpam-3003	311	3	<	<	X
ejpam-3003	311	4	(	(	PUNCT
ejpam-3003	311	5	ρ+	ρ+	NOUN
ejpam-3003	311	6	1)d̃	1)d̃	NUM
ejpam-3003	311	7	,	,	PUNCT
ejpam-3003	311	8	0	0	NUM
ejpam-3003	311	9	≤	≤	NUM
ejpam-3003	311	10	t	t	NOUN
ejpam-3003	311	11	<	<	X
ejpam-3003	311	12	∞	∞	PROPN
ejpam-3003	311	13	,	,	PUNCT
ejpam-3003	311	14	(	(	PUNCT
ejpam-3003	311	15	3.20	3.20	NUM
ejpam-3003	311	16	)	)	PUNCT
ejpam-3003	311	17	∫	∫	PROPN
ejpam-3003	312	1	t	t	PROPN
ejpam-3003	312	2	0	0	NUM
ejpam-3003	312	3	‖u′m‖	‖u′m‖	PROPN
ejpam-3003	312	4	q+1	q+1	NUM
ejpam-3003	312	5	γ1,q+1ds	γ1,q+1ds	NOUN
ejpam-3003	312	6	<	<	X
ejpam-3003	312	7	d̃	d̃	PROPN
ejpam-3003	312	8	,	,	PUNCT
ejpam-3003	312	9	0	0	NUM
ejpam-3003	312	10	≤	≤	NUM
ejpam-3003	313	1	t	t	PROPN
ejpam-3003	313	2	<	<	X
ejpam-3003	313	3	∞.	∞.	PROPN
ejpam-3003	313	4	(	(	PUNCT
ejpam-3003	313	5	3.21	3.21	NUM
ejpam-3003	313	6	)	)	PUNCT
ejpam-3003	313	7	using	use	VERB
ejpam-3003	313	8	the	the	DET
ejpam-3003	313	9	sobolev	sobolev	NOUN
ejpam-3003	313	10	inequality	inequality	NOUN
ejpam-3003	313	11	and	and	CCONJ
ejpam-3003	313	12	(	(	PUNCT
ejpam-3003	313	13	3.19	3.19	NUM
ejpam-3003	313	14	)	)	PUNCT
ejpam-3003	313	15	,	,	PUNCT
ejpam-3003	313	16	it	it	PRON
ejpam-3003	313	17	follows	follow	VERB
ejpam-3003	313	18	that	that	SCONJ
ejpam-3003	313	19	‖um‖2p+1	‖um‖2p+1	PRON
ejpam-3003	313	20	≤	≤	NUM
ejpam-3003	313	21	b2	b2	PROPN
ejpam-3003	313	22	p+1‖∇um‖22	p+1‖∇um‖22	NOUN
ejpam-3003	313	23	<	<	X
ejpam-3003	313	24	b2	b2	NOUN
ejpam-3003	313	25	p+1	p+1	NOUN
ejpam-3003	313	26	2(p+	2(p+	NUM
ejpam-3003	313	27	1	1	NUM
ejpam-3003	313	28	)	)	PUNCT
ejpam-3003	313	29	(	(	PUNCT
ejpam-3003	313	30	p−	p−	NOUN
ejpam-3003	313	31	1)b	1)b	PROPN
ejpam-3003	313	32	d̃	d̃	PROPN
ejpam-3003	313	33	,	,	PUNCT
ejpam-3003	313	34	0	0	NUM
ejpam-3003	313	35	≤	≤	NUM
ejpam-3003	314	1	t	t	PROPN
ejpam-3003	314	2	<	<	X
ejpam-3003	314	3	∞.	∞.	PROPN
ejpam-3003	314	4	(	(	PUNCT
ejpam-3003	314	5	3.22	3.22	NUM
ejpam-3003	314	6	)	)	PUNCT
ejpam-3003	314	7	furthermore	furthermore	ADV
ejpam-3003	314	8	,	,	PUNCT
ejpam-3003	314	9	by	by	ADP
ejpam-3003	314	10	(	(	PUNCT
ejpam-3003	314	11	3.20	3.20	NUM
ejpam-3003	314	12	)	)	PUNCT
ejpam-3003	314	13	and	and	CCONJ
ejpam-3003	314	14	(	(	PUNCT
ejpam-3003	314	15	3.22	3.22	NUM
ejpam-3003	314	16	)	)	PUNCT
ejpam-3003	314	17	,	,	PUNCT
ejpam-3003	314	18	we	we	PRON
ejpam-3003	314	19	get	get	VERB
ejpam-3003	314	20	|(|u′m|ρ−1u′m	|(|u′m|ρ−1u′m	NOUN
ejpam-3003	314	21	,	,	PUNCT
ejpam-3003	314	22	u	u	NOUN
ejpam-3003	314	23	′	′	NOUN
ejpam-3003	314	24	m)|	m)|	ADJ
ejpam-3003	314	25	≤	≤	PROPN
ejpam-3003	314	26	‖u′m‖	‖u′m‖	NUM
ejpam-3003	315	1	ρ+1	ρ+1	NOUN
ejpam-3003	315	2	ρ+1	ρ+1	NOUN
ejpam-3003	315	3	<	<	X
ejpam-3003	315	4	(	(	PUNCT
ejpam-3003	315	5	ρ+	ρ+	NOUN
ejpam-3003	315	6	1)d̃	1)d̃	NUM
ejpam-3003	315	7	,	,	PUNCT
ejpam-3003	315	8	0	0	NUM
ejpam-3003	315	9	≤	≤	NUM
ejpam-3003	315	10	t	t	NOUN
ejpam-3003	315	11	<	<	X
ejpam-3003	315	12	∞	∞	PROPN
ejpam-3003	315	13	,	,	PUNCT
ejpam-3003	315	14	(	(	PUNCT
ejpam-3003	315	15	3.23	3.23	NUM
ejpam-3003	315	16	)	)	PUNCT
ejpam-3003	315	17	|(|um|p−1um	|(|um|p−1um	NOUN
ejpam-3003	315	18	,	,	PUNCT
ejpam-3003	315	19	um)|	um)|	VERB
ejpam-3003	315	20	≤	≤	PUNCT
ejpam-3003	316	1	‖um‖p+1	‖um‖p+1	ADP
ejpam-3003	316	2	p+1	p+1	X
ejpam-3003	316	3	<	<	X
ejpam-3003	316	4	bp+1	bp+1	PROPN
ejpam-3003	316	5	p+1	p+1	NOUN
ejpam-3003	316	6	(	(	PUNCT
ejpam-3003	316	7	2(p+	2(p+	NUM
ejpam-3003	316	8	1	1	NUM
ejpam-3003	316	9	)	)	PUNCT
ejpam-3003	316	10	(	(	PUNCT
ejpam-3003	316	11	p−	p−	NOUN
ejpam-3003	316	12	1)b	1)b	X
ejpam-3003	316	13	d̃	d̃	PROPN
ejpam-3003	316	14	)	)	PUNCT
ejpam-3003	317	1	p+1	p+1	NOUN
ejpam-3003	317	2	2	2	NUM
ejpam-3003	317	3	,	,	PUNCT
ejpam-3003	317	4	0	0	NUM
ejpam-3003	317	5	≤	≤	NUM
ejpam-3003	317	6	t	t	PROPN
ejpam-3003	317	7	<	<	X
ejpam-3003	317	8	∞.	∞.	PROPN
ejpam-3003	317	9	(	(	PUNCT
ejpam-3003	317	10	3.24	3.24	NUM
ejpam-3003	317	11	)	)	PUNCT
ejpam-3003	317	12	the	the	DET
ejpam-3003	317	13	estimates	estimate	NOUN
ejpam-3003	317	14	(	(	PUNCT
ejpam-3003	317	15	3.19)-(3.24	3.19)-(3.24	NUM
ejpam-3003	317	16	)	)	PUNCT
ejpam-3003	317	17	permit	permit	VERB
ejpam-3003	317	18	us	we	PRON
ejpam-3003	317	19	to	to	PART
ejpam-3003	317	20	obtain	obtain	VERB
ejpam-3003	317	21	a	a	DET
ejpam-3003	317	22	subsequences	subsequence	NOUN
ejpam-3003	317	23	of	of	ADP
ejpam-3003	317	24	{	{	PUNCT
ejpam-3003	317	25	um	um	INTJ
ejpam-3003	317	26	}	}	PUNCT
ejpam-3003	317	27	which	which	PRON
ejpam-3003	317	28	from	from	ADP
ejpam-3003	317	29	now	now	ADV
ejpam-3003	317	30	on	on	ADV
ejpam-3003	317	31	will	will	AUX
ejpam-3003	317	32	be	be	AUX
ejpam-3003	317	33	also	also	ADV
ejpam-3003	317	34	denoted	denote	VERB
ejpam-3003	317	35	by	by	ADP
ejpam-3003	317	36	{	{	PUNCT
ejpam-3003	317	37	um	um	INTJ
ejpam-3003	317	38	}	}	PUNCT
ejpam-3003	317	39	and	and	CCONJ
ejpam-3003	317	40	functions	function	VERB
ejpam-3003	317	41	u	u	PROPN
ejpam-3003	317	42	,	,	PUNCT
ejpam-3003	317	43	χ1	χ1	NOUN
ejpam-3003	317	44	,	,	PUNCT
ejpam-3003	317	45	χ2	χ2	PROPN
ejpam-3003	317	46	,	,	PUNCT
ejpam-3003	317	47	χ3	χ3	VERB
ejpam-3003	317	48	such	such	ADJ
ejpam-3003	317	49	that	that	SCONJ
ejpam-3003	317	50	um	um	INTJ
ejpam-3003	317	51	→	→	SYM
ejpam-3003	317	52	u	u	NOUN
ejpam-3003	317	53	in	in	ADP
ejpam-3003	317	54	l∞(0,∞;h1	l∞(0,∞;h1	ADJ
ejpam-3003	317	55	γ0	γ0	PROPN
ejpam-3003	317	56	(	(	PUNCT
ejpam-3003	317	57	ω	ω	NOUN
ejpam-3003	317	58	)	)	PUNCT
ejpam-3003	317	59	)	)	PUNCT
ejpam-3003	317	60	weakly	weakly	ADJ
ejpam-3003	317	61	star	star	NOUN
ejpam-3003	317	62	,	,	PUNCT
ejpam-3003	317	63	m	m	PROPN
ejpam-3003	317	64	−→∞	−→∞	PROPN
ejpam-3003	317	65	,	,	PUNCT
ejpam-3003	317	66	(	(	PUNCT
ejpam-3003	317	67	3.25	3.25	NUM
ejpam-3003	317	68	)	)	PUNCT
ejpam-3003	317	69	u′m	u′m	NOUN
ejpam-3003	317	70	→	→	PUNCT
ejpam-3003	317	71	u′	u′	X
ejpam-3003	317	72	in	in	ADP
ejpam-3003	317	73	l∞(0,∞;lρ+1(ω	l∞(0,∞;lρ+1(ω	NOUN
ejpam-3003	317	74	)	)	PUNCT
ejpam-3003	317	75	)	)	PUNCT
ejpam-3003	317	76	weakly	weakly	ADJ
ejpam-3003	317	77	star	star	NOUN
ejpam-3003	317	78	,	,	PUNCT
ejpam-3003	317	79	m	m	PROPN
ejpam-3003	317	80	−→∞	−→∞	PROPN
ejpam-3003	317	81	,	,	PUNCT
ejpam-3003	317	82	(	(	PUNCT
ejpam-3003	317	83	3.26	3.26	NUM
ejpam-3003	317	84	)	)	PUNCT
ejpam-3003	317	85	|u′m|q−1u′m	|u′m|q−1u′m	NOUN
ejpam-3003	317	86	→	→	SYM
ejpam-3003	317	87	χ1	χ1	NOUN
ejpam-3003	317	88	in	in	ADP
ejpam-3003	317	89	l	l	PROPN
ejpam-3003	317	90	q+1	q+1	X
ejpam-3003	317	91	q	q	X
ejpam-3003	317	92	(	(	PUNCT
ejpam-3003	317	93	0,∞;l	0,∞;l	NUM
ejpam-3003	317	94	q+1	q+1	NUM
ejpam-3003	317	95	q	q	X
ejpam-3003	317	96	(	(	PUNCT
ejpam-3003	317	97	γ1	γ1	PROPN
ejpam-3003	317	98	)	)	PUNCT
ejpam-3003	317	99	)	)	PUNCT
ejpam-3003	317	100	weakly	weakly	ADV
ejpam-3003	317	101	,	,	PUNCT
ejpam-3003	317	102	m	m	PROPN
ejpam-3003	317	103	−→∞	−→∞	PROPN
ejpam-3003	317	104	,	,	PUNCT
ejpam-3003	317	105	(	(	PUNCT
ejpam-3003	317	106	3.27	3.27	NUM
ejpam-3003	317	107	)	)	PUNCT
ejpam-3003	317	108	h.f	h.f	PROPN
ejpam-3003	317	109	.	.	PROPN
ejpam-3003	317	110	di	di	PROPN
ejpam-3003	317	111	,	,	PUNCT
ejpam-3003	317	112	y.d	y.d	PROPN
ejpam-3003	317	113	.	.	PROPN
ejpam-3003	317	114	shang	shang	PROPN
ejpam-3003	317	115	/	/	SYM
ejpam-3003	317	116	eur	eur	PROPN
ejpam-3003	317	117	.	.	PUNCT
ejpam-3003	318	1	j.	j.	PROPN
ejpam-3003	318	2	pure	pure	PROPN
ejpam-3003	318	3	appl	appl	PROPN
ejpam-3003	318	4	.	.	PROPN
ejpam-3003	318	5	math	math	PROPN
ejpam-3003	318	6	,	,	PUNCT
ejpam-3003	318	7	10	10	NUM
ejpam-3003	318	8	(	(	PUNCT
ejpam-3003	318	9	4	4	NUM
ejpam-3003	318	10	)	)	PUNCT
ejpam-3003	318	11	(	(	PUNCT
ejpam-3003	318	12	2017	2017	NUM
ejpam-3003	318	13	)	)	PUNCT
ejpam-3003	318	14	,	,	PUNCT
ejpam-3003	318	15	668	668	NUM
ejpam-3003	318	16	-	-	SYM
ejpam-3003	318	17	701	701	NUM
ejpam-3003	318	18	681	681	NUM
ejpam-3003	318	19	|um|p−1um	|um|p−1um	NOUN
ejpam-3003	318	20	→	→	SYM
ejpam-3003	318	21	χ2	χ2	PROPN
ejpam-3003	318	22	in	in	ADP
ejpam-3003	318	23	l	l	PROPN
ejpam-3003	318	24	∞(0,∞;l	∞(0,∞;l	NOUN
ejpam-3003	319	1	p+1	p+1	NOUN
ejpam-3003	319	2	p	p	PROPN
ejpam-3003	319	3	(	(	PUNCT
ejpam-3003	319	4	ω	ω	NOUN
ejpam-3003	319	5	)	)	PUNCT
ejpam-3003	319	6	)	)	PUNCT
ejpam-3003	319	7	weakly	weakly	ADJ
ejpam-3003	319	8	star	star	NOUN
ejpam-3003	319	9	,	,	PUNCT
ejpam-3003	319	10	m	m	PROPN
ejpam-3003	319	11	−→∞	−→∞	PROPN
ejpam-3003	319	12	,	,	PUNCT
ejpam-3003	319	13	(	(	PUNCT
ejpam-3003	319	14	3.28	3.28	NUM
ejpam-3003	319	15	)	)	PUNCT
ejpam-3003	319	16	|u′m|ρ−1u′m	|u′m|ρ−1u′m	NOUN
ejpam-3003	319	17	→	→	SYM
ejpam-3003	319	18	χ3	χ3	NOUN
ejpam-3003	319	19	in	in	ADP
ejpam-3003	319	20	l	l	PROPN
ejpam-3003	319	21	∞(0,∞;l	∞(0,∞;l	NOUN
ejpam-3003	319	22	ρ+1	ρ+1	NOUN
ejpam-3003	319	23	ρ	ρ	PROPN
ejpam-3003	319	24	(	(	PUNCT
ejpam-3003	319	25	ω	ω	NOUN
ejpam-3003	319	26	)	)	PUNCT
ejpam-3003	319	27	)	)	PUNCT
ejpam-3003	319	28	weakly	weakly	ADJ
ejpam-3003	319	29	star	star	NOUN
ejpam-3003	319	30	,	,	PUNCT
ejpam-3003	319	31	m	m	VERB
ejpam-3003	319	32	−→∞.	−→∞.	NOUN
ejpam-3003	319	33	(	(	PUNCT
ejpam-3003	319	34	3.29	3.29	NUM
ejpam-3003	319	35	)	)	PUNCT
ejpam-3003	319	36	since	since	SCONJ
ejpam-3003	319	37	h1	h1	PROPN
ejpam-3003	319	38	γ0	γ0	PROPN
ejpam-3003	319	39	(	(	PUNCT
ejpam-3003	319	40	ω	ω	NOUN
ejpam-3003	319	41	)	)	PUNCT
ejpam-3003	319	42	↪	↪	PROPN
ejpam-3003	319	43	→	→	SYM
ejpam-3003	319	44	l2(ω	l2(ω	NOUN
ejpam-3003	319	45	)	)	PUNCT
ejpam-3003	319	46	are	be	AUX
ejpam-3003	319	47	compact(see	compact(see	VERB
ejpam-3003	319	48	[	[	X
ejpam-3003	319	49	25	25	NUM
ejpam-3003	319	50	]	]	PUNCT
ejpam-3003	319	51	for	for	ADP
ejpam-3003	319	52	details	detail	NOUN
ejpam-3003	319	53	)	)	PUNCT
ejpam-3003	319	54	,	,	PUNCT
ejpam-3003	319	55	we	we	PRON
ejpam-3003	319	56	have	have	VERB
ejpam-3003	319	57	,	,	PUNCT
ejpam-3003	319	58	thanks	thank	NOUN
ejpam-3003	319	59	to	to	ADP
ejpam-3003	319	60	aubin	aubin	PROPN
ejpam-3003	319	61	-	-	PUNCT
ejpam-3003	319	62	lions	lion	NOUN
ejpam-3003	319	63	theorem	theorem	VERB
ejpam-3003	319	64	,	,	PUNCT
ejpam-3003	319	65	that	that	SCONJ
ejpam-3003	319	66	um	um	INTJ
ejpam-3003	319	67	→	→	SYM
ejpam-3003	319	68	u	u	PROPN
ejpam-3003	319	69	in	in	ADP
ejpam-3003	319	70	l2(0,∞;l2(ω	l2(0,∞;l2(ω	PROPN
ejpam-3003	319	71	)	)	PUNCT
ejpam-3003	319	72	)	)	PUNCT
ejpam-3003	320	1	strongly	strongly	ADV
ejpam-3003	320	2	,	,	PUNCT
ejpam-3003	320	3	m	m	PROPN
ejpam-3003	320	4	−→∞	−→∞	PROPN
ejpam-3003	320	5	,	,	PUNCT
ejpam-3003	320	6	(	(	PUNCT
ejpam-3003	320	7	3.30	3.30	NUM
ejpam-3003	320	8	)	)	PUNCT
ejpam-3003	320	9	and	and	CCONJ
ejpam-3003	320	10	consequently	consequently	ADV
ejpam-3003	320	11	,	,	PUNCT
ejpam-3003	320	12	making	make	VERB
ejpam-3003	320	13	use	use	NOUN
ejpam-3003	320	14	of	of	ADP
ejpam-3003	320	15	the	the	DET
ejpam-3003	320	16	lemma	lemma	PROPN
ejpam-3003	320	17	1.3	1.3	NUM
ejpam-3003	320	18	in	in	ADP
ejpam-3003	320	19	[	[	X
ejpam-3003	320	20	30	30	NUM
ejpam-3003	320	21	]	]	PUNCT
ejpam-3003	320	22	,	,	PUNCT
ejpam-3003	320	23	we	we	PRON
ejpam-3003	320	24	deduce	deduce	VERB
ejpam-3003	320	25	|um|p−1um	|um|p−1um	NOUN
ejpam-3003	320	26	→	→	SYM
ejpam-3003	320	27	χ2	χ2	NOUN
ejpam-3003	320	28	=	=	PUNCT
ejpam-3003	320	29	|u|p−1u	|u|p−1u	NOUN
ejpam-3003	320	30	in	in	ADP
ejpam-3003	320	31	l∞(0,∞;l	l∞(0,∞;l	PROPN
ejpam-3003	321	1	p+1	p+1	NOUN
ejpam-3003	321	2	p	p	PROPN
ejpam-3003	321	3	(	(	PUNCT
ejpam-3003	321	4	ω	ω	NOUN
ejpam-3003	321	5	)	)	PUNCT
ejpam-3003	321	6	)	)	PUNCT
ejpam-3003	321	7	weakly	weakly	ADJ
ejpam-3003	321	8	star	star	NOUN
ejpam-3003	321	9	,	,	PUNCT
ejpam-3003	321	10	m	m	VERB
ejpam-3003	321	11	−→∞.	−→∞.	NOUN
ejpam-3003	321	12	(	(	PUNCT
ejpam-3003	321	13	3.31	3.31	NUM
ejpam-3003	321	14	)	)	PUNCT
ejpam-3003	321	15	from	from	ADP
ejpam-3003	321	16	the	the	DET
ejpam-3003	321	17	trace	trace	NOUN
ejpam-3003	321	18	theorem	theorem	NOUN
ejpam-3003	321	19	and	and	CCONJ
ejpam-3003	321	20	(	(	PUNCT
ejpam-3003	321	21	3.25	3.25	NUM
ejpam-3003	321	22	)	)	PUNCT
ejpam-3003	321	23	,	,	PUNCT
ejpam-3003	321	24	we	we	PRON
ejpam-3003	321	25	deduce	deduce	VERB
ejpam-3003	321	26	that	that	SCONJ
ejpam-3003	321	27	∂um	∂um	PROPN
ejpam-3003	321	28	∂ν	∂ν	PROPN
ejpam-3003	321	29	∈	∈	PROPN
ejpam-3003	321	30	l∞(0,∞;h	l∞(0,∞;h	NOUN
ejpam-3003	321	31	−	−	NOUN
ejpam-3003	321	32	1	1	NUM
ejpam-3003	321	33	2	2	NUM
ejpam-3003	321	34	γ0	γ0	NOUN
ejpam-3003	321	35	(	(	PUNCT
ejpam-3003	321	36	ω	ω	NOUN
ejpam-3003	321	37	)	)	PUNCT
ejpam-3003	321	38	)	)	PUNCT
ejpam-3003	321	39	,	,	PUNCT
ejpam-3003	321	40	which	which	PRON
ejpam-3003	321	41	implies	imply	VERB
ejpam-3003	321	42	that	that	SCONJ
ejpam-3003	321	43	|u′m|q−1u′m	|u′m|q−1u′m	PROPN
ejpam-3003	321	44	=	=	PUNCT
ejpam-3003	321	45	−∂um	−∂um	PROPN
ejpam-3003	321	46	∂ν	∂ν	PROPN
ejpam-3003	321	47	+	+	CCONJ
ejpam-3003	321	48	∫	∫	PROPN
ejpam-3003	321	49	t	t	PROPN
ejpam-3003	321	50	0	0	NUM
ejpam-3003	321	51	g(t−	g(t−	PROPN
ejpam-3003	321	52	s)∂um	s)∂um	X
ejpam-3003	321	53	∂ν	∂ν	X
ejpam-3003	321	54	(	(	PUNCT
ejpam-3003	321	55	s)ds→	s)ds→	NOUN
ejpam-3003	321	56	−∂u	−∂u	NUM
ejpam-3003	321	57	∂ν	∂ν	PROPN
ejpam-3003	322	1	+	+	CCONJ
ejpam-3003	322	2	∫	∫	PROPN
ejpam-3003	322	3	t	t	PROPN
ejpam-3003	322	4	0	0	NUM
ejpam-3003	322	5	g(t−	g(t−	PROPN
ejpam-3003	322	6	s)∂u	s)∂u	ADJ
ejpam-3003	322	7	∂ν	∂ν	PROPN
ejpam-3003	322	8	(	(	PUNCT
ejpam-3003	322	9	s)ds	s)ds	PROPN
ejpam-3003	322	10	=	=	SYM
ejpam-3003	322	11	|u′|q−1u′	|u′|q−1u′	PROPN
ejpam-3003	322	12	in	in	ADP
ejpam-3003	322	13	l∞(0,∞;h	l∞(0,∞;h	ADJ
ejpam-3003	322	14	−	−	PROPN
ejpam-3003	322	15	1	1	NUM
ejpam-3003	322	16	2	2	NUM
ejpam-3003	322	17	γ0	γ0	NOUN
ejpam-3003	322	18	(	(	PUNCT
ejpam-3003	322	19	ω	ω	NOUN
ejpam-3003	322	20	)	)	PUNCT
ejpam-3003	322	21	)	)	PUNCT
ejpam-3003	322	22	weakly	weakly	ADJ
ejpam-3003	322	23	star	star	NOUN
ejpam-3003	322	24	,	,	PUNCT
ejpam-3003	322	25	m	m	VERB
ejpam-3003	322	26	−→∞.	−→∞.	NOUN
ejpam-3003	322	27	(	(	PUNCT
ejpam-3003	322	28	3.32	3.32	NUM
ejpam-3003	322	29	)	)	PUNCT
ejpam-3003	322	30	combining	combine	VERB
ejpam-3003	322	31	(	(	PUNCT
ejpam-3003	322	32	3.27	3.27	NUM
ejpam-3003	322	33	)	)	PUNCT
ejpam-3003	322	34	and	and	CCONJ
ejpam-3003	322	35	the	the	DET
ejpam-3003	322	36	above	above	ADJ
ejpam-3003	322	37	convergence	convergence	NOUN
ejpam-3003	322	38	,	,	PUNCT
ejpam-3003	322	39	we	we	PRON
ejpam-3003	322	40	have	have	VERB
ejpam-3003	322	41	|u′m|q−1u′m	|u′m|q−1u′m	NOUN
ejpam-3003	322	42	→	→	SYM
ejpam-3003	322	43	χ1	χ1	NOUN
ejpam-3003	322	44	=	=	PUNCT
ejpam-3003	322	45	|u′|q−1u′	|u′|q−1u′	PROPN
ejpam-3003	322	46	in	in	ADP
ejpam-3003	322	47	l	l	PROPN
ejpam-3003	322	48	q+1	q+1	X
ejpam-3003	322	49	q	q	X
ejpam-3003	322	50	(	(	PUNCT
ejpam-3003	322	51	0,∞;l	0,∞;l	NUM
ejpam-3003	322	52	q+1	q+1	NUM
ejpam-3003	322	53	q	q	X
ejpam-3003	322	54	(	(	PUNCT
ejpam-3003	322	55	γ1	γ1	PROPN
ejpam-3003	322	56	)	)	PUNCT
ejpam-3003	322	57	)	)	PUNCT
ejpam-3003	323	1	weakly	weakly	ADV
ejpam-3003	323	2	,	,	PUNCT
ejpam-3003	323	3	m	m	PROPN
ejpam-3003	323	4	−→∞	−→∞	PROPN
ejpam-3003	323	5	,	,	PUNCT
ejpam-3003	323	6	(	(	PUNCT
ejpam-3003	323	7	3.33	3.33	NUM
ejpam-3003	323	8	)	)	PUNCT
ejpam-3003	323	9	passing	pass	VERB
ejpam-3003	323	10	to	to	ADP
ejpam-3003	323	11	the	the	DET
ejpam-3003	323	12	limit	limit	NOUN
ejpam-3003	323	13	in	in	ADP
ejpam-3003	323	14	(	(	PUNCT
ejpam-3003	323	15	3.4	3.4	NUM
ejpam-3003	323	16	)	)	PUNCT
ejpam-3003	323	17	and	and	CCONJ
ejpam-3003	323	18	making	make	VERB
ejpam-3003	323	19	use	use	NOUN
ejpam-3003	323	20	of	of	ADP
ejpam-3003	323	21	(	(	PUNCT
ejpam-3003	323	22	3.25)-(3.27	3.25)-(3.27	NUM
ejpam-3003	323	23	)	)	PUNCT
ejpam-3003	323	24	,	,	PUNCT
ejpam-3003	323	25	(	(	PUNCT
ejpam-3003	323	26	3.29	3.29	NUM
ejpam-3003	323	27	)	)	PUNCT
ejpam-3003	323	28	,	,	PUNCT
ejpam-3003	323	29	(	(	PUNCT
ejpam-3003	323	30	3.31	3.31	NUM
ejpam-3003	323	31	)	)	PUNCT
ejpam-3003	323	32	and	and	CCONJ
ejpam-3003	323	33	(	(	PUNCT
ejpam-3003	323	34	3.33	3.33	NUM
ejpam-3003	323	35	)	)	PUNCT
ejpam-3003	323	36	,	,	PUNCT
ejpam-3003	323	37	we	we	PRON
ejpam-3003	323	38	obtain	obtain	VERB
ejpam-3003	323	39	1	1	NUM
ejpam-3003	323	40	ρ	ρ	NOUN
ejpam-3003	323	41	(	(	PUNCT
ejpam-3003	323	42	χ3	χ3	PROPN
ejpam-3003	323	43	,	,	PUNCT
ejpam-3003	323	44	wj	wj	PROPN
ejpam-3003	323	45	)	)	PUNCT
ejpam-3003	324	1	+	+	CCONJ
ejpam-3003	324	2	∫	∫	PROPN
ejpam-3003	324	3	t	t	NOUN
ejpam-3003	324	4	0	0	NUM
ejpam-3003	324	5	b1(u	b1(u	NOUN
ejpam-3003	324	6	,	,	PUNCT
ejpam-3003	324	7	wj)ds+	wj)ds+	ADJ
ejpam-3003	324	8	∫	∫	PROPN
ejpam-3003	324	9	t	t	PROPN
ejpam-3003	324	10	0	0	NUM
ejpam-3003	325	1	b2(u	b2(u	PROPN
ejpam-3003	325	2	,	,	PUNCT
ejpam-3003	325	3	wj)ds	wj)ds	PROPN
ejpam-3003	325	4	+	+	CCONJ
ejpam-3003	325	5	∫	∫	PROPN
ejpam-3003	325	6	t	t	PROPN
ejpam-3003	325	7	0	0	NUM
ejpam-3003	325	8	(	(	PUNCT
ejpam-3003	325	9	|u′|q−1u′	|u′|q−1u′	PROPN
ejpam-3003	325	10	,	,	PUNCT
ejpam-3003	325	11	wj)γ1ds−	wj)γ1ds−	VERB
ejpam-3003	325	12	∫	∫	PROPN
ejpam-3003	325	13	t	t	PROPN
ejpam-3003	325	14	0	0	NUM
ejpam-3003	325	15	(	(	PUNCT
ejpam-3003	325	16	|u|p−1u	|u|p−1u	INTJ
ejpam-3003	325	17	,	,	PUNCT
ejpam-3003	325	18	wj)ds	wj)ds	X
ejpam-3003	325	19	=	=	SYM
ejpam-3003	325	20	1	1	NUM
ejpam-3003	325	21	ρ	ρ	NOUN
ejpam-3003	325	22	(	(	PUNCT
ejpam-3003	325	23	|u1|ρ−1u1	|u1|ρ−1u1	NOUN
ejpam-3003	325	24	,	,	PUNCT
ejpam-3003	325	25	wj	wj	PROPN
ejpam-3003	325	26	)	)	PUNCT
ejpam-3003	325	27	.	.	PUNCT
ejpam-3003	326	1	(	(	PUNCT
ejpam-3003	326	2	3.34	3.34	NUM
ejpam-3003	326	3	)	)	PUNCT
ejpam-3003	326	4	since	since	SCONJ
ejpam-3003	326	5	{	{	PUNCT
ejpam-3003	326	6	wj(x	wj(x	PROPN
ejpam-3003	326	7	)	)	PUNCT
ejpam-3003	326	8	}	}	PUNCT
ejpam-3003	326	9	is	be	AUX
ejpam-3003	326	10	a	a	DET
ejpam-3003	326	11	basic	basic	ADJ
ejpam-3003	326	12	of	of	ADP
ejpam-3003	326	13	h1	h1	PROPN
ejpam-3003	326	14	γ0	γ0	PROPN
ejpam-3003	326	15	(	(	PUNCT
ejpam-3003	326	16	ω	ω	NOUN
ejpam-3003	326	17	)	)	PUNCT
ejpam-3003	326	18	∩	∩	NOUN
ejpam-3003	326	19	lq+1(γ1	lq+1(γ1	NOUN
ejpam-3003	326	20	)	)	PUNCT
ejpam-3003	326	21	∩	∩	NOUN
ejpam-3003	326	22	lρ+1(ω	lρ+1(ω	PROPN
ejpam-3003	326	23	)	)	PUNCT
ejpam-3003	326	24	,	,	PUNCT
ejpam-3003	326	25	then	then	ADV
ejpam-3003	326	26	for	for	ADP
ejpam-3003	326	27	all	all	DET
ejpam-3003	326	28	t	t	PROPN
ejpam-3003	326	29	>	>	X
ejpam-3003	326	30	0	0	NUM
ejpam-3003	326	31	,	,	PUNCT
ejpam-3003	326	32	multiplying	multiply	VERB
ejpam-3003	326	33	(	(	PUNCT
ejpam-3003	326	34	3.34	3.34	NUM
ejpam-3003	326	35	)	)	PUNCT
ejpam-3003	326	36	by	by	ADP
ejpam-3003	326	37	d′mj(t	d′mj(t	PROPN
ejpam-3003	326	38	)	)	PUNCT
ejpam-3003	326	39	,	,	PUNCT
ejpam-3003	326	40	and	and	CCONJ
ejpam-3003	326	41	summing	sum	VERB
ejpam-3003	326	42	for	for	ADP
ejpam-3003	326	43	j	j	PROPN
ejpam-3003	326	44	=	=	SYM
ejpam-3003	326	45	1	1	NUM
ejpam-3003	326	46	,	,	PUNCT
ejpam-3003	326	47	·	·	PUNCT
ejpam-3003	326	48	·	·	PUNCT
ejpam-3003	326	49	·	·	PUNCT
ejpam-3003	326	50	·	·	PUNCT
ejpam-3003	326	51	·	·	PUNCT
ejpam-3003	326	52	·	·	PUNCT
ejpam-3003	326	53	,	,	PUNCT
ejpam-3003	326	54	then	then	ADV
ejpam-3003	326	55	we	we	PRON
ejpam-3003	326	56	have	have	VERB
ejpam-3003	326	57	1	1	NUM
ejpam-3003	326	58	ρ	ρ	NOUN
ejpam-3003	326	59	(	(	PUNCT
ejpam-3003	326	60	χ3	χ3	PROPN
ejpam-3003	326	61	,	,	PUNCT
ejpam-3003	326	62	u	u	NOUN
ejpam-3003	326	63	′	′	NOUN
ejpam-3003	326	64	)	)	PUNCT
ejpam-3003	327	1	+	+	CCONJ
ejpam-3003	327	2	∫	∫	PROPN
ejpam-3003	327	3	t	t	NOUN
ejpam-3003	327	4	0	0	NUM
ejpam-3003	327	5	b1(u	b1(u	NOUN
ejpam-3003	327	6	,	,	PUNCT
ejpam-3003	327	7	u′)ds+	u′)ds+	PROPN
ejpam-3003	327	8	∫	∫	PROPN
ejpam-3003	327	9	t	t	PROPN
ejpam-3003	327	10	0	0	NUM
ejpam-3003	327	11	b2(u	b2(u	PROPN
ejpam-3003	327	12	,	,	PUNCT
ejpam-3003	327	13	u′)ds	u′)ds	PROPN
ejpam-3003	327	14	+	+	CCONJ
ejpam-3003	327	15	∫	∫	PROPN
ejpam-3003	327	16	t	t	PROPN
ejpam-3003	327	17	0	0	NUM
ejpam-3003	327	18	(	(	PUNCT
ejpam-3003	327	19	|u′|q−1u′	|u′|q−1u′	PROPN
ejpam-3003	327	20	,	,	PUNCT
ejpam-3003	327	21	u′)γ1ds−	u′)γ1ds−	PROPN
ejpam-3003	327	22	∫	∫	PROPN
ejpam-3003	327	23	t	t	PROPN
ejpam-3003	327	24	0	0	NUM
ejpam-3003	327	25	(	(	PUNCT
ejpam-3003	327	26	|u|p−1u	|u|p−1u	INTJ
ejpam-3003	327	27	,	,	PUNCT
ejpam-3003	327	28	u′)ds	u′)ds	ADJ
ejpam-3003	327	29	=	=	SYM
ejpam-3003	327	30	1	1	NUM
ejpam-3003	327	31	ρ	ρ	NOUN
ejpam-3003	327	32	(	(	PUNCT
ejpam-3003	327	33	|u1|ρ−1u1	|u1|ρ−1u1	NOUN
ejpam-3003	327	34	,	,	PUNCT
ejpam-3003	327	35	u	u	NOUN
ejpam-3003	327	36	′	′	NOUN
ejpam-3003	327	37	)	)	PUNCT
ejpam-3003	327	38	.	.	PUNCT
ejpam-3003	328	1	(	(	PUNCT
ejpam-3003	328	2	3.35	3.35	NUM
ejpam-3003	328	3	)	)	PUNCT
ejpam-3003	328	4	in	in	ADP
ejpam-3003	328	5	what	what	PRON
ejpam-3003	328	6	follows	follow	VERB
ejpam-3003	328	7	,	,	PUNCT
ejpam-3003	328	8	multiplying	multiply	VERB
ejpam-3003	328	9	(	(	PUNCT
ejpam-3003	328	10	3.4	3.4	NUM
ejpam-3003	328	11	)	)	PUNCT
ejpam-3003	328	12	by	by	ADP
ejpam-3003	328	13	d′mj(t	d′mj(t	PROPN
ejpam-3003	328	14	)	)	PUNCT
ejpam-3003	328	15	,	,	PUNCT
ejpam-3003	328	16	and	and	CCONJ
ejpam-3003	328	17	summing	sum	VERB
ejpam-3003	328	18	for	for	ADP
ejpam-3003	328	19	j	j	PROPN
ejpam-3003	328	20	=	=	SYM
ejpam-3003	328	21	1	1	NUM
ejpam-3003	328	22	,	,	PUNCT
ejpam-3003	328	23	·	·	PUNCT
ejpam-3003	328	24	·	·	PUNCT
ejpam-3003	328	25	·	·	PUNCT
ejpam-3003	328	26	,	,	PUNCT
ejpam-3003	328	27	m	m	PROPN
ejpam-3003	328	28	,	,	PUNCT
ejpam-3003	328	29	then	then	ADV
ejpam-3003	328	30	we	we	PRON
ejpam-3003	328	31	obtain	obtain	VERB
ejpam-3003	328	32	1	1	NUM
ejpam-3003	328	33	ρ	ρ	NOUN
ejpam-3003	328	34	(	(	PUNCT
ejpam-3003	328	35	|u′m|ρ−1u′m	|u′m|ρ−1u′m	PROPN
ejpam-3003	328	36	,	,	PUNCT
ejpam-3003	328	37	u	u	NOUN
ejpam-3003	328	38	′	′	NOUN
ejpam-3003	328	39	m	m	VERB
ejpam-3003	328	40	)	)	PUNCT
ejpam-3003	329	1	+	+	CCONJ
ejpam-3003	330	1	∫	∫	PROPN
ejpam-3003	330	2	t	t	PROPN
ejpam-3003	330	3	0	0	NUM
ejpam-3003	330	4	b1(um	b1(um	NUM
ejpam-3003	330	5	,	,	PUNCT
ejpam-3003	330	6	u	u	NOUN
ejpam-3003	330	7	′	′	NOUN
ejpam-3003	330	8	m)ds+	m)ds+	ADJ
ejpam-3003	330	9	∫	∫	PROPN
ejpam-3003	331	1	t	t	PROPN
ejpam-3003	331	2	0	0	NUM
ejpam-3003	331	3	(	(	PUNCT
ejpam-3003	331	4	|u′m|q−1u′m	|u′m|q−1u′m	NOUN
ejpam-3003	331	5	,	,	PUNCT
ejpam-3003	331	6	u	u	NOUN
ejpam-3003	331	7	′	′	NOUN
ejpam-3003	331	8	m)γ1ds	m)γ1ds	PROPN
ejpam-3003	331	9	h.f	h.f	PROPN
ejpam-3003	331	10	.	.	PROPN
ejpam-3003	331	11	di	di	PROPN
ejpam-3003	331	12	,	,	PUNCT
ejpam-3003	331	13	y.d	y.d	PROPN
ejpam-3003	331	14	.	.	PROPN
ejpam-3003	331	15	shang	shang	PROPN
ejpam-3003	331	16	/	/	SYM
ejpam-3003	331	17	eur	eur	PROPN
ejpam-3003	331	18	.	.	PUNCT
ejpam-3003	332	1	j.	j.	PROPN
ejpam-3003	332	2	pure	pure	PROPN
ejpam-3003	332	3	appl	appl	PROPN
ejpam-3003	332	4	.	.	PROPN
ejpam-3003	332	5	math	math	PROPN
ejpam-3003	332	6	,	,	PUNCT
ejpam-3003	332	7	10	10	NUM
ejpam-3003	332	8	(	(	PUNCT
ejpam-3003	332	9	4	4	NUM
ejpam-3003	332	10	)	)	PUNCT
ejpam-3003	332	11	(	(	PUNCT
ejpam-3003	332	12	2017	2017	NUM
ejpam-3003	332	13	)	)	PUNCT
ejpam-3003	332	14	,	,	PUNCT
ejpam-3003	332	15	668	668	NUM
ejpam-3003	332	16	-	-	SYM
ejpam-3003	332	17	701	701	NUM
ejpam-3003	332	18	682	682	NUM
ejpam-3003	332	19	+	+	NUM
ejpam-3003	332	20	∫	∫	PROPN
ejpam-3003	332	21	t	t	PROPN
ejpam-3003	332	22	0	0	NUM
ejpam-3003	333	1	b2(um	b2(um	PROPN
ejpam-3003	333	2	,	,	PUNCT
ejpam-3003	333	3	u	u	NOUN
ejpam-3003	333	4	′	′	PROPN
ejpam-3003	333	5	m)ds−	m)ds−	PROPN
ejpam-3003	333	6	∫	∫	PROPN
ejpam-3003	333	7	t	t	NOUN
ejpam-3003	333	8	0	0	NUM
ejpam-3003	333	9	(	(	PUNCT
ejpam-3003	333	10	|um|p−1um	|um|p−1um	PROPN
ejpam-3003	333	11	,	,	PUNCT
ejpam-3003	333	12	u	u	NOUN
ejpam-3003	333	13	′	′	NOUN
ejpam-3003	334	1	m)ds	m)ds	NOUN
ejpam-3003	334	2	=	=	NOUN
ejpam-3003	334	3	1	1	NUM
ejpam-3003	334	4	ρ	ρ	NOUN
ejpam-3003	334	5	(	(	PUNCT
ejpam-3003	334	6	|u′m(0)|ρ−1u′m(0	|u′m(0)|ρ−1u′m(0	NOUN
ejpam-3003	334	7	)	)	PUNCT
ejpam-3003	334	8	,	,	PUNCT
ejpam-3003	334	9	u′m	u′m	NOUN
ejpam-3003	334	10	)	)	PUNCT
ejpam-3003	334	11	.	.	PUNCT
ejpam-3003	335	1	(	(	PUNCT
ejpam-3003	335	2	3.36	3.36	NUM
ejpam-3003	335	3	)	)	PUNCT
ejpam-3003	335	4	taking	take	VERB
ejpam-3003	335	5	m→∞	m→∞	NOUN
ejpam-3003	335	6	in	in	ADP
ejpam-3003	335	7	(	(	PUNCT
ejpam-3003	335	8	3.36	3.36	NUM
ejpam-3003	335	9	)	)	PUNCT
ejpam-3003	335	10	,	,	PUNCT
ejpam-3003	335	11	it	it	PRON
ejpam-3003	335	12	follows	follow	VERB
ejpam-3003	335	13	that	that	SCONJ
ejpam-3003	335	14	1	1	NUM
ejpam-3003	335	15	ρ	ρ	NUM
ejpam-3003	335	16	lim	lim	PROPN
ejpam-3003	335	17	m→∞	m→∞	NOUN
ejpam-3003	335	18	(	(	PUNCT
ejpam-3003	335	19	|u′m|ρ−1u′m	|u′m|ρ−1u′m	NOUN
ejpam-3003	335	20	,	,	PUNCT
ejpam-3003	335	21	u	u	NOUN
ejpam-3003	335	22	′	′	NOUN
ejpam-3003	335	23	m	m	VERB
ejpam-3003	335	24	)	)	PUNCT
ejpam-3003	336	1	+	+	CCONJ
ejpam-3003	336	2	∫	∫	PROPN
ejpam-3003	336	3	t	t	NOUN
ejpam-3003	336	4	0	0	NUM
ejpam-3003	336	5	b1(u	b1(u	NOUN
ejpam-3003	336	6	,	,	PUNCT
ejpam-3003	336	7	u′)ds+	u′)ds+	PROPN
ejpam-3003	336	8	∫	∫	PROPN
ejpam-3003	336	9	t	t	PROPN
ejpam-3003	336	10	0	0	NUM
ejpam-3003	336	11	(	(	PUNCT
ejpam-3003	336	12	|u′|q−1u′	|u′|q−1u′	PROPN
ejpam-3003	336	13	,	,	PUNCT
ejpam-3003	336	14	u′)γ1ds	u′)γ1ds	NOUN
ejpam-3003	336	15	+	+	CCONJ
ejpam-3003	336	16	∫	∫	PROPN
ejpam-3003	336	17	t	t	PROPN
ejpam-3003	336	18	0	0	NUM
ejpam-3003	336	19	b2(u	b2(u	PROPN
ejpam-3003	336	20	,	,	PUNCT
ejpam-3003	336	21	u′)ds−	u′)ds−	PROPN
ejpam-3003	336	22	∫	∫	PROPN
ejpam-3003	336	23	t	t	PROPN
ejpam-3003	336	24	0	0	NUM
ejpam-3003	337	1	(	(	PUNCT
ejpam-3003	337	2	|u|p−1u	|u|p−1u	INTJ
ejpam-3003	337	3	,	,	PUNCT
ejpam-3003	337	4	u′)ds	u′)ds	ADJ
ejpam-3003	337	5	=	=	SYM
ejpam-3003	337	6	1	1	NUM
ejpam-3003	337	7	ρ	ρ	NOUN
ejpam-3003	337	8	(	(	PUNCT
ejpam-3003	337	9	|u1|ρ−1u1	|u1|ρ−1u1	NOUN
ejpam-3003	337	10	,	,	PUNCT
ejpam-3003	337	11	u	u	NOUN
ejpam-3003	337	12	′	′	NOUN
ejpam-3003	337	13	)	)	PUNCT
ejpam-3003	337	14	.	.	PUNCT
ejpam-3003	338	1	(	(	PUNCT
ejpam-3003	338	2	3.37	3.37	NUM
ejpam-3003	338	3	)	)	PUNCT
ejpam-3003	338	4	combining	combine	VERB
ejpam-3003	338	5	(	(	PUNCT
ejpam-3003	338	6	3.35	3.35	NUM
ejpam-3003	338	7	)	)	PUNCT
ejpam-3003	338	8	and	and	CCONJ
ejpam-3003	338	9	(	(	PUNCT
ejpam-3003	338	10	3.37	3.37	NUM
ejpam-3003	338	11	)	)	PUNCT
ejpam-3003	338	12	,	,	PUNCT
ejpam-3003	338	13	we	we	PRON
ejpam-3003	338	14	deduce	deduce	VERB
ejpam-3003	338	15	that	that	PRON
ejpam-3003	338	16	(	(	PUNCT
ejpam-3003	338	17	χ3	χ3	NOUN
ejpam-3003	338	18	,	,	PUNCT
ejpam-3003	338	19	u	u	NOUN
ejpam-3003	338	20	′	′	NOUN
ejpam-3003	338	21	)	)	PUNCT
ejpam-3003	339	1	=	=	SYM
ejpam-3003	339	2	lim	lim	PROPN
ejpam-3003	339	3	m→∞	m→∞	NOUN
ejpam-3003	339	4	(	(	PUNCT
ejpam-3003	339	5	|u′m|ρ−1u′m	|u′m|ρ−1u′m	NOUN
ejpam-3003	339	6	,	,	PUNCT
ejpam-3003	339	7	u	u	NOUN
ejpam-3003	339	8	′	′	NOUN
ejpam-3003	339	9	m	m	NOUN
ejpam-3003	339	10	)	)	PUNCT
ejpam-3003	339	11	.	.	PUNCT
ejpam-3003	340	1	(	(	PUNCT
ejpam-3003	340	2	3.38	3.38	NUM
ejpam-3003	340	3	)	)	PUNCT
ejpam-3003	340	4	on	on	ADP
ejpam-3003	340	5	the	the	DET
ejpam-3003	340	6	other	other	ADJ
ejpam-3003	340	7	hand	hand	NOUN
ejpam-3003	340	8	,	,	PUNCT
ejpam-3003	340	9	utilizing	utilize	VERB
ejpam-3003	340	10	the	the	DET
ejpam-3003	340	11	non	non	ADJ
ejpam-3003	340	12	-	-	ADJ
ejpam-3003	340	13	decreasing	decrease	VERB
ejpam-3003	340	14	monotonicity	monotonicity	NOUN
ejpam-3003	340	15	of	of	ADP
ejpam-3003	340	16	the	the	DET
ejpam-3003	340	17	function	function	NOUN
ejpam-3003	340	18	|s|ρ−1s	|s|ρ−1s	NOUN
ejpam-3003	340	19	,	,	PUNCT
ejpam-3003	340	20	s	s	PART
ejpam-3003	340	21	∈	∈	PROPN
ejpam-3003	340	22	r	r	NOUN
ejpam-3003	340	23	,	,	PUNCT
ejpam-3003	340	24	we	we	PRON
ejpam-3003	340	25	have	have	VERB
ejpam-3003	340	26	(	(	PUNCT
ejpam-3003	340	27	|u′m|ρ−1u′m	|u′m|ρ−1u′m	NOUN
ejpam-3003	340	28	−	−	PROPN
ejpam-3003	340	29	|ψ|ρ−1ψ	|ψ|ρ−1ψ	PROPN
ejpam-3003	340	30	,	,	PUNCT
ejpam-3003	340	31	u′m	u′m	VERB
ejpam-3003	340	32	−	−	NOUN
ejpam-3003	340	33	ψ	ψ	NOUN
ejpam-3003	340	34	)	)	PUNCT
ejpam-3003	340	35	≥	≥	NOUN
ejpam-3003	340	36	0	0	NUM
ejpam-3003	340	37	,	,	PUNCT
ejpam-3003	340	38	(	(	PUNCT
ejpam-3003	340	39	3.39	3.39	NUM
ejpam-3003	340	40	)	)	PUNCT
ejpam-3003	340	41	for	for	ADP
ejpam-3003	340	42	all	all	DET
ejpam-3003	340	43	ψ	ψ	DET
ejpam-3003	340	44	∈	∈	PROPN
ejpam-3003	340	45	lρ+1(ω	lρ+1(ω	PROPN
ejpam-3003	340	46	)	)	PUNCT
ejpam-3003	340	47	.	.	PUNCT
ejpam-3003	341	1	thus	thus	ADV
ejpam-3003	341	2	,	,	PUNCT
ejpam-3003	341	3	we	we	PRON
ejpam-3003	341	4	get	get	VERB
ejpam-3003	341	5	from	from	ADP
ejpam-3003	341	6	the	the	DET
ejpam-3003	341	7	inequality	inequality	NOUN
ejpam-3003	341	8	(	(	PUNCT
ejpam-3003	341	9	3.39	3.39	NUM
ejpam-3003	341	10	)	)	PUNCT
ejpam-3003	341	11	that	that	SCONJ
ejpam-3003	341	12	(	(	PUNCT
ejpam-3003	341	13	|u′m|ρ−1u′m	|u′m|ρ−1u′m	NOUN
ejpam-3003	341	14	,	,	PUNCT
ejpam-3003	341	15	ψ	ψ	NOUN
ejpam-3003	341	16	)	)	PUNCT
ejpam-3003	341	17	+	+	CCONJ
ejpam-3003	341	18	(	(	PUNCT
ejpam-3003	341	19	|ψ|ρ−1ψ	|ψ|ρ−1ψ	PROPN
ejpam-3003	341	20	,	,	PUNCT
ejpam-3003	341	21	u′m	u′m	NOUN
ejpam-3003	341	22	−	−	NOUN
ejpam-3003	341	23	ψ	ψ	NOUN
ejpam-3003	341	24	)	)	PUNCT
ejpam-3003	341	25	≤	≤	NOUN
ejpam-3003	341	26	(	(	PUNCT
ejpam-3003	341	27	|u′m|ρ−1u′m	|u′m|ρ−1u′m	NOUN
ejpam-3003	341	28	,	,	PUNCT
ejpam-3003	341	29	u	u	NOUN
ejpam-3003	341	30	′	′	NOUN
ejpam-3003	341	31	m	m	NOUN
ejpam-3003	341	32	)	)	PUNCT
ejpam-3003	341	33	.	.	PUNCT
ejpam-3003	342	1	(	(	PUNCT
ejpam-3003	342	2	3.40	3.40	NUM
ejpam-3003	342	3	)	)	PUNCT
ejpam-3003	342	4	passing	pass	VERB
ejpam-3003	342	5	to	to	ADP
ejpam-3003	342	6	the	the	DET
ejpam-3003	342	7	limit	limit	NOUN
ejpam-3003	342	8	in	in	ADP
ejpam-3003	342	9	(	(	PUNCT
ejpam-3003	342	10	3.40	3.40	NUM
ejpam-3003	342	11	)	)	PUNCT
ejpam-3003	342	12	as	as	ADP
ejpam-3003	342	13	m→∞	m→∞	NOUN
ejpam-3003	342	14	,	,	PUNCT
ejpam-3003	342	15	it	it	PRON
ejpam-3003	342	16	follows	follow	VERB
ejpam-3003	342	17	that	that	SCONJ
ejpam-3003	342	18	(	(	PUNCT
ejpam-3003	342	19	χ3	χ3	VERB
ejpam-3003	342	20	−	−	PROPN
ejpam-3003	342	21	|ψ|ρ−1ψ	|ψ|ρ−1ψ	PROPN
ejpam-3003	342	22	,	,	PUNCT
ejpam-3003	342	23	u′	u′	PRON
ejpam-3003	342	24	−	−	NOUN
ejpam-3003	342	25	ψ	ψ	SYM
ejpam-3003	342	26	)	)	PUNCT
ejpam-3003	342	27	≥	≥	NOUN
ejpam-3003	342	28	0	0	NUM
ejpam-3003	342	29	.	.	PUNCT
ejpam-3003	343	1	(	(	PUNCT
ejpam-3003	343	2	3.41	3.41	NUM
ejpam-3003	343	3	)	)	PUNCT
ejpam-3003	343	4	in	in	ADP
ejpam-3003	343	5	order	order	NOUN
ejpam-3003	343	6	to	to	PART
ejpam-3003	343	7	prove	prove	VERB
ejpam-3003	343	8	χ3	χ3	NOUN
ejpam-3003	343	9	=	=	VERB
ejpam-3003	344	1	|u′|ρ−1u′	|u′|ρ−1u′	NOUN
ejpam-3003	344	2	from	from	ADP
ejpam-3003	344	3	(	(	PUNCT
ejpam-3003	344	4	3.41	3.41	NUM
ejpam-3003	344	5	)	)	PUNCT
ejpam-3003	344	6	,	,	PUNCT
ejpam-3003	344	7	we	we	PRON
ejpam-3003	344	8	use	use	VERB
ejpam-3003	344	9	the	the	DET
ejpam-3003	344	10	semi	semi	NOUN
ejpam-3003	344	11	-	-	NOUN
ejpam-3003	344	12	continuity	continuity	NOUN
ejpam-3003	344	13	of	of	ADP
ejpam-3003	344	14	the	the	DET
ejpam-3003	344	15	function	function	NOUN
ejpam-3003	344	16	|s|ρ−1s	|s|ρ−1s	NOUN
ejpam-3003	344	17	,	,	PUNCT
ejpam-3003	344	18	s	s	NOUN
ejpam-3003	344	19	∈	∈	PROPN
ejpam-3003	344	20	r	r	NOUN
ejpam-3003	344	21	(	(	PUNCT
ejpam-3003	344	22	[	[	X
ejpam-3003	344	23	30	30	NUM
ejpam-3003	344	24	]	]	PUNCT
ejpam-3003	344	25	,	,	PUNCT
ejpam-3003	344	26	chapter	chapter	NOUN
ejpam-3003	344	27	2	2	NUM
ejpam-3003	344	28	)	)	PUNCT
ejpam-3003	344	29	.	.	PUNCT
ejpam-3003	345	1	let	let	VERB
ejpam-3003	345	2	ψ	ψ	VERB
ejpam-3003	345	3	=	=	PUNCT
ejpam-3003	345	4	u′	u′	PROPN
ejpam-3003	345	5	−	−	NOUN
ejpam-3003	345	6	µφ	µφ	NOUN
ejpam-3003	345	7	,	,	PUNCT
ejpam-3003	345	8	µ	µ	X
ejpam-3003	345	9	≥	≥	NOUN
ejpam-3003	345	10	0	0	NUM
ejpam-3003	345	11	and	and	CCONJ
ejpam-3003	345	12	∀	∀	NUM
ejpam-3003	345	13	φ	φ	PROPN
ejpam-3003	345	14	∈	∈	PROPN
ejpam-3003	345	15	lρ+1(ω	lρ+1(ω	PROPN
ejpam-3003	345	16	)	)	PUNCT
ejpam-3003	345	17	,	,	PUNCT
ejpam-3003	345	18	then	then	ADV
ejpam-3003	345	19	(	(	PUNCT
ejpam-3003	345	20	χ3	χ3	VERB
ejpam-3003	345	21	−	−	PROPN
ejpam-3003	345	22	|u′	|u′	NOUN
ejpam-3003	345	23	−	−	PROPN
ejpam-3003	345	24	µφ|ρ−1(u′	µφ|ρ−1(u′	NOUN
ejpam-3003	345	25	−	−	NUM
ejpam-3003	345	26	µφ	µφ	NOUN
ejpam-3003	345	27	)	)	PUNCT
ejpam-3003	345	28	,	,	PUNCT
ejpam-3003	345	29	φ	φ	NUM
ejpam-3003	345	30	)	)	PUNCT
ejpam-3003	345	31	≥	≥	NOUN
ejpam-3003	345	32	0	0	NUM
ejpam-3003	345	33	.	.	PUNCT
ejpam-3003	346	1	(	(	PUNCT
ejpam-3003	346	2	3.42	3.42	NUM
ejpam-3003	346	3	)	)	PUNCT
ejpam-3003	346	4	passing	pass	VERB
ejpam-3003	346	5	to	to	ADP
ejpam-3003	346	6	the	the	DET
ejpam-3003	346	7	limit	limit	NOUN
ejpam-3003	346	8	in	in	ADP
ejpam-3003	346	9	(	(	PUNCT
ejpam-3003	346	10	3.42	3.42	NUM
ejpam-3003	346	11	)	)	PUNCT
ejpam-3003	346	12	as	as	ADP
ejpam-3003	346	13	µ→	µ→	X
ejpam-3003	346	14	0	0	NUM
ejpam-3003	346	15	,	,	PUNCT
ejpam-3003	346	16	we	we	PRON
ejpam-3003	346	17	have	have	AUX
ejpam-3003	346	18	(	(	PUNCT
ejpam-3003	346	19	χ3	χ3	VERB
ejpam-3003	346	20	−	−	PROPN
ejpam-3003	346	21	|u′|ρ−1u′	|u′|ρ−1u′	PROPN
ejpam-3003	346	22	,	,	PUNCT
ejpam-3003	346	23	φ	φ	NUM
ejpam-3003	346	24	)	)	PUNCT
ejpam-3003	346	25	≥	≥	NOUN
ejpam-3003	346	26	0	0	NUM
ejpam-3003	346	27	,	,	PUNCT
ejpam-3003	346	28	∀	∀	NUM
ejpam-3003	346	29	φ	φ	PROPN
ejpam-3003	346	30	∈	∈	PROPN
ejpam-3003	346	31	lρ+1(ω	lρ+1(ω	PROPN
ejpam-3003	346	32	)	)	PUNCT
ejpam-3003	346	33	.	.	PUNCT
ejpam-3003	347	1	(	(	PUNCT
ejpam-3003	347	2	3.43	3.43	NUM
ejpam-3003	347	3	)	)	PUNCT
ejpam-3003	347	4	in	in	ADP
ejpam-3003	347	5	a	a	DET
ejpam-3003	347	6	similar	similar	ADJ
ejpam-3003	347	7	way	way	NOUN
ejpam-3003	347	8	,	,	PUNCT
ejpam-3003	347	9	let	let	VERB
ejpam-3003	347	10	ψ	ψ	X
ejpam-3003	347	11	=	=	PUNCT
ejpam-3003	347	12	u′	u′	PROPN
ejpam-3003	347	13	−	−	NOUN
ejpam-3003	347	14	µφ	µφ	NOUN
ejpam-3003	347	15	,	,	PUNCT
ejpam-3003	347	16	µ	µ	X
ejpam-3003	347	17	≤	≤	NOUN
ejpam-3003	347	18	0	0	NUM
ejpam-3003	347	19	and	and	CCONJ
ejpam-3003	347	20	∀	∀	NUM
ejpam-3003	347	21	φ	φ	PROPN
ejpam-3003	347	22	∈	∈	PROPN
ejpam-3003	347	23	lρ+1(ω	lρ+1(ω	PROPN
ejpam-3003	347	24	)	)	PUNCT
ejpam-3003	347	25	,	,	PUNCT
ejpam-3003	347	26	then	then	ADV
ejpam-3003	347	27	we	we	PRON
ejpam-3003	347	28	obtain	obtain	VERB
ejpam-3003	347	29	(	(	PUNCT
ejpam-3003	347	30	χ3	χ3	VERB
ejpam-3003	347	31	−	−	PROPN
ejpam-3003	347	32	|u′|ρ−1u′	|u′|ρ−1u′	PROPN
ejpam-3003	347	33	,	,	PUNCT
ejpam-3003	347	34	φ	φ	NOUN
ejpam-3003	347	35	)	)	PUNCT
ejpam-3003	347	36	≤	≤	NOUN
ejpam-3003	347	37	0	0	NUM
ejpam-3003	347	38	,	,	PUNCT
ejpam-3003	347	39	∀	∀	NUM
ejpam-3003	347	40	φ	φ	PROPN
ejpam-3003	347	41	∈	∈	PROPN
ejpam-3003	347	42	lρ+1(ω	lρ+1(ω	PROPN
ejpam-3003	347	43	)	)	PUNCT
ejpam-3003	347	44	.	.	PUNCT
ejpam-3003	348	1	(	(	PUNCT
ejpam-3003	348	2	3.44	3.44	NUM
ejpam-3003	348	3	)	)	PUNCT
ejpam-3003	348	4	from	from	ADP
ejpam-3003	348	5	the	the	DET
ejpam-3003	348	6	combination	combination	NOUN
ejpam-3003	348	7	of	of	ADP
ejpam-3003	348	8	(	(	PUNCT
ejpam-3003	348	9	3.43	3.43	NUM
ejpam-3003	348	10	)	)	PUNCT
ejpam-3003	348	11	and	and	CCONJ
ejpam-3003	348	12	(	(	PUNCT
ejpam-3003	348	13	3.44	3.44	NUM
ejpam-3003	348	14	)	)	PUNCT
ejpam-3003	348	15	,	,	PUNCT
ejpam-3003	348	16	we	we	PRON
ejpam-3003	348	17	see	see	VERB
ejpam-3003	348	18	that	that	DET
ejpam-3003	348	19	χ3	χ3	NOUN
ejpam-3003	348	20	=	=	PUNCT
ejpam-3003	348	21	|u′|ρ−1u′.	|u′|ρ−1u′.	NOUN
ejpam-3003	348	22	(	(	PUNCT
ejpam-3003	348	23	3.45	3.45	NUM
ejpam-3003	348	24	)	)	PUNCT
ejpam-3003	348	25	next	next	ADV
ejpam-3003	348	26	,	,	PUNCT
ejpam-3003	348	27	we	we	PRON
ejpam-3003	348	28	shall	shall	AUX
ejpam-3003	348	29	prove	prove	VERB
ejpam-3003	348	30	that	that	SCONJ
ejpam-3003	348	31	u	u	PRON
ejpam-3003	348	32	satisfies	satisfie	NOUN
ejpam-3003	348	33	(	(	PUNCT
ejpam-3003	348	34	2.13	2.13	NUM
ejpam-3003	348	35	)	)	PUNCT
ejpam-3003	348	36	.	.	PUNCT
ejpam-3003	349	1	from	from	ADP
ejpam-3003	349	2	the	the	DET
ejpam-3003	349	3	discussion	discussion	NOUN
ejpam-3003	349	4	above	above	ADV
ejpam-3003	349	5	,	,	PUNCT
ejpam-3003	349	6	we	we	PRON
ejpam-3003	349	7	obtain	obtain	VERB
ejpam-3003	349	8	for	for	ADP
ejpam-3003	349	9	each	each	DET
ejpam-3003	349	10	fixed	fix	VERB
ejpam-3003	349	11	t	t	PROPN
ejpam-3003	349	12	>	>	X
ejpam-3003	349	13	0	0	PUNCT
ejpam-3003	350	1	that	that	PRON
ejpam-3003	350	2	|(g	|(g	PROPN
ejpam-3003	350	3	◦	◦	VERB
ejpam-3003	350	4	∇u)(t)−	∇u)(t)−	PROPN
ejpam-3003	350	5	(	(	PUNCT
ejpam-3003	350	6	g	g	NOUN
ejpam-3003	350	7	◦	◦	VERB
ejpam-3003	350	8	∇um)(t)|	∇um)(t)|	ADJ
ejpam-3003	350	9	h.f	h.f	PROPN
ejpam-3003	350	10	.	.	PROPN
ejpam-3003	350	11	di	di	PROPN
ejpam-3003	350	12	,	,	PUNCT
ejpam-3003	350	13	y.d	y.d	PROPN
ejpam-3003	350	14	.	.	PROPN
ejpam-3003	350	15	shang	shang	PROPN
ejpam-3003	350	16	/	/	SYM
ejpam-3003	350	17	eur	eur	PROPN
ejpam-3003	350	18	.	.	PUNCT
ejpam-3003	351	1	j.	j.	PROPN
ejpam-3003	351	2	pure	pure	PROPN
ejpam-3003	351	3	appl	appl	PROPN
ejpam-3003	351	4	.	.	PROPN
ejpam-3003	351	5	math	math	PROPN
ejpam-3003	351	6	,	,	PUNCT
ejpam-3003	351	7	10	10	NUM
ejpam-3003	351	8	(	(	PUNCT
ejpam-3003	351	9	4	4	NUM
ejpam-3003	351	10	)	)	PUNCT
ejpam-3003	351	11	(	(	PUNCT
ejpam-3003	351	12	2017	2017	NUM
ejpam-3003	351	13	)	)	PUNCT
ejpam-3003	351	14	,	,	PUNCT
ejpam-3003	351	15	668	668	NUM
ejpam-3003	351	16	-	-	SYM
ejpam-3003	351	17	701	701	NUM
ejpam-3003	351	18	683	683	NUM
ejpam-3003	351	19	=	=	NUM
ejpam-3003	351	20	∣∣	∣∣	NUM
ejpam-3003	351	21	∫	∫	PROPN
ejpam-3003	351	22	t	t	PROPN
ejpam-3003	351	23	0	0	NUM
ejpam-3003	351	24	g(t−	g(t−	PROPN
ejpam-3003	351	25	s	s	PART
ejpam-3003	351	26	)	)	PUNCT
ejpam-3003	351	27	∫	∫	PROPN
ejpam-3003	351	28	ω	ω	PROPN
ejpam-3003	351	29	|∇u(s)−∇u(t)|2dxds−	|∇u(s)−∇u(t)|2dxds−	PROPN
ejpam-3003	351	30	∫	∫	PROPN
ejpam-3003	351	31	t	t	PROPN
ejpam-3003	351	32	0	0	NUM
ejpam-3003	351	33	g(t−	g(t−	PROPN
ejpam-3003	351	34	s	s	PART
ejpam-3003	351	35	)	)	PUNCT
ejpam-3003	352	1	∫	∫	PROPN
ejpam-3003	353	1	ω	ω	NUM
ejpam-3003	353	2	|∇um(s)−∇um(t)|2dxds	|∇um(s)−∇um(t)|2dxds	NOUN
ejpam-3003	353	3	∣∣	∣∣	PROPN
ejpam-3003	353	4	≤	≤	NUM
ejpam-3003	353	5	∫	∫	PROPN
ejpam-3003	353	6	t	t	PROPN
ejpam-3003	353	7	0	0	NUM
ejpam-3003	353	8	g(t−	g(t−	PROPN
ejpam-3003	353	9	s)‖∇u(s)−∇um(s)‖2‖∇u(s	s)‖∇u(s)−∇um(s)‖2‖∇u(s	PROPN
ejpam-3003	353	10	)	)	PUNCT
ejpam-3003	354	1	+	+	VERB
ejpam-3003	354	2	∇um(s)‖2ds	∇um(s)‖2ds	NOUN
ejpam-3003	354	3	+	+	CCONJ
ejpam-3003	354	4	∫	∫	PROPN
ejpam-3003	354	5	t	t	PROPN
ejpam-3003	354	6	0	0	NUM
ejpam-3003	354	7	g(t−	g(t−	PROPN
ejpam-3003	354	8	s)‖∇u(s)−∇um(s)‖2ds‖∇u(t	s)‖∇u(s)−∇um(s)‖2ds‖∇u(t	PROPN
ejpam-3003	354	9	)	)	PUNCT
ejpam-3003	355	1	+	+	NOUN
ejpam-3003	355	2	∇um(t)‖2	∇um(t)‖2	PROPN
ejpam-3003	355	3	+	+	NUM
ejpam-3003	355	4	∫	∫	PROPN
ejpam-3003	355	5	t	t	PROPN
ejpam-3003	355	6	0	0	NUM
ejpam-3003	355	7	g(t−	g(t−	PROPN
ejpam-3003	355	8	s)‖∇u(s	s)‖∇u(s	PROPN
ejpam-3003	355	9	)	)	PUNCT
ejpam-3003	356	1	+	+	NOUN
ejpam-3003	356	2	∇um(s)‖2ds‖∇u(t)−∇um(t)‖2	∇um(s)‖2ds‖∇u(t)−∇um(t)‖2	NUM
ejpam-3003	356	3	+	+	NUM
ejpam-3003	356	4	∫	∫	PROPN
ejpam-3003	356	5	t	t	NOUN
ejpam-3003	356	6	0	0	NUM
ejpam-3003	356	7	g(s)ds‖∇u(t	g(s)ds‖∇u(t	PROPN
ejpam-3003	356	8	)	)	PUNCT
ejpam-3003	357	1	+	+	X
ejpam-3003	357	2	∇um(t)‖2‖∇u(t)−∇um(t)‖2	∇um(t)‖2‖∇u(t)−∇um(t)‖2	ADJ
ejpam-3003	357	3	≤	≤	NUM
ejpam-3003	357	4	c	c	NOUN
ejpam-3003	357	5	∫	∫	PROPN
ejpam-3003	357	6	t	t	PROPN
ejpam-3003	357	7	0	0	NUM
ejpam-3003	357	8	g(t−	g(t−	PROPN
ejpam-3003	357	9	s)‖∇u(s)−∇um(s)‖2ds+	s)‖∇u(s)−∇um(s)‖2ds+	PUNCT
ejpam-3003	358	1	c	c	NOUN
ejpam-3003	358	2	∫	∫	PROPN
ejpam-3003	358	3	t	t	PROPN
ejpam-3003	358	4	0	0	PUNCT
ejpam-3003	359	1	g(s)ds‖∇u(t)−∇um(t)‖2	g(s)ds‖∇u(t)−∇um(t)‖2	PROPN
ejpam-3003	359	2	→	→	SYM
ejpam-3003	359	3	0	0	NUM
ejpam-3003	359	4	,	,	PUNCT
ejpam-3003	359	5	(	(	PUNCT
ejpam-3003	359	6	3.46	3.46	NUM
ejpam-3003	359	7	)	)	PUNCT
ejpam-3003	359	8	as	as	ADP
ejpam-3003	359	9	m→∞.	m→∞.	NOUN
ejpam-3003	359	10	taking	take	VERB
ejpam-3003	359	11	into	into	ADP
ejpam-3003	359	12	account	account	NOUN
ejpam-3003	359	13	the	the	DET
ejpam-3003	359	14	nonlinear	nonlinear	ADJ
ejpam-3003	359	15	term	term	NOUN
ejpam-3003	359	16	of	of	ADP
ejpam-3003	359	17	the	the	DET
ejpam-3003	359	18	functional	functional	ADJ
ejpam-3003	359	19	j(u	j(u	PROPN
ejpam-3003	359	20	)	)	PUNCT
ejpam-3003	359	21	,	,	PUNCT
ejpam-3003	359	22	we	we	PRON
ejpam-3003	359	23	deduce	deduce	VERB
ejpam-3003	359	24	‖um‖p+1	‖um‖p+1	ADV
ejpam-3003	360	1	p+1	p+1	NOUN
ejpam-3003	360	2	−	−	PUNCT
ejpam-3003	361	1	‖u‖	‖u‖	INTJ
ejpam-3003	361	2	p+1	p+1	NOUN
ejpam-3003	362	1	p+1	p+1	NOUN
ejpam-3003	362	2	≤	≤	NUM
ejpam-3003	362	3	(	(	PUNCT
ejpam-3003	362	4	p+	p+	NOUN
ejpam-3003	362	5	1)|	1)|	NUM
ejpam-3003	362	6	∫	∫	PROPN
ejpam-3003	362	7	ω	ω	PROPN
ejpam-3003	362	8	|u+	|u+	PROPN
ejpam-3003	362	9	θmum|p−1(u+	θmum|p−1(u+	PROPN
ejpam-3003	362	10	θmum)(um	θmum)(um	PROPN
ejpam-3003	362	11	−	−	PROPN
ejpam-3003	362	12	u)dx|	u)dx|	PROPN
ejpam-3003	362	13	≤	≤	PROPN
ejpam-3003	362	14	(	(	PUNCT
ejpam-3003	362	15	p+	p+	NOUN
ejpam-3003	362	16	1)‖u+	1)‖u+	NUM
ejpam-3003	362	17	θmum‖pp+1‖um	θmum‖pp+1‖um	PROPN
ejpam-3003	362	18	−	−	PROPN
ejpam-3003	362	19	u‖p+1	u‖p+1	SYM
ejpam-3003	362	20	≤	≤	NUM
ejpam-3003	363	1	c‖um	c‖um	DET
ejpam-3003	363	2	−	−	NOUN
ejpam-3003	363	3	u‖p+1	u‖p+1	PUNCT
ejpam-3003	363	4	→	→	SYM
ejpam-3003	363	5	0	0	NUM
ejpam-3003	363	6	,	,	PUNCT
ejpam-3003	363	7	(	(	PUNCT
ejpam-3003	363	8	3.47	3.47	NUM
ejpam-3003	363	9	)	)	PUNCT
ejpam-3003	363	10	as	as	ADP
ejpam-3003	363	11	m→∞	m→∞	NOUN
ejpam-3003	363	12	,	,	PUNCT
ejpam-3003	363	13	where	where	SCONJ
ejpam-3003	363	14	0	0	X
ejpam-3003	363	15	<	<	X
ejpam-3003	363	16	θm	θm	X
ejpam-3003	363	17	<	<	X
ejpam-3003	363	18	1	1	NUM
ejpam-3003	363	19	.	.	PUNCT
ejpam-3003	364	1	hence	hence	ADV
ejpam-3003	364	2	,	,	PUNCT
ejpam-3003	364	3	we	we	PRON
ejpam-3003	364	4	have	have	VERB
ejpam-3003	364	5	lim	lim	PROPN
ejpam-3003	364	6	m→∞	m→∞	NOUN
ejpam-3003	364	7	(	(	PUNCT
ejpam-3003	364	8	g	g	PROPN
ejpam-3003	364	9	◦	◦	NOUN
ejpam-3003	364	10	∇um)(t	∇um)(t	PROPN
ejpam-3003	364	11	)	)	PUNCT
ejpam-3003	364	12	=	=	PUNCT
ejpam-3003	364	13	(	(	PUNCT
ejpam-3003	364	14	g	g	PROPN
ejpam-3003	364	15	◦	◦	PROPN
ejpam-3003	364	16	∇u)(t	∇u)(t	PROPN
ejpam-3003	364	17	)	)	PUNCT
ejpam-3003	364	18	,	,	PUNCT
ejpam-3003	364	19	lim	lim	PROPN
ejpam-3003	364	20	m→∞	m→∞	NOUN
ejpam-3003	365	1	‖um‖p+1	‖um‖p+1	NOUN
ejpam-3003	365	2	p+1	p+1	NOUN
ejpam-3003	365	3	=	=	PUNCT
ejpam-3003	365	4	‖u‖p+1	‖u‖p+1	PROPN
ejpam-3003	365	5	p+1	p+1	NOUN
ejpam-3003	365	6	.	.	PUNCT
ejpam-3003	366	1	(	(	PUNCT
ejpam-3003	366	2	3.48	3.48	NUM
ejpam-3003	366	3	)	)	PUNCT
ejpam-3003	366	4	from	from	ADP
ejpam-3003	366	5	(	(	PUNCT
ejpam-3003	366	6	3.5),(3.6	3.5),(3.6	PROPN
ejpam-3003	366	7	)	)	PUNCT
ejpam-3003	366	8	,	,	PUNCT
ejpam-3003	366	9	it	it	PRON
ejpam-3003	366	10	follows	follow	VERB
ejpam-3003	366	11	that	that	SCONJ
ejpam-3003	366	12	em(0	em(0	VERB
ejpam-3003	366	13	)	)	PUNCT
ejpam-3003	366	14	→	→	PUNCT
ejpam-3003	366	15	e(0	e(0	NOUN
ejpam-3003	366	16	)	)	PUNCT
ejpam-3003	366	17	as	as	ADP
ejpam-3003	366	18	m	m	PROPN
ejpam-3003	366	19	→	→	SYM
ejpam-3003	366	20	∞.	∞.	PROPN
ejpam-3003	366	21	therefore	therefore	ADV
ejpam-3003	366	22	,	,	PUNCT
ejpam-3003	366	23	making	make	VERB
ejpam-3003	366	24	use	use	NOUN
ejpam-3003	366	25	of	of	ADP
ejpam-3003	366	26	fatou	fatou	NOUN
ejpam-3003	366	27	’s	’s	PART
ejpam-3003	366	28	lemma	lemma	PROPN
ejpam-3003	366	29	and	and	CCONJ
ejpam-3003	366	30	(	(	PUNCT
ejpam-3003	366	31	3.14	3.14	NUM
ejpam-3003	366	32	)	)	PUNCT
ejpam-3003	366	33	,	,	PUNCT
ejpam-3003	366	34	we	we	PRON
ejpam-3003	366	35	deduce	deduce	VERB
ejpam-3003	366	36	1	1	NUM
ejpam-3003	366	37	ρ+	ρ+	NUM
ejpam-3003	366	38	1	1	NUM
ejpam-3003	366	39	‖u′‖ρ+1	‖u′‖ρ+1	NOUN
ejpam-3003	366	40	ρ+1	ρ+1	NOUN
ejpam-3003	367	1	+	+	CCONJ
ejpam-3003	367	2	1	1	NUM
ejpam-3003	367	3	2	2	NUM
ejpam-3003	367	4	l‖∇u‖22	l‖∇u‖22	PROPN
ejpam-3003	367	5	≤	≤	NUM
ejpam-3003	367	6	lim	lim	PROPN
ejpam-3003	367	7	inf	inf	PROPN
ejpam-3003	367	8	m→∞	m→∞	NOUN
ejpam-3003	367	9	[	[	PUNCT
ejpam-3003	367	10	1	1	NUM
ejpam-3003	367	11	ρ+	ρ+	NUM
ejpam-3003	367	12	1	1	NUM
ejpam-3003	367	13	‖um‖ρ+1	‖um‖ρ+1	NUM
ejpam-3003	367	14	ρ+1	ρ+1	NUM
ejpam-3003	367	15	+	+	CCONJ
ejpam-3003	367	16	1	1	NUM
ejpam-3003	367	17	2	2	NUM
ejpam-3003	367	18	l(t)‖∇um‖22	l(t)‖∇um‖22	NUM
ejpam-3003	367	19	]	]	X
ejpam-3003	367	20	=	=	SYM
ejpam-3003	367	21	lim	lim	PROPN
ejpam-3003	367	22	inf	inf	PROPN
ejpam-3003	367	23	m→∞	m→∞	NOUN
ejpam-3003	367	24	[	[	X
ejpam-3003	367	25	em(t	em(t	NOUN
ejpam-3003	367	26	)	)	PUNCT
ejpam-3003	368	1	+	+	CCONJ
ejpam-3003	368	2	1	1	NUM
ejpam-3003	368	3	p+	p+	NOUN
ejpam-3003	368	4	1	1	NUM
ejpam-3003	368	5	‖um‖p+1	‖um‖p+1	NOUN
ejpam-3003	368	6	p+1	p+1	NOUN
ejpam-3003	368	7	−	−	NUM
ejpam-3003	368	8	1	1	NUM
ejpam-3003	368	9	2	2	NUM
ejpam-3003	368	10	(	(	PUNCT
ejpam-3003	368	11	g	g	PROPN
ejpam-3003	368	12	◦	◦	NOUN
ejpam-3003	368	13	∇um)(t	∇um)(t	PROPN
ejpam-3003	368	14	)	)	PUNCT
ejpam-3003	368	15	]	]	PUNCT
ejpam-3003	368	16	≤	≤	NUM
ejpam-3003	368	17	lim	lim	PROPN
ejpam-3003	368	18	m→∞	m→∞	NOUN
ejpam-3003	368	19	[	[	X
ejpam-3003	368	20	em(0	em(0	X
ejpam-3003	368	21	)	)	PUNCT
ejpam-3003	369	1	+	+	CCONJ
ejpam-3003	369	2	1	1	NUM
ejpam-3003	369	3	p+	p+	NOUN
ejpam-3003	369	4	1	1	NUM
ejpam-3003	369	5	‖um‖p+1	‖um‖p+1	NOUN
ejpam-3003	369	6	p+1	p+1	NOUN
ejpam-3003	369	7	−	−	NUM
ejpam-3003	369	8	1	1	NUM
ejpam-3003	369	9	2	2	NUM
ejpam-3003	369	10	(	(	PUNCT
ejpam-3003	369	11	g	g	PROPN
ejpam-3003	369	12	◦	◦	NOUN
ejpam-3003	369	13	∇um)(t	∇um)(t	PROPN
ejpam-3003	369	14	)	)	PUNCT
ejpam-3003	369	15	]	]	PUNCT
ejpam-3003	370	1	=	=	PUNCT
ejpam-3003	370	2	e(0	e(0	NOUN
ejpam-3003	370	3	)	)	PUNCT
ejpam-3003	371	1	+	+	CCONJ
ejpam-3003	371	2	1	1	NUM
ejpam-3003	371	3	p+	p+	NOUN
ejpam-3003	371	4	1	1	NUM
ejpam-3003	371	5	‖u‖p+1	‖u‖p+1	NOUN
ejpam-3003	371	6	p+1	p+1	NOUN
ejpam-3003	371	7	−	−	NOUN
ejpam-3003	371	8	1	1	NUM
ejpam-3003	371	9	2	2	NUM
ejpam-3003	371	10	(	(	PUNCT
ejpam-3003	371	11	g	g	PROPN
ejpam-3003	371	12	◦	◦	PROPN
ejpam-3003	371	13	∇u)(t	∇u)(t	PROPN
ejpam-3003	371	14	)	)	PUNCT
ejpam-3003	371	15	.	.	PUNCT
ejpam-3003	372	1	(	(	PUNCT
ejpam-3003	372	2	3.49	3.49	NUM
ejpam-3003	372	3	)	)	PUNCT
ejpam-3003	372	4	which	which	PRON
ejpam-3003	372	5	yields	yield	VERB
ejpam-3003	372	6	(	(	PUNCT
ejpam-3003	372	7	2.13	2.13	NUM
ejpam-3003	372	8	)	)	PUNCT
ejpam-3003	372	9	.	.	PUNCT
ejpam-3003	373	1	thus	thus	ADV
ejpam-3003	373	2	,	,	PUNCT
ejpam-3003	373	3	we	we	PRON
ejpam-3003	373	4	obtain	obtain	VERB
ejpam-3003	373	5	that	that	SCONJ
ejpam-3003	373	6	u	u	NOUN
ejpam-3003	373	7	is	be	AUX
ejpam-3003	373	8	a	a	DET
ejpam-3003	373	9	global	global	ADJ
ejpam-3003	373	10	weak	weak	ADJ
ejpam-3003	373	11	solution	solution	NOUN
ejpam-3003	373	12	of	of	ADP
ejpam-3003	373	13	problem	problem	NOUN
ejpam-3003	373	14	(	(	PUNCT
ejpam-3003	373	15	1.1	1.1	NUM
ejpam-3003	373	16	)	)	PUNCT
ejpam-3003	373	17	.	.	PUNCT
ejpam-3003	374	1	then	then	ADV
ejpam-3003	374	2	,	,	PUNCT
ejpam-3003	374	3	making	make	VERB
ejpam-3003	374	4	use	use	NOUN
ejpam-3003	374	5	of	of	ADP
ejpam-3003	374	6	lemma	lemma	PROPN
ejpam-3003	374	7	3	3	NUM
ejpam-3003	374	8	(	(	PUNCT
ejpam-3003	374	9	1	1	NUM
ejpam-3003	374	10	)	)	PUNCT
ejpam-3003	374	11	again	again	ADV
ejpam-3003	374	12	,	,	PUNCT
ejpam-3003	374	13	we	we	PRON
ejpam-3003	374	14	get	get	VERB
ejpam-3003	374	15	u(t	u(t	NOUN
ejpam-3003	374	16	)	)	PUNCT
ejpam-3003	374	17	∈	∈	PROPN
ejpam-3003	374	18	w	w	NOUN
ejpam-3003	374	19	for	for	ADP
ejpam-3003	374	20	0	0	NUM
ejpam-3003	374	21	≤	≤	NUM
ejpam-3003	374	22	t	t	PROPN
ejpam-3003	374	23	<	<	AUX
ejpam-3003	374	24	∞.	∞.	PROPN
ejpam-3003	374	25	finally	finally	ADV
ejpam-3003	374	26	,	,	PUNCT
ejpam-3003	374	27	taking	take	VERB
ejpam-3003	374	28	m→∞	m→∞	NOUN
ejpam-3003	374	29	in	in	ADP
ejpam-3003	374	30	(	(	PUNCT
ejpam-3003	374	31	3.17	3.17	NUM
ejpam-3003	374	32	)	)	PUNCT
ejpam-3003	374	33	,	,	PUNCT
ejpam-3003	374	34	we	we	PRON
ejpam-3003	374	35	deduce	deduce	VERB
ejpam-3003	374	36	that	that	SCONJ
ejpam-3003	374	37	the	the	DET
ejpam-3003	374	38	energy	energy	NOUN
ejpam-3003	374	39	identity	identity	NOUN
ejpam-3003	374	40	(	(	PUNCT
ejpam-3003	374	41	3.1	3.1	NUM
ejpam-3003	374	42	)	)	PUNCT
ejpam-3003	374	43	also	also	ADV
ejpam-3003	374	44	holds	hold	VERB
ejpam-3003	374	45	for	for	ADP
ejpam-3003	374	46	0	0	NUM
ejpam-3003	374	47	≤	≤	NOUN
ejpam-3003	374	48	t	t	PROPN
ejpam-3003	374	49	<	<	X
ejpam-3003	374	50	∞.	∞.	PROPN
ejpam-3003	374	51	h.f	h.f	PROPN
ejpam-3003	374	52	.	.	PROPN
ejpam-3003	374	53	di	di	PROPN
ejpam-3003	374	54	,	,	PUNCT
ejpam-3003	374	55	y.d	y.d	PROPN
ejpam-3003	374	56	.	.	PROPN
ejpam-3003	374	57	shang	shang	PROPN
ejpam-3003	374	58	/	/	SYM
ejpam-3003	374	59	eur	eur	PROPN
ejpam-3003	374	60	.	.	PUNCT
ejpam-3003	375	1	j.	j.	PROPN
ejpam-3003	375	2	pure	pure	PROPN
ejpam-3003	375	3	appl	appl	PROPN
ejpam-3003	375	4	.	.	PROPN
ejpam-3003	375	5	math	math	PROPN
ejpam-3003	375	6	,	,	PUNCT
ejpam-3003	375	7	10	10	NUM
ejpam-3003	375	8	(	(	PUNCT
ejpam-3003	375	9	4	4	NUM
ejpam-3003	375	10	)	)	PUNCT
ejpam-3003	375	11	(	(	PUNCT
ejpam-3003	375	12	2017	2017	NUM
ejpam-3003	375	13	)	)	PUNCT
ejpam-3003	375	14	,	,	PUNCT
ejpam-3003	375	15	668	668	NUM
ejpam-3003	375	16	-	-	SYM
ejpam-3003	375	17	701	701	NUM
ejpam-3003	375	18	684	684	NUM
ejpam-3003	375	19	4	4	NUM
ejpam-3003	375	20	.	.	PUNCT
ejpam-3003	376	1	decay	decay	NOUN
ejpam-3003	376	2	estimate	estimate	NOUN
ejpam-3003	376	3	in	in	ADP
ejpam-3003	376	4	this	this	DET
ejpam-3003	376	5	section	section	NOUN
ejpam-3003	376	6	,	,	PUNCT
ejpam-3003	376	7	we	we	PRON
ejpam-3003	376	8	shall	shall	AUX
ejpam-3003	376	9	prove	prove	VERB
ejpam-3003	376	10	the	the	DET
ejpam-3003	376	11	energy	energy	NOUN
ejpam-3003	376	12	decay	decay	NOUN
ejpam-3003	376	13	estimate	estimate	NOUN
ejpam-3003	376	14	of	of	ADP
ejpam-3003	376	15	the	the	DET
ejpam-3003	376	16	global	global	ADJ
ejpam-3003	376	17	solutions	solution	NOUN
ejpam-3003	376	18	obtained	obtain	VERB
ejpam-3003	376	19	in	in	ADP
ejpam-3003	376	20	the	the	DET
ejpam-3003	376	21	previous	previous	ADJ
ejpam-3003	376	22	section	section	NOUN
ejpam-3003	376	23	by	by	ADP
ejpam-3003	376	24	making	make	VERB
ejpam-3003	376	25	use	use	NOUN
ejpam-3003	376	26	of	of	ADP
ejpam-3003	376	27	the	the	DET
ejpam-3003	376	28	perturbed	perturb	VERB
ejpam-3003	376	29	energy	energy	NOUN
ejpam-3003	376	30	method	method	NOUN
ejpam-3003	376	31	introduced	introduce	VERB
ejpam-3003	376	32	by	by	ADP
ejpam-3003	376	33	cavalcanti	cavalcanti	PROPN
ejpam-3003	376	34	et	et	PROPN
ejpam-3003	376	35	al.[16,18,23	al.[16,18,23	PROPN
ejpam-3003	376	36	]	]	PUNCT
ejpam-3003	376	37	,	,	PUNCT
ejpam-3003	376	38	messaoudi	messaoudi	NOUN
ejpam-3003	376	39	and	and	CCONJ
ejpam-3003	376	40	tatar	tatar	NOUN
ejpam-3003	376	41	[	[	X
ejpam-3003	376	42	14,24	14,24	X
ejpam-3003	376	43	]	]	X
ejpam-3003	376	44	and	and	CCONJ
ejpam-3003	376	45	liu	liu	PROPN
ejpam-3003	377	1	[	[	X
ejpam-3003	377	2	22	22	NUM
ejpam-3003	377	3	]	]	PUNCT
ejpam-3003	377	4	coupled	couple	VERB
ejpam-3003	377	5	with	with	ADP
ejpam-3003	377	6	some	some	DET
ejpam-3003	377	7	new	new	ADJ
ejpam-3003	377	8	technical	technical	ADJ
ejpam-3003	377	9	lemmas	lemmas	NOUN
ejpam-3003	377	10	.	.	PUNCT
ejpam-3003	378	1	theorem	theorem	VERB
ejpam-3003	378	2	6	6	NUM
ejpam-3003	378	3	.	.	PUNCT
ejpam-3003	379	1	let	let	VERB
ejpam-3003	379	2	the	the	DET
ejpam-3003	379	3	assumptions	assumption	NOUN
ejpam-3003	379	4	(	(	PUNCT
ejpam-3003	379	5	a1)−	a1)−	PROPN
ejpam-3003	379	6	(	(	PUNCT
ejpam-3003	379	7	a3	a3	NOUN
ejpam-3003	379	8	)	)	PUNCT
ejpam-3003	379	9	hold	hold	VERB
ejpam-3003	379	10	,	,	PUNCT
ejpam-3003	379	11	u0(x	u0(x	NOUN
ejpam-3003	379	12	)	)	PUNCT
ejpam-3003	379	13	∈	∈	PROPN
ejpam-3003	379	14	h1	h1	PROPN
ejpam-3003	379	15	γ0	γ0	PROPN
ejpam-3003	379	16	(	(	PUNCT
ejpam-3003	379	17	ω	ω	NOUN
ejpam-3003	379	18	)	)	PUNCT
ejpam-3003	379	19	,	,	PUNCT
ejpam-3003	379	20	u1(x	u1(x	NOUN
ejpam-3003	379	21	)	)	PUNCT
ejpam-3003	379	22	∈	∈	PROPN
ejpam-3003	379	23	lρ+1(ω	lρ+1(ω	X
ejpam-3003	379	24	)	)	PUNCT
ejpam-3003	379	25	∩	∩	NOUN
ejpam-3003	379	26	lq+1(γ1	lq+1(γ1	NOUN
ejpam-3003	379	27	)	)	PUNCT
ejpam-3003	379	28	.	.	PUNCT
ejpam-3003	380	1	further	far	ADV
ejpam-3003	380	2	assume	assume	VERB
ejpam-3003	380	3	that	that	SCONJ
ejpam-3003	380	4	1	1	NUM
ejpam-3003	380	5	<	<	X
ejpam-3003	380	6	ρ	ρ	X
ejpam-3003	380	7	<	<	X
ejpam-3003	380	8	∞	∞	PROPN
ejpam-3003	380	9	if	if	SCONJ
ejpam-3003	380	10	n	n	NOUN
ejpam-3003	380	11	≤	≤	ADV
ejpam-3003	380	12	2	2	NUM
ejpam-3003	380	13	,	,	PUNCT
ejpam-3003	380	14	1	1	NUM
ejpam-3003	380	15	<	<	X
ejpam-3003	380	16	ρ	ρ	X
ejpam-3003	380	17	≤	≤	PROPN
ejpam-3003	380	18	n+2	n+2	NUM
ejpam-3003	380	19	n−2	n−2	PROPN
ejpam-3003	380	20	if	if	SCONJ
ejpam-3003	380	21	n	n	PRON
ejpam-3003	380	22	≥	≥	NOUN
ejpam-3003	380	23	3	3	NUM
ejpam-3003	380	24	,	,	PUNCT
ejpam-3003	380	25	e(0	e(0	NOUN
ejpam-3003	380	26	)	)	PUNCT
ejpam-3003	380	27	<	<	X
ejpam-3003	380	28	d̃	d̃	PROPN
ejpam-3003	380	29	and	and	CCONJ
ejpam-3003	380	30	i(u0	i(u0	PROPN
ejpam-3003	380	31	)	)	PUNCT
ejpam-3003	380	32	>	>	X
ejpam-3003	380	33	0	0	NUM
ejpam-3003	380	34	,	,	PUNCT
ejpam-3003	380	35	then	then	ADV
ejpam-3003	380	36	for	for	ADP
ejpam-3003	380	37	each	each	DET
ejpam-3003	380	38	t0	t0	PROPN
ejpam-3003	380	39	>	>	X
ejpam-3003	380	40	0	0	NUM
ejpam-3003	380	41	,	,	PUNCT
ejpam-3003	380	42	there	there	PRON
ejpam-3003	380	43	exist	exist	VERB
ejpam-3003	380	44	two	two	NUM
ejpam-3003	380	45	positive	positive	ADJ
ejpam-3003	380	46	constants	constant	NOUN
ejpam-3003	380	47	l	l	NOUN
ejpam-3003	380	48	and	and	CCONJ
ejpam-3003	380	49	η	η	PROPN
ejpam-3003	380	50	such	such	ADJ
ejpam-3003	380	51	that	that	SCONJ
ejpam-3003	380	52	the	the	DET
ejpam-3003	380	53	solutions	solution	NOUN
ejpam-3003	380	54	of	of	ADP
ejpam-3003	380	55	the	the	DET
ejpam-3003	380	56	problem	problem	NOUN
ejpam-3003	380	57	(	(	PUNCT
ejpam-3003	380	58	1.1	1.1	NUM
ejpam-3003	380	59	)	)	PUNCT
ejpam-3003	380	60	satisfies	satisfie	NOUN
ejpam-3003	380	61	e(t	e(t	NOUN
ejpam-3003	380	62	)	)	PUNCT
ejpam-3003	380	63	≤	≤	NUM
ejpam-3003	380	64	le−η	le−η	NOUN
ejpam-3003	380	65	∫	∫	PROPN
ejpam-3003	380	66	t	t	PROPN
ejpam-3003	380	67	t0	t0	PROPN
ejpam-3003	380	68	ξ(s)ds	ξ(s)ds	PROPN
ejpam-3003	380	69	,	,	PUNCT
ejpam-3003	380	70	t	t	PROPN
ejpam-3003	380	71	≥	≥	PROPN
ejpam-3003	380	72	t0	t0	PROPN
ejpam-3003	380	73	.	.	PUNCT
ejpam-3003	381	1	for	for	ADP
ejpam-3003	381	2	this	this	DET
ejpam-3003	381	3	purpose	purpose	NOUN
ejpam-3003	381	4	,	,	PUNCT
ejpam-3003	381	5	we	we	PRON
ejpam-3003	381	6	introduce	introduce	VERB
ejpam-3003	381	7	the	the	DET
ejpam-3003	381	8	functional	functional	ADJ
ejpam-3003	381	9	f	f	X
ejpam-3003	381	10	(	(	PUNCT
ejpam-3003	381	11	t	t	PROPN
ejpam-3003	381	12	)	)	PUNCT
ejpam-3003	381	13	=	=	PUNCT
ejpam-3003	381	14	me(t	me(t	X
ejpam-3003	381	15	)	)	PUNCT
ejpam-3003	381	16	+	+	CCONJ
ejpam-3003	381	17	εψ(t	εψ(t	X
ejpam-3003	381	18	)	)	PUNCT
ejpam-3003	381	19	+	+	SYM
ejpam-3003	381	20	φ(t	φ(t	NOUN
ejpam-3003	381	21	)	)	PUNCT
ejpam-3003	381	22	,	,	PUNCT
ejpam-3003	381	23	(	(	PUNCT
ejpam-3003	381	24	4.1	4.1	NUM
ejpam-3003	381	25	)	)	PUNCT
ejpam-3003	381	26	where	where	SCONJ
ejpam-3003	381	27	ε	ε	PROPN
ejpam-3003	381	28	,	,	PUNCT
ejpam-3003	381	29	m	m	VERB
ejpam-3003	381	30	are	be	AUX
ejpam-3003	381	31	positive	positive	ADJ
ejpam-3003	381	32	constants	constant	NOUN
ejpam-3003	381	33	which	which	PRON
ejpam-3003	381	34	shall	shall	AUX
ejpam-3003	381	35	be	be	AUX
ejpam-3003	381	36	determined	determine	VERB
ejpam-3003	381	37	later	later	ADV
ejpam-3003	381	38	,	,	PUNCT
ejpam-3003	381	39	and	and	CCONJ
ejpam-3003	381	40	ψ(t	ψ(t	PROPN
ejpam-3003	381	41	)	)	PUNCT
ejpam-3003	381	42	=	=	SYM
ejpam-3003	381	43	ξ(t	ξ(t	PROPN
ejpam-3003	381	44	)	)	PUNCT
ejpam-3003	381	45	ρ	ρ	PROPN
ejpam-3003	381	46	∫	∫	PROPN
ejpam-3003	381	47	ω	ω	NUM
ejpam-3003	381	48	|ut|ρ−1utudx	|ut|ρ−1utudx	PROPN
ejpam-3003	381	49	,	,	PUNCT
ejpam-3003	381	50	(	(	PUNCT
ejpam-3003	381	51	4.2	4.2	NUM
ejpam-3003	381	52	)	)	PUNCT
ejpam-3003	381	53	φ(t	φ(t	PROPN
ejpam-3003	381	54	)	)	PUNCT
ejpam-3003	381	55	=	=	SYM
ejpam-3003	381	56	−ξ(t	−ξ(t	NOUN
ejpam-3003	381	57	)	)	PUNCT
ejpam-3003	381	58	ρ	ρ	PROPN
ejpam-3003	381	59	∫	∫	PROPN
ejpam-3003	381	60	ω	ω	PROPN
ejpam-3003	381	61	|ut|ρ−1ut	|ut|ρ−1ut	PROPN
ejpam-3003	381	62	∫	∫	PROPN
ejpam-3003	381	63	t	t	PROPN
ejpam-3003	381	64	0	0	NUM
ejpam-3003	381	65	g(t−	g(t−	PROPN
ejpam-3003	381	66	s)[u(t)−	s)[u(t)−	PROPN
ejpam-3003	381	67	u(s)]dsdx	u(s)]dsdx	PROPN
ejpam-3003	381	68	.	.	PUNCT
ejpam-3003	382	1	(	(	PUNCT
ejpam-3003	382	2	4.3	4.3	NUM
ejpam-3003	382	3	)	)	PUNCT
ejpam-3003	382	4	remark	remark	NOUN
ejpam-3003	382	5	2	2	NUM
ejpam-3003	382	6	.	.	PUNCT
ejpam-3003	383	1	this	this	DET
ejpam-3003	383	2	functional	functional	ADJ
ejpam-3003	383	3	was	be	AUX
ejpam-3003	383	4	first	first	ADV
ejpam-3003	383	5	introduced	introduce	VERB
ejpam-3003	383	6	in	in	ADP
ejpam-3003	383	7	[	[	X
ejpam-3003	383	8	14	14	NUM
ejpam-3003	383	9	]	]	PUNCT
ejpam-3003	383	10	but	but	CCONJ
ejpam-3003	383	11	choose	choose	VERB
ejpam-3003	383	12	ξ(t	ξ(t	NOUN
ejpam-3003	383	13	)	)	PUNCT
ejpam-3003	383	14	≡	≡	PROPN
ejpam-3003	383	15	1	1	NUM
ejpam-3003	383	16	and	and	CCONJ
ejpam-3003	383	17	in	in	ADP
ejpam-3003	383	18	[	[	X
ejpam-3003	383	19	22,24	22,24	X
ejpam-3003	383	20	]	]	X
ejpam-3003	383	21	for	for	ADP
ejpam-3003	383	22	ξ(t	ξ(t	NOUN
ejpam-3003	383	23	)	)	PUNCT
ejpam-3003	383	24	6≡	6≡	NUM
ejpam-3003	383	25	1	1	NUM
ejpam-3003	383	26	.	.	PUNCT
ejpam-3003	384	1	here	here	ADV
ejpam-3003	384	2	,	,	PUNCT
ejpam-3003	384	3	we	we	PRON
ejpam-3003	384	4	can	can	AUX
ejpam-3003	384	5	choose	choose	VERB
ejpam-3003	384	6	ε	ε	PROPN
ejpam-3003	384	7	sufficiently	sufficiently	ADV
ejpam-3003	384	8	small	small	ADJ
ejpam-3003	384	9	and	and	CCONJ
ejpam-3003	384	10	m	m	VERB
ejpam-3003	384	11	sufficiently	sufficiently	ADV
ejpam-3003	384	12	large	large	ADJ
ejpam-3003	384	13	(	(	PUNCT
ejpam-3003	384	14	if	if	SCONJ
ejpam-3003	384	15	needed	need	VERB
ejpam-3003	384	16	)	)	PUNCT
ejpam-3003	384	17	in	in	ADP
ejpam-3003	384	18	(	(	PUNCT
ejpam-3003	384	19	4.1	4.1	NUM
ejpam-3003	384	20	)	)	PUNCT
ejpam-3003	384	21	so	so	SCONJ
ejpam-3003	384	22	that	that	SCONJ
ejpam-3003	384	23	f	f	PROPN
ejpam-3003	384	24	(	(	PUNCT
ejpam-3003	384	25	t	t	NOUN
ejpam-3003	384	26	)	)	PUNCT
ejpam-3003	384	27	∼	∼	NOUN
ejpam-3003	384	28	e(t	e(t	NOUN
ejpam-3003	384	29	)	)	PUNCT
ejpam-3003	384	30	.	.	PUNCT
ejpam-3003	385	1	firstly	firstly	ADV
ejpam-3003	385	2	,	,	PUNCT
ejpam-3003	385	3	we	we	PRON
ejpam-3003	385	4	state	state	VERB
ejpam-3003	385	5	several	several	ADJ
ejpam-3003	385	6	lemmas	lemma	NOUN
ejpam-3003	385	7	to	to	PART
ejpam-3003	385	8	prove	prove	VERB
ejpam-3003	385	9	the	the	DET
ejpam-3003	385	10	decay	decay	NOUN
ejpam-3003	385	11	rate	rate	NOUN
ejpam-3003	385	12	estimate	estimate	NOUN
ejpam-3003	385	13	of	of	ADP
ejpam-3003	385	14	the	the	DET
ejpam-3003	385	15	energy	energy	NOUN
ejpam-3003	385	16	.	.	PUNCT
ejpam-3003	386	1	lemma	lemma	PROPN
ejpam-3003	386	2	7	7	X
ejpam-3003	386	3	.	.	PUNCT
ejpam-3003	387	1	let	let	VERB
ejpam-3003	387	2	u	u	PRON
ejpam-3003	387	3	∈	∈	NOUN
ejpam-3003	387	4	l∞(0,∞;h1	l∞(0,∞;h1	PROPN
ejpam-3003	387	5	γ0	γ0	PROPN
ejpam-3003	387	6	(	(	PUNCT
ejpam-3003	387	7	ω	ω	NOUN
ejpam-3003	387	8	)	)	PUNCT
ejpam-3003	387	9	)	)	PUNCT
ejpam-3003	387	10	be	be	AUX
ejpam-3003	387	11	the	the	DET
ejpam-3003	387	12	solution	solution	NOUN
ejpam-3003	387	13	of	of	ADP
ejpam-3003	387	14	(	(	PUNCT
ejpam-3003	387	15	1.1	1.1	NUM
ejpam-3003	387	16	)	)	PUNCT
ejpam-3003	387	17	and	and	CCONJ
ejpam-3003	387	18	e(0	e(0	NOUN
ejpam-3003	387	19	)	)	PUNCT
ejpam-3003	387	20	<	<	X
ejpam-3003	387	21	d̃	d̃	PROPN
ejpam-3003	387	22	,	,	PUNCT
ejpam-3003	387	23	i(u0	i(u0	PROPN
ejpam-3003	387	24	)	)	PUNCT
ejpam-3003	387	25	>	>	X
ejpam-3003	387	26	0	0	NUM
ejpam-3003	387	27	,	,	PUNCT
ejpam-3003	387	28	then	then	ADV
ejpam-3003	387	29	we	we	PRON
ejpam-3003	387	30	have∫	have∫	VERB
ejpam-3003	387	31	ω	ω	PROPN
ejpam-3003	387	32	(	(	PUNCT
ejpam-3003	387	33	∫	∫	PROPN
ejpam-3003	387	34	t	t	PROPN
ejpam-3003	387	35	0	0	NUM
ejpam-3003	387	36	g(t−	g(t−	PROPN
ejpam-3003	387	37	s)[u(t)−	s)[u(t)−	PROPN
ejpam-3003	387	38	u(s)]ds	u(s)]ds	NOUN
ejpam-3003	387	39	)	)	PUNCT
ejpam-3003	388	1	ρ+1	ρ+1	NUM
ejpam-3003	388	2	dx	dx	PROPN
ejpam-3003	388	3	≤	≤	NUM
ejpam-3003	388	4	bρ+1	bρ+1	CCONJ
ejpam-3003	388	5	ρ+1(1−	ρ+1(1−	NUM
ejpam-3003	388	6	b)ρ	b)ρ	NOUN
ejpam-3003	388	7	(	(	PUNCT
ejpam-3003	388	8	4(p+	4(p+	NUM
ejpam-3003	388	9	1)e(0	1)e(0	NOUN
ejpam-3003	388	10	)	)	PUNCT
ejpam-3003	388	11	(	(	PUNCT
ejpam-3003	388	12	p−	p−	NOUN
ejpam-3003	388	13	1)b	1)b	X
ejpam-3003	388	14	)	)	PUNCT
ejpam-3003	388	15	ρ−1	ρ−1	PROPN
ejpam-3003	388	16	2	2	NUM
ejpam-3003	388	17	(	(	PUNCT
ejpam-3003	388	18	g	g	PROPN
ejpam-3003	388	19	◦	◦	PROPN
ejpam-3003	388	20	∇u)(t	∇u)(t	PROPN
ejpam-3003	388	21	)	)	PUNCT
ejpam-3003	388	22	,	,	PUNCT
ejpam-3003	388	23	(	(	PUNCT
ejpam-3003	388	24	4.4	4.4	NUM
ejpam-3003	388	25	)	)	PUNCT
ejpam-3003	388	26	where	where	SCONJ
ejpam-3003	388	27	bρ+1	bρ+1	PRON
ejpam-3003	388	28	is	be	AUX
ejpam-3003	388	29	the	the	DET
ejpam-3003	388	30	optimal	optimal	ADJ
ejpam-3003	388	31	constant	constant	ADJ
ejpam-3003	388	32	satisfying	satisfy	VERB
ejpam-3003	388	33	the	the	DET
ejpam-3003	388	34	sobolev	sobolev	NOUN
ejpam-3003	388	35	inequality	inequality	NOUN
ejpam-3003	388	36	‖u‖ρ+1	‖u‖ρ+1	PROPN
ejpam-3003	388	37	≤	≤	X
ejpam-3003	388	38	bρ+1‖∇u‖2	bρ+1‖∇u‖2	NOUN
ejpam-3003	388	39	.	.	PUNCT
ejpam-3003	389	1	proof	proof	NOUN
ejpam-3003	389	2	.	.	PUNCT
ejpam-3003	390	1	from	from	ADP
ejpam-3003	390	2	e(0	e(0	NOUN
ejpam-3003	390	3	)	)	PUNCT
ejpam-3003	390	4	<	<	X
ejpam-3003	390	5	d̃	d̃	PROPN
ejpam-3003	390	6	,	,	PUNCT
ejpam-3003	390	7	i(u0	i(u0	PROPN
ejpam-3003	390	8	)	)	PUNCT
ejpam-3003	390	9	>	>	X
ejpam-3003	390	10	0	0	PUNCT
ejpam-3003	391	1	and	and	CCONJ
ejpam-3003	391	2	lemma	lemma	PROPN
ejpam-3003	391	3	3	3	NUM
ejpam-3003	391	4	(	(	PUNCT
ejpam-3003	391	5	1	1	NUM
ejpam-3003	391	6	)	)	PUNCT
ejpam-3003	391	7	,	,	PUNCT
ejpam-3003	391	8	we	we	PRON
ejpam-3003	391	9	can	can	AUX
ejpam-3003	391	10	obtain	obtain	VERB
ejpam-3003	391	11	u(t	u(t	NOUN
ejpam-3003	391	12	)	)	PUNCT
ejpam-3003	391	13	∈	∈	PROPN
ejpam-3003	391	14	w	w	NOUN
ejpam-3003	391	15	for	for	ADP
ejpam-3003	391	16	0	0	NUM
ejpam-3003	391	17	≤	≤	NOUN
ejpam-3003	391	18	t	t	PROPN
ejpam-3003	391	19	<	<	X
ejpam-3003	391	20	∞.	∞.	PROPN
ejpam-3003	392	1	thus	thus	ADV
ejpam-3003	392	2	we	we	PRON
ejpam-3003	392	3	have	have	VERB
ejpam-3003	392	4	1	1	NUM
ejpam-3003	392	5	ρ+	ρ+	NUM
ejpam-3003	392	6	1	1	NUM
ejpam-3003	392	7	‖u′‖ρ+1	‖u′‖ρ+1	NOUN
ejpam-3003	392	8	ρ+1	ρ+1	NOUN
ejpam-3003	393	1	+	+	CCONJ
ejpam-3003	393	2	p−	p−	NOUN
ejpam-3003	393	3	1	1	NUM
ejpam-3003	393	4	2(p+	2(p+	NUM
ejpam-3003	393	5	1	1	NUM
ejpam-3003	393	6	)	)	PUNCT
ejpam-3003	394	1	[	[	X
ejpam-3003	394	2	l(t)‖∇u‖22	l(t)‖∇u‖22	X
ejpam-3003	394	3	+	+	CCONJ
ejpam-3003	394	4	(	(	PUNCT
ejpam-3003	394	5	g	g	PROPN
ejpam-3003	394	6	◦	◦	PROPN
ejpam-3003	394	7	∇u)(t	∇u)(t	PROPN
ejpam-3003	394	8	)	)	PUNCT
ejpam-3003	394	9	]	]	PUNCT
ejpam-3003	395	1	≤	≤	NUM
ejpam-3003	395	2	1	1	NUM
ejpam-3003	395	3	ρ+	ρ+	NUM
ejpam-3003	395	4	1	1	NUM
ejpam-3003	395	5	‖u′‖ρ+1	‖u′‖ρ+1	NOUN
ejpam-3003	395	6	ρ+1	ρ+1	NOUN
ejpam-3003	395	7	+	+	CCONJ
ejpam-3003	395	8	p−	p−	NOUN
ejpam-3003	395	9	1	1	NUM
ejpam-3003	395	10	2(p+	2(p+	NUM
ejpam-3003	395	11	1	1	NUM
ejpam-3003	395	12	)	)	PUNCT
ejpam-3003	396	1	[	[	X
ejpam-3003	396	2	l(t)‖∇u‖22	l(t)‖∇u‖22	X
ejpam-3003	396	3	+	+	CCONJ
ejpam-3003	396	4	(	(	PUNCT
ejpam-3003	396	5	g	g	PROPN
ejpam-3003	396	6	◦	◦	PROPN
ejpam-3003	396	7	∇u)(t	∇u)(t	PROPN
ejpam-3003	396	8	)	)	PUNCT
ejpam-3003	396	9	]	]	PUNCT
ejpam-3003	397	1	+	+	CCONJ
ejpam-3003	397	2	1	1	NUM
ejpam-3003	397	3	p+	p+	NOUN
ejpam-3003	397	4	1	1	NUM
ejpam-3003	397	5	i(u	i(u	PROPN
ejpam-3003	397	6	)	)	PUNCT
ejpam-3003	397	7	h.f	h.f	PROPN
ejpam-3003	397	8	.	.	PROPN
ejpam-3003	397	9	di	di	PROPN
ejpam-3003	397	10	,	,	PUNCT
ejpam-3003	397	11	y.d	y.d	PROPN
ejpam-3003	397	12	.	.	PROPN
ejpam-3003	397	13	shang	shang	PROPN
ejpam-3003	397	14	/	/	SYM
ejpam-3003	397	15	eur	eur	PROPN
ejpam-3003	397	16	.	.	PUNCT
ejpam-3003	398	1	j.	j.	PROPN
ejpam-3003	398	2	pure	pure	PROPN
ejpam-3003	398	3	appl	appl	PROPN
ejpam-3003	398	4	.	.	PROPN
ejpam-3003	398	5	math	math	PROPN
ejpam-3003	398	6	,	,	PUNCT
ejpam-3003	398	7	10	10	NUM
ejpam-3003	398	8	(	(	PUNCT
ejpam-3003	398	9	4	4	NUM
ejpam-3003	398	10	)	)	PUNCT
ejpam-3003	398	11	(	(	PUNCT
ejpam-3003	398	12	2017	2017	NUM
ejpam-3003	398	13	)	)	PUNCT
ejpam-3003	398	14	,	,	PUNCT
ejpam-3003	398	15	668	668	NUM
ejpam-3003	398	16	-	-	SYM
ejpam-3003	398	17	701	701	NUM
ejpam-3003	398	18	685	685	NUM
ejpam-3003	398	19	=	=	SYM
ejpam-3003	398	20	1	1	NUM
ejpam-3003	398	21	ρ+	ρ+	NUM
ejpam-3003	398	22	1	1	NUM
ejpam-3003	398	23	‖u′‖ρ+1	‖u′‖ρ+1	NOUN
ejpam-3003	398	24	ρ+1	ρ+1	NOUN
ejpam-3003	398	25	+	+	NUM
ejpam-3003	398	26	j(u	j(u	NOUN
ejpam-3003	398	27	)	)	PUNCT
ejpam-3003	398	28	=	=	SYM
ejpam-3003	398	29	e(t	e(t	NOUN
ejpam-3003	398	30	)	)	PUNCT
ejpam-3003	398	31	≤	≤	NOUN
ejpam-3003	399	1	e(0	e(0	NOUN
ejpam-3003	399	2	)	)	PUNCT
ejpam-3003	399	3	<	<	X
ejpam-3003	400	1	d̃.	d̃.	PROPN
ejpam-3003	400	2	(	(	PUNCT
ejpam-3003	400	3	4.5	4.5	NUM
ejpam-3003	400	4	)	)	PUNCT
ejpam-3003	400	5	taking	take	VERB
ejpam-3003	400	6	the	the	DET
ejpam-3003	400	7	hölder	hölder	NOUN
ejpam-3003	400	8	inequality	inequality	NOUN
ejpam-3003	400	9	and	and	CCONJ
ejpam-3003	400	10	(	(	PUNCT
ejpam-3003	400	11	4.5	4.5	NUM
ejpam-3003	400	12	)	)	PUNCT
ejpam-3003	400	13	into	into	ADP
ejpam-3003	400	14	account	account	NOUN
ejpam-3003	400	15	,	,	PUNCT
ejpam-3003	400	16	we	we	PRON
ejpam-3003	400	17	have∫	have∫	VERB
ejpam-3003	400	18	ω	ω	PROPN
ejpam-3003	400	19	(	(	PUNCT
ejpam-3003	400	20	∫	∫	PROPN
ejpam-3003	400	21	t	t	PROPN
ejpam-3003	400	22	0	0	NUM
ejpam-3003	400	23	g(t−	g(t−	PROPN
ejpam-3003	400	24	s)[u(t)−	s)[u(t)−	PROPN
ejpam-3003	400	25	u(s)]ds	u(s)]ds	NOUN
ejpam-3003	400	26	)	)	PUNCT
ejpam-3003	401	1	ρ+1	ρ+1	NUM
ejpam-3003	401	2	dx	dx	PROPN
ejpam-3003	401	3	=	=	SYM
ejpam-3003	401	4	∫	∫	PROPN
ejpam-3003	401	5	ω	ω	PROPN
ejpam-3003	401	6	(	(	PUNCT
ejpam-3003	401	7	∫	∫	PROPN
ejpam-3003	401	8	t	t	PROPN
ejpam-3003	401	9	0	0	NUM
ejpam-3003	402	1	[	[	X
ejpam-3003	402	2	g(t−	g(t−	NOUN
ejpam-3003	402	3	s	s	PART
ejpam-3003	402	4	)	)	PUNCT
ejpam-3003	402	5	]	]	PUNCT
ejpam-3003	403	1	ρ	ρ	PUNCT
ejpam-3003	403	2	ρ+1	ρ+1	NOUN
ejpam-3003	404	1	[	[	X
ejpam-3003	404	2	g(t−	g(t−	NOUN
ejpam-3003	404	3	s	s	PART
ejpam-3003	404	4	)	)	PUNCT
ejpam-3003	404	5	]	]	PUNCT
ejpam-3003	405	1	1	1	NUM
ejpam-3003	405	2	ρ+1	ρ+1	NUM
ejpam-3003	405	3	[	[	X
ejpam-3003	405	4	u(t)−	u(t)−	PROPN
ejpam-3003	405	5	u(s)]ds	u(s)]ds	NOUN
ejpam-3003	405	6	)	)	PUNCT
ejpam-3003	405	7	ρ+1	ρ+1	NUM
ejpam-3003	405	8	dx	dx	X
ejpam-3003	405	9	≤	≤	NUM
ejpam-3003	405	10	(	(	PUNCT
ejpam-3003	405	11	∫	∫	PROPN
ejpam-3003	405	12	t	t	PROPN
ejpam-3003	405	13	0	0	NUM
ejpam-3003	406	1	g(s)ds)ρ	g(s)ds)ρ	NOUN
ejpam-3003	406	2	∫	∫	PROPN
ejpam-3003	406	3	t	t	PROPN
ejpam-3003	406	4	0	0	NUM
ejpam-3003	406	5	g(t−	g(t−	PROPN
ejpam-3003	406	6	s	s	PART
ejpam-3003	406	7	)	)	PUNCT
ejpam-3003	406	8	∫	∫	PROPN
ejpam-3003	406	9	ω	ω	PROPN
ejpam-3003	406	10	|u(t)−	|u(t)−	PROPN
ejpam-3003	406	11	u(s)|ρ+1dxds	u(s)|ρ+1dxds	PROPN
ejpam-3003	406	12	≤	≤	PROPN
ejpam-3003	406	13	(	(	PUNCT
ejpam-3003	406	14	1−	1−	NUM
ejpam-3003	406	15	l(t))ρbρ+1	l(t))ρbρ+1	SYM
ejpam-3003	407	1	ρ+1	ρ+1	NUM
ejpam-3003	407	2	∫	∫	NOUN
ejpam-3003	407	3	t	t	PROPN
ejpam-3003	407	4	0	0	NUM
ejpam-3003	407	5	g(t−	g(t−	PROPN
ejpam-3003	407	6	s)‖∇u(t)−∇u(s)‖ρ+1	s)‖∇u(t)−∇u(s)‖ρ+1	VERB
ejpam-3003	407	7	2	2	NUM
ejpam-3003	407	8	ds	ds	ADJ
ejpam-3003	407	9	≤	≤	NUM
ejpam-3003	407	10	bρ+1	bρ+1	ADP
ejpam-3003	407	11	ρ+1(1−	ρ+1(1−	NUM
ejpam-3003	407	12	b)ρ	b)ρ	NOUN
ejpam-3003	407	13	(	(	PUNCT
ejpam-3003	407	14	4(p+	4(p+	NUM
ejpam-3003	407	15	1)e(0	1)e(0	NOUN
ejpam-3003	407	16	)	)	PUNCT
ejpam-3003	407	17	(	(	PUNCT
ejpam-3003	407	18	p−	p−	NOUN
ejpam-3003	407	19	1)b	1)b	X
ejpam-3003	407	20	)	)	PUNCT
ejpam-3003	408	1	ρ−1	ρ−1	PROPN
ejpam-3003	408	2	2	2	NUM
ejpam-3003	408	3	(	(	PUNCT
ejpam-3003	408	4	g	g	PROPN
ejpam-3003	408	5	◦	◦	PROPN
ejpam-3003	408	6	∇u)(t	∇u)(t	PROPN
ejpam-3003	408	7	)	)	PUNCT
ejpam-3003	408	8	.	.	PUNCT
ejpam-3003	409	1	(	(	PUNCT
ejpam-3003	409	2	4.6	4.6	X
ejpam-3003	409	3	)	)	PUNCT
ejpam-3003	409	4	lemma	lemma	PROPN
ejpam-3003	409	5	8	8	NUM
ejpam-3003	409	6	.	.	PUNCT
ejpam-3003	410	1	for	for	ADP
ejpam-3003	410	2	ε	ε	PROPN
ejpam-3003	410	3	>	>	X
ejpam-3003	410	4	0	0	PUNCT
ejpam-3003	410	5	is	be	AUX
ejpam-3003	410	6	small	small	ADJ
ejpam-3003	410	7	enough	enough	ADV
ejpam-3003	410	8	and	and	CCONJ
ejpam-3003	410	9	m	m	VERB
ejpam-3003	410	10	>	>	X
ejpam-3003	410	11	0	0	PUNCT
ejpam-3003	410	12	is	be	AUX
ejpam-3003	410	13	large	large	ADJ
ejpam-3003	410	14	enough	enough	ADV
ejpam-3003	410	15	,	,	PUNCT
ejpam-3003	410	16	the	the	DET
ejpam-3003	410	17	inequality	inequality	NOUN
ejpam-3003	410	18	c1f	c1f	X
ejpam-3003	410	19	(	(	PUNCT
ejpam-3003	410	20	t	t	NOUN
ejpam-3003	410	21	)	)	PUNCT
ejpam-3003	410	22	≤	≤	NOUN
ejpam-3003	410	23	e(t	e(t	NOUN
ejpam-3003	410	24	)	)	PUNCT
ejpam-3003	410	25	≤	≤	PROPN
ejpam-3003	411	1	c2f	c2f	X
ejpam-3003	411	2	(	(	PUNCT
ejpam-3003	411	3	t	t	PROPN
ejpam-3003	411	4	)	)	PUNCT
ejpam-3003	411	5	(	(	PUNCT
ejpam-3003	411	6	4.7	4.7	NUM
ejpam-3003	411	7	)	)	PUNCT
ejpam-3003	411	8	holds	hold	VERB
ejpam-3003	411	9	for	for	ADP
ejpam-3003	411	10	two	two	NUM
ejpam-3003	411	11	positive	positive	ADJ
ejpam-3003	411	12	constants	constant	NOUN
ejpam-3003	411	13	c1	c1	PROPN
ejpam-3003	411	14	and	and	CCONJ
ejpam-3003	411	15	c2	c2	PROPN
ejpam-3003	411	16	.	.	PUNCT
ejpam-3003	412	1	proof	proof	NOUN
ejpam-3003	412	2	.	.	PUNCT
ejpam-3003	413	1	by	by	ADP
ejpam-3003	413	2	using	use	VERB
ejpam-3003	413	3	young	young	ADJ
ejpam-3003	413	4	inequality	inequality	NOUN
ejpam-3003	413	5	,	,	PUNCT
ejpam-3003	413	6	sobolev	sobolev	NOUN
ejpam-3003	413	7	embedding	embed	VERB
ejpam-3003	413	8	theorem	theorem	NOUN
ejpam-3003	413	9	and	and	CCONJ
ejpam-3003	413	10	(	(	PUNCT
ejpam-3003	413	11	4.5	4.5	NUM
ejpam-3003	413	12	)	)	PUNCT
ejpam-3003	413	13	,	,	PUNCT
ejpam-3003	413	14	we	we	PRON
ejpam-3003	413	15	deduce	deduce	VERB
ejpam-3003	413	16	that	that	SCONJ
ejpam-3003	413	17	|1	|1	NUM
ejpam-3003	413	18	ρ	ρ	NUM
ejpam-3003	413	19	∫	∫	PROPN
ejpam-3003	413	20	ω	ω	PROPN
ejpam-3003	413	21	|ut|ρ−1utudx|	|ut|ρ−1utudx|	NOUN
ejpam-3003	413	22	≤	≤	NUM
ejpam-3003	413	23	1	1	NUM
ejpam-3003	413	24	ρ+	ρ+	NUM
ejpam-3003	413	25	1	1	NUM
ejpam-3003	413	26	‖ut‖ρ+1	‖ut‖ρ+1	SYM
ejpam-3003	413	27	ρ+1	ρ+1	NUM
ejpam-3003	413	28	+	+	CCONJ
ejpam-3003	413	29	1	1	NUM
ejpam-3003	413	30	ρ(ρ+	ρ(ρ+	NUM
ejpam-3003	413	31	1	1	NUM
ejpam-3003	413	32	)	)	PUNCT
ejpam-3003	413	33	‖u‖ρ+1	‖u‖ρ+1	NOUN
ejpam-3003	414	1	ρ+1	ρ+1	NUM
ejpam-3003	414	2	≤	≤	NUM
ejpam-3003	414	3	1	1	NUM
ejpam-3003	414	4	ρ+	ρ+	NOUN
ejpam-3003	414	5	1	1	NUM
ejpam-3003	414	6	‖ut‖ρ+1	‖ut‖ρ+1	SYM
ejpam-3003	414	7	ρ+1	ρ+1	NOUN
ejpam-3003	414	8	+	+	CCONJ
ejpam-3003	414	9	bρ+1	bρ+1	NUM
ejpam-3003	414	10	ρ+1	ρ+1	NUM
ejpam-3003	414	11	ρ(ρ+	ρ(ρ+	NOUN
ejpam-3003	414	12	1	1	NUM
ejpam-3003	414	13	)	)	PUNCT
ejpam-3003	414	14	‖∇u‖ρ+1	‖∇u‖ρ+1	NUM
ejpam-3003	414	15	2	2	NUM
ejpam-3003	414	16	≤	≤	NUM
ejpam-3003	414	17	1	1	NUM
ejpam-3003	414	18	ρ+	ρ+	NOUN
ejpam-3003	414	19	1	1	NUM
ejpam-3003	414	20	‖ut‖ρ+1	‖ut‖ρ+1	SYM
ejpam-3003	414	21	ρ+1	ρ+1	NOUN
ejpam-3003	414	22	+	+	CCONJ
ejpam-3003	414	23	bρ+1	bρ+1	NUM
ejpam-3003	414	24	ρ+1	ρ+1	NUM
ejpam-3003	414	25	ρ(ρ+	ρ(ρ+	NOUN
ejpam-3003	414	26	1	1	NUM
ejpam-3003	414	27	)	)	PUNCT
ejpam-3003	414	28	(	(	PUNCT
ejpam-3003	414	29	2(p+	2(p+	NUM
ejpam-3003	414	30	1)e(0	1)e(0	NOUN
ejpam-3003	414	31	)	)	PUNCT
ejpam-3003	414	32	(	(	PUNCT
ejpam-3003	414	33	p−	p−	NOUN
ejpam-3003	414	34	1)b	1)b	X
ejpam-3003	414	35	)	)	PUNCT
ejpam-3003	414	36	ρ−1	ρ−1	PROPN
ejpam-3003	414	37	2	2	NUM
ejpam-3003	414	38	‖∇u‖22	‖∇u‖22	NOUN
ejpam-3003	414	39	.	.	PUNCT
ejpam-3003	415	1	(	(	PUNCT
ejpam-3003	415	2	4.8	4.8	NUM
ejpam-3003	415	3	)	)	PUNCT
ejpam-3003	415	4	from	from	ADP
ejpam-3003	415	5	the	the	DET
ejpam-3003	415	6	young	young	ADJ
ejpam-3003	415	7	inequality	inequality	NOUN
ejpam-3003	415	8	,	,	PUNCT
ejpam-3003	415	9	(	(	PUNCT
ejpam-3003	415	10	4.5	4.5	NUM
ejpam-3003	415	11	)	)	PUNCT
ejpam-3003	415	12	and	and	CCONJ
ejpam-3003	415	13	lemma	lemma	PROPN
ejpam-3003	415	14	5	5	NUM
ejpam-3003	415	15	,	,	PUNCT
ejpam-3003	415	16	we	we	PRON
ejpam-3003	415	17	get	get	VERB
ejpam-3003	415	18	that	that	PRON
ejpam-3003	415	19	|1	|1	NUM
ejpam-3003	416	1	ρ	ρ	NUM
ejpam-3003	416	2	∫	∫	PROPN
ejpam-3003	416	3	ω	ω	PROPN
ejpam-3003	417	1	|ut|ρ−1ut	|ut|ρ−1ut	PROPN
ejpam-3003	417	2	∫	∫	PROPN
ejpam-3003	417	3	t	t	PROPN
ejpam-3003	417	4	0	0	NUM
ejpam-3003	417	5	g(t−	g(t−	PROPN
ejpam-3003	417	6	s)[u(t)−	s)[u(t)−	PROPN
ejpam-3003	417	7	u(s)]dsdx|	u(s)]dsdx|	ADJ
ejpam-3003	417	8	≤	≤	NUM
ejpam-3003	417	9	1	1	NUM
ejpam-3003	417	10	ρ+	ρ+	NOUN
ejpam-3003	417	11	1	1	NUM
ejpam-3003	417	12	‖ut‖ρ+1	‖ut‖ρ+1	SYM
ejpam-3003	417	13	ρ+1	ρ+1	NUM
ejpam-3003	417	14	+	+	CCONJ
ejpam-3003	417	15	1	1	NUM
ejpam-3003	417	16	ρ(ρ+	ρ(ρ+	NUM
ejpam-3003	417	17	1	1	NUM
ejpam-3003	417	18	)	)	PUNCT
ejpam-3003	418	1	∫	∫	PROPN
ejpam-3003	418	2	ω	ω	PROPN
ejpam-3003	418	3	(	(	PUNCT
ejpam-3003	418	4	∫	∫	PROPN
ejpam-3003	418	5	t	t	PROPN
ejpam-3003	418	6	0	0	NUM
ejpam-3003	418	7	g(t−	g(t−	PROPN
ejpam-3003	418	8	s)[u(t)−	s)[u(t)−	PROPN
ejpam-3003	418	9	u(s)]ds	u(s)]ds	NOUN
ejpam-3003	418	10	)	)	PUNCT
ejpam-3003	419	1	ρ+1	ρ+1	NOUN
ejpam-3003	419	2	dx	dx	PROPN
ejpam-3003	419	3	h.f	h.f	PROPN
ejpam-3003	419	4	.	.	PROPN
ejpam-3003	419	5	di	di	PROPN
ejpam-3003	419	6	,	,	PUNCT
ejpam-3003	419	7	y.d	y.d	PROPN
ejpam-3003	419	8	.	.	PROPN
ejpam-3003	419	9	shang	shang	PROPN
ejpam-3003	419	10	/	/	SYM
ejpam-3003	419	11	eur	eur	PROPN
ejpam-3003	419	12	.	.	PUNCT
ejpam-3003	420	1	j.	j.	PROPN
ejpam-3003	420	2	pure	pure	PROPN
ejpam-3003	420	3	appl	appl	PROPN
ejpam-3003	420	4	.	.	PROPN
ejpam-3003	420	5	math	math	PROPN
ejpam-3003	420	6	,	,	PUNCT
ejpam-3003	420	7	10	10	NUM
ejpam-3003	420	8	(	(	PUNCT
ejpam-3003	420	9	4	4	NUM
ejpam-3003	420	10	)	)	PUNCT
ejpam-3003	420	11	(	(	PUNCT
ejpam-3003	420	12	2017	2017	NUM
ejpam-3003	420	13	)	)	PUNCT
ejpam-3003	420	14	,	,	PUNCT
ejpam-3003	420	15	668	668	NUM
ejpam-3003	420	16	-	-	SYM
ejpam-3003	420	17	701	701	NUM
ejpam-3003	420	18	686	686	NUM
ejpam-3003	420	19	≤	≤	NUM
ejpam-3003	420	20	1	1	NUM
ejpam-3003	420	21	ρ+	ρ+	NOUN
ejpam-3003	420	22	1	1	NUM
ejpam-3003	420	23	‖ut‖ρ+1	‖ut‖ρ+1	SYM
ejpam-3003	420	24	ρ+1	ρ+1	NOUN
ejpam-3003	420	25	+	+	CCONJ
ejpam-3003	420	26	bρ+1	bρ+1	NUM
ejpam-3003	420	27	ρ+1	ρ+1	NUM
ejpam-3003	420	28	ρ(ρ+	ρ(ρ+	NOUN
ejpam-3003	420	29	1	1	NUM
ejpam-3003	420	30	)	)	PUNCT
ejpam-3003	420	31	(	(	PUNCT
ejpam-3003	420	32	1−	1−	NUM
ejpam-3003	420	33	b)ρ	b)ρ	NOUN
ejpam-3003	420	34	(	(	PUNCT
ejpam-3003	420	35	4(p+	4(p+	NUM
ejpam-3003	420	36	1)e(0	1)e(0	NOUN
ejpam-3003	420	37	)	)	PUNCT
ejpam-3003	420	38	(	(	PUNCT
ejpam-3003	420	39	p−	p−	NOUN
ejpam-3003	420	40	1)b	1)b	X
ejpam-3003	420	41	)	)	PUNCT
ejpam-3003	421	1	ρ−1	ρ−1	PROPN
ejpam-3003	421	2	2	2	NUM
ejpam-3003	421	3	(	(	PUNCT
ejpam-3003	421	4	g	g	PROPN
ejpam-3003	421	5	◦	◦	PROPN
ejpam-3003	421	6	∇u)(t	∇u)(t	PROPN
ejpam-3003	421	7	)	)	PUNCT
ejpam-3003	421	8	.	.	PUNCT
ejpam-3003	422	1	(	(	PUNCT
ejpam-3003	422	2	4.9	4.9	NUM
ejpam-3003	422	3	)	)	PUNCT
ejpam-3003	422	4	considering	consider	VERB
ejpam-3003	422	5	the	the	DET
ejpam-3003	422	6	expressions	expression	NOUN
ejpam-3003	422	7	of	of	ADP
ejpam-3003	422	8	f	f	PROPN
ejpam-3003	422	9	(	(	PUNCT
ejpam-3003	422	10	t	t	PROPN
ejpam-3003	422	11	)	)	PUNCT
ejpam-3003	422	12	,	,	PUNCT
ejpam-3003	422	13	e(t	e(t	NOUN
ejpam-3003	422	14	)	)	PUNCT
ejpam-3003	422	15	,	,	PUNCT
ejpam-3003	422	16	ψ(t	ψ(t	PROPN
ejpam-3003	422	17	)	)	PUNCT
ejpam-3003	422	18	,	,	PUNCT
ejpam-3003	422	19	φ(t	φ(t	PROPN
ejpam-3003	422	20	)	)	PUNCT
ejpam-3003	422	21	and	and	CCONJ
ejpam-3003	422	22	the	the	DET
ejpam-3003	422	23	conditions	condition	NOUN
ejpam-3003	422	24	(	(	PUNCT
ejpam-3003	422	25	a2	a2	PROPN
ejpam-3003	422	26	)	)	PUNCT
ejpam-3003	422	27	,	,	PUNCT
ejpam-3003	422	28	it	it	PRON
ejpam-3003	422	29	follows	follow	VERB
ejpam-3003	422	30	that	that	SCONJ
ejpam-3003	423	1	f	f	PROPN
ejpam-3003	423	2	(	(	PUNCT
ejpam-3003	423	3	t	t	PROPN
ejpam-3003	423	4	)	)	PUNCT
ejpam-3003	423	5	≤me(t	≤me(t	NUM
ejpam-3003	423	6	)	)	PUNCT
ejpam-3003	424	1	+	+	CCONJ
ejpam-3003	424	2	(	(	PUNCT
ejpam-3003	424	3	1	1	NUM
ejpam-3003	424	4	ρ+	ρ+	NUM
ejpam-3003	424	5	1	1	NUM
ejpam-3003	424	6	+	+	CCONJ
ejpam-3003	424	7	ε	ε	PROPN
ejpam-3003	424	8	ρ+	ρ+	NUM
ejpam-3003	424	9	1	1	NUM
ejpam-3003	424	10	)	)	PUNCT
ejpam-3003	424	11	ξ(t)‖ut‖ρ+1	ξ(t)‖ut‖ρ+1	X
ejpam-3003	425	1	ρ+1	ρ+1	NOUN
ejpam-3003	425	2	+	+	CCONJ
ejpam-3003	425	3	ε	ε	X
ejpam-3003	425	4	bρ+1	bρ+1	NUM
ejpam-3003	425	5	ρ+1	ρ+1	NUM
ejpam-3003	425	6	ρ(ρ+	ρ(ρ+	NOUN
ejpam-3003	425	7	1	1	NUM
ejpam-3003	425	8	)	)	PUNCT
ejpam-3003	425	9	(	(	PUNCT
ejpam-3003	425	10	2(p+	2(p+	NUM
ejpam-3003	425	11	1)e(0	1)e(0	NOUN
ejpam-3003	425	12	)	)	PUNCT
ejpam-3003	425	13	(	(	PUNCT
ejpam-3003	425	14	p−	p−	NOUN
ejpam-3003	425	15	1)b	1)b	X
ejpam-3003	425	16	)	)	PUNCT
ejpam-3003	425	17	ρ−1	ρ−1	PROPN
ejpam-3003	425	18	2	2	NUM
ejpam-3003	425	19	ξ(t)‖∇u‖22	ξ(t)‖∇u‖22	PUNCT
ejpam-3003	426	1	+	+	NUM
ejpam-3003	426	2	bρ+1	bρ+1	NUM
ejpam-3003	426	3	ρ+1	ρ+1	NUM
ejpam-3003	426	4	ρ(ρ+	ρ(ρ+	NOUN
ejpam-3003	426	5	1	1	NUM
ejpam-3003	426	6	)	)	PUNCT
ejpam-3003	426	7	(	(	PUNCT
ejpam-3003	426	8	1−	1−	NUM
ejpam-3003	426	9	l(t))ρ	l(t))ρ	INTJ
ejpam-3003	426	10	(	(	PUNCT
ejpam-3003	426	11	4(p+	4(p+	PROPN
ejpam-3003	426	12	1)e(0	1)e(0	NOUN
ejpam-3003	426	13	)	)	PUNCT
ejpam-3003	426	14	(	(	PUNCT
ejpam-3003	426	15	p−	p−	NOUN
ejpam-3003	426	16	1)b	1)b	X
ejpam-3003	426	17	)	)	PUNCT
ejpam-3003	426	18	ρ−1	ρ−1	PROPN
ejpam-3003	426	19	2	2	NUM
ejpam-3003	426	20	ξ(t)(g	ξ(t)(g	ADP
ejpam-3003	426	21	◦	◦	PROPN
ejpam-3003	426	22	∇u)(t	∇u)(t	PROPN
ejpam-3003	426	23	)	)	PUNCT
ejpam-3003	426	24	≤me(t	≤me(t	NUM
ejpam-3003	426	25	)	)	PUNCT
ejpam-3003	427	1	+	+	CCONJ
ejpam-3003	427	2	(	(	PUNCT
ejpam-3003	427	3	1	1	NUM
ejpam-3003	427	4	ρ+	ρ+	NUM
ejpam-3003	427	5	1	1	NUM
ejpam-3003	427	6	+	+	CCONJ
ejpam-3003	427	7	ε	ε	PROPN
ejpam-3003	427	8	ρ+	ρ+	NUM
ejpam-3003	427	9	1	1	NUM
ejpam-3003	427	10	)	)	PUNCT
ejpam-3003	427	11	ξ(0)‖ut‖ρ+1	ξ(0)‖ut‖ρ+1	X
ejpam-3003	427	12	ρ+1	ρ+1	NOUN
ejpam-3003	427	13	+	+	CCONJ
ejpam-3003	427	14	ε	ε	X
ejpam-3003	427	15	bρ+1	bρ+1	NUM
ejpam-3003	427	16	ρ+1	ρ+1	NUM
ejpam-3003	427	17	ρ(ρ+	ρ(ρ+	NOUN
ejpam-3003	427	18	1	1	NUM
ejpam-3003	427	19	)	)	PUNCT
ejpam-3003	427	20	(	(	PUNCT
ejpam-3003	427	21	2(p+	2(p+	NUM
ejpam-3003	427	22	1)e(0	1)e(0	NOUN
ejpam-3003	427	23	)	)	PUNCT
ejpam-3003	427	24	(	(	PUNCT
ejpam-3003	427	25	p−	p−	NOUN
ejpam-3003	427	26	1)b	1)b	X
ejpam-3003	427	27	)	)	PUNCT
ejpam-3003	427	28	ρ−1	ρ−1	PROPN
ejpam-3003	427	29	2	2	NUM
ejpam-3003	427	30	ξ(0)‖∇u‖22	ξ(0)‖∇u‖22	NOUN
ejpam-3003	427	31	+	+	CCONJ
ejpam-3003	427	32	bρ+1	bρ+1	NUM
ejpam-3003	427	33	ρ+1	ρ+1	NUM
ejpam-3003	427	34	ρ(ρ+	ρ(ρ+	NOUN
ejpam-3003	427	35	1	1	NUM
ejpam-3003	427	36	)	)	PUNCT
ejpam-3003	427	37	(	(	PUNCT
ejpam-3003	427	38	1−	1−	NUM
ejpam-3003	427	39	b)ρ	b)ρ	NOUN
ejpam-3003	427	40	(	(	PUNCT
ejpam-3003	427	41	4(p+	4(p+	NUM
ejpam-3003	427	42	1)e(0	1)e(0	NOUN
ejpam-3003	427	43	)	)	PUNCT
ejpam-3003	427	44	(	(	PUNCT
ejpam-3003	427	45	p−	p−	NOUN
ejpam-3003	427	46	1)b	1)b	X
ejpam-3003	427	47	)	)	PUNCT
ejpam-3003	427	48	ρ−1	ρ−1	PROPN
ejpam-3003	427	49	2	2	NUM
ejpam-3003	427	50	ξ(0)(g	ξ(0)(g	PROPN
ejpam-3003	427	51	◦	◦	PROPN
ejpam-3003	427	52	∇u)(t	∇u)(t	PROPN
ejpam-3003	427	53	)	)	PUNCT
ejpam-3003	427	54	≤	≤	NUM
ejpam-3003	427	55	1	1	NUM
ejpam-3003	427	56	c1	c1	PROPN
ejpam-3003	427	57	e(t	e(t	PROPN
ejpam-3003	427	58	)	)	PUNCT
ejpam-3003	427	59	,	,	PUNCT
ejpam-3003	427	60	(	(	PUNCT
ejpam-3003	427	61	4.10	4.10	NUM
ejpam-3003	427	62	)	)	PUNCT
ejpam-3003	427	63	and	and	CCONJ
ejpam-3003	427	64	f	f	PROPN
ejpam-3003	427	65	(	(	PUNCT
ejpam-3003	427	66	t	t	PROPN
ejpam-3003	427	67	)	)	PUNCT
ejpam-3003	427	68	≥me(t)−	≥me(t)−	PROPN
ejpam-3003	427	69	(	(	PUNCT
ejpam-3003	427	70	1	1	NUM
ejpam-3003	427	71	ρ+	ρ+	NUM
ejpam-3003	427	72	1	1	NUM
ejpam-3003	427	73	+	+	CCONJ
ejpam-3003	427	74	ε	ε	PROPN
ejpam-3003	427	75	ρ+	ρ+	NUM
ejpam-3003	427	76	1	1	NUM
ejpam-3003	427	77	)	)	PUNCT
ejpam-3003	427	78	ξ(0)‖ut‖ρ+1	ξ(0)‖ut‖ρ+1	PROPN
ejpam-3003	428	1	ρ+1	ρ+1	NOUN
ejpam-3003	428	2	−	−	PROPN
ejpam-3003	428	3	ε	ε	PROPN
ejpam-3003	428	4	bρ+1	bρ+1	NUM
ejpam-3003	428	5	ρ+1	ρ+1	NUM
ejpam-3003	428	6	ρ(ρ+	ρ(ρ+	NOUN
ejpam-3003	428	7	1	1	NUM
ejpam-3003	428	8	)	)	PUNCT
ejpam-3003	428	9	(	(	PUNCT
ejpam-3003	428	10	2(p+	2(p+	NUM
ejpam-3003	428	11	1)e(0	1)e(0	NOUN
ejpam-3003	428	12	)	)	PUNCT
ejpam-3003	428	13	(	(	PUNCT
ejpam-3003	428	14	p−	p−	NOUN
ejpam-3003	428	15	1)b	1)b	X
ejpam-3003	428	16	)	)	PUNCT
ejpam-3003	428	17	ρ−1	ρ−1	PROPN
ejpam-3003	428	18	2	2	NUM
ejpam-3003	428	19	ξ(0)‖∇u‖22	ξ(0)‖∇u‖22	NOUN
ejpam-3003	428	20	−	−	NOUN
ejpam-3003	428	21	bρ+1	bρ+1	NUM
ejpam-3003	428	22	ρ+1	ρ+1	NUM
ejpam-3003	428	23	ρ(ρ+	ρ(ρ+	NOUN
ejpam-3003	428	24	1	1	NUM
ejpam-3003	428	25	)	)	PUNCT
ejpam-3003	428	26	(	(	PUNCT
ejpam-3003	428	27	1−	1−	NUM
ejpam-3003	428	28	l(t))ρ	l(t))ρ	INTJ
ejpam-3003	428	29	(	(	PUNCT
ejpam-3003	428	30	4(p+	4(p+	PROPN
ejpam-3003	428	31	1)e(0	1)e(0	NOUN
ejpam-3003	428	32	)	)	PUNCT
ejpam-3003	428	33	(	(	PUNCT
ejpam-3003	428	34	p−	p−	NOUN
ejpam-3003	428	35	1)b	1)b	X
ejpam-3003	428	36	)	)	PUNCT
ejpam-3003	428	37	ρ−1	ρ−1	PROPN
ejpam-3003	428	38	2	2	NUM
ejpam-3003	428	39	ξ(0)(g	ξ(0)(g	PROPN
ejpam-3003	428	40	◦	◦	PROPN
ejpam-3003	428	41	∇u)(t	∇u)(t	PROPN
ejpam-3003	428	42	)	)	PUNCT
ejpam-3003	428	43	≥	≥	NOUN
ejpam-3003	428	44	[	[	PUNCT
ejpam-3003	428	45	m	m	NOUN
ejpam-3003	428	46	ρ+	ρ+	NUM
ejpam-3003	428	47	1	1	NUM
ejpam-3003	428	48	−	−	PROPN
ejpam-3003	428	49	(	(	PUNCT
ejpam-3003	428	50	1	1	NUM
ejpam-3003	428	51	ρ+	ρ+	NUM
ejpam-3003	428	52	1	1	NUM
ejpam-3003	428	53	+	+	CCONJ
ejpam-3003	428	54	ε	ε	PROPN
ejpam-3003	428	55	ρ+	ρ+	NUM
ejpam-3003	428	56	1	1	NUM
ejpam-3003	428	57	)	)	PUNCT
ejpam-3003	428	58	ξ(0	ξ(0	NOUN
ejpam-3003	428	59	)	)	PUNCT
ejpam-3003	428	60	]	]	PUNCT
ejpam-3003	429	1	‖ut‖ρ+1	‖ut‖ρ+1	VERB
ejpam-3003	429	2	ρ+1	ρ+1	NOUN
ejpam-3003	429	3	+	+	CCONJ
ejpam-3003	429	4	[	[	PUNCT
ejpam-3003	429	5	m(p−	m(p−	X
ejpam-3003	429	6	1)b	1)b	PROPN
ejpam-3003	429	7	2(p+	2(p+	NUM
ejpam-3003	429	8	1	1	NUM
ejpam-3003	429	9	)	)	PUNCT
ejpam-3003	429	10	−	−	PROPN
ejpam-3003	429	11	ε	ε	PROPN
ejpam-3003	429	12	bρ+1	bρ+1	NUM
ejpam-3003	429	13	ρ+1	ρ+1	NUM
ejpam-3003	429	14	ρ(ρ+	ρ(ρ+	NOUN
ejpam-3003	429	15	1	1	NUM
ejpam-3003	429	16	)	)	PUNCT
ejpam-3003	429	17	(	(	PUNCT
ejpam-3003	429	18	2(p+	2(p+	NUM
ejpam-3003	429	19	1)e(0	1)e(0	NOUN
ejpam-3003	429	20	)	)	PUNCT
ejpam-3003	429	21	(	(	PUNCT
ejpam-3003	429	22	p−	p−	NOUN
ejpam-3003	429	23	1)b	1)b	X
ejpam-3003	429	24	)	)	PUNCT
ejpam-3003	430	1	ρ−1	ρ−1	PROPN
ejpam-3003	430	2	2	2	NUM
ejpam-3003	430	3	ξ(0	ξ(0	NOUN
ejpam-3003	430	4	)	)	PUNCT
ejpam-3003	430	5	]	]	PUNCT
ejpam-3003	431	1	‖∇u‖22	‖∇u‖22	NOUN
ejpam-3003	432	1	+	+	CCONJ
ejpam-3003	432	2	[	[	PUNCT
ejpam-3003	432	3	m(p−	m(p−	X
ejpam-3003	432	4	1	1	NUM
ejpam-3003	432	5	)	)	PUNCT
ejpam-3003	432	6	2(p+	2(p+	NUM
ejpam-3003	432	7	1	1	NUM
ejpam-3003	432	8	)	)	PUNCT
ejpam-3003	432	9	−	−	NOUN
ejpam-3003	432	10	bρ+1	bρ+1	NUM
ejpam-3003	432	11	ρ+1	ρ+1	NUM
ejpam-3003	432	12	ρ(ρ+	ρ(ρ+	NOUN
ejpam-3003	432	13	1	1	NUM
ejpam-3003	432	14	)	)	PUNCT
ejpam-3003	432	15	(	(	PUNCT
ejpam-3003	432	16	1−	1−	NUM
ejpam-3003	432	17	b)ρ	b)ρ	NOUN
ejpam-3003	432	18	(	(	PUNCT
ejpam-3003	432	19	4(p+	4(p+	NUM
ejpam-3003	432	20	1)e(0	1)e(0	NOUN
ejpam-3003	432	21	)	)	PUNCT
ejpam-3003	432	22	(	(	PUNCT
ejpam-3003	432	23	p−	p−	NOUN
ejpam-3003	432	24	1)b	1)b	X
ejpam-3003	432	25	)	)	PUNCT
ejpam-3003	432	26	ρ−1	ρ−1	PROPN
ejpam-3003	432	27	2	2	NUM
ejpam-3003	432	28	ξ(0	ξ(0	NOUN
ejpam-3003	432	29	)	)	PUNCT
ejpam-3003	432	30	]	]	PUNCT
ejpam-3003	432	31	(	(	PUNCT
ejpam-3003	432	32	g	g	PROPN
ejpam-3003	432	33	◦	◦	PROPN
ejpam-3003	432	34	∇u)(t	∇u)(t	PROPN
ejpam-3003	432	35	)	)	PUNCT
ejpam-3003	432	36	≥	≥	NOUN
ejpam-3003	432	37	1	1	NUM
ejpam-3003	432	38	c2	c2	PROPN
ejpam-3003	432	39	e(t	e(t	PROPN
ejpam-3003	432	40	)	)	PUNCT
ejpam-3003	432	41	,	,	PUNCT
ejpam-3003	432	42	(	(	PUNCT
ejpam-3003	432	43	4.11	4.11	NUM
ejpam-3003	432	44	)	)	PUNCT
ejpam-3003	432	45	where	where	SCONJ
ejpam-3003	432	46	ε	ε	PROPN
ejpam-3003	432	47	>	>	X
ejpam-3003	432	48	0	0	NUM
ejpam-3003	432	49	is	be	AUX
ejpam-3003	432	50	small	small	ADJ
ejpam-3003	432	51	enough	enough	ADV
ejpam-3003	432	52	and	and	CCONJ
ejpam-3003	432	53	m	m	VERB
ejpam-3003	432	54	>	>	X
ejpam-3003	432	55	0	0	PUNCT
ejpam-3003	432	56	is	be	AUX
ejpam-3003	432	57	large	large	ADJ
ejpam-3003	432	58	enough	enough	ADV
ejpam-3003	432	59	.	.	PUNCT
ejpam-3003	433	1	lemma	lemma	PROPN
ejpam-3003	433	2	9	9	NUM
ejpam-3003	433	3	.	.	PUNCT
ejpam-3003	434	1	let	let	VERB
ejpam-3003	434	2	the	the	DET
ejpam-3003	434	3	assumptions	assumption	NOUN
ejpam-3003	434	4	(	(	PUNCT
ejpam-3003	434	5	a1)-(a3	a1)-(a3	NOUN
ejpam-3003	434	6	)	)	PUNCT
ejpam-3003	434	7	hold	hold	NOUN
ejpam-3003	434	8	and	and	CCONJ
ejpam-3003	434	9	1	1	NUM
ejpam-3003	434	10	<	<	X
ejpam-3003	434	11	ρ	ρ	X
ejpam-3003	434	12	<	<	X
ejpam-3003	434	13	∞	∞	PROPN
ejpam-3003	434	14	if	if	SCONJ
ejpam-3003	434	15	n	n	NOUN
ejpam-3003	434	16	≤	≤	ADV
ejpam-3003	434	17	2	2	NUM
ejpam-3003	434	18	,	,	PUNCT
ejpam-3003	434	19	1	1	NUM
ejpam-3003	434	20	<	<	X
ejpam-3003	434	21	ρ	ρ	X
ejpam-3003	434	22	≤	≤	PROPN
ejpam-3003	435	1	n+2	n+2	NUM
ejpam-3003	435	2	n−2	n−2	PROPN
ejpam-3003	435	3	if	if	SCONJ
ejpam-3003	435	4	n	n	PRON
ejpam-3003	435	5	≥	≥	NOUN
ejpam-3003	435	6	3	3	NUM
ejpam-3003	435	7	.	.	PUNCT
ejpam-3003	435	8	furthermore	furthermore	ADV
ejpam-3003	435	9	assume	assume	VERB
ejpam-3003	435	10	that	that	SCONJ
ejpam-3003	435	11	e(0	e(0	NOUN
ejpam-3003	435	12	)	)	PUNCT
ejpam-3003	435	13	<	<	X
ejpam-3003	435	14	d̃	d̃	PROPN
ejpam-3003	435	15	and	and	CCONJ
ejpam-3003	435	16	i(u0	i(u0	PROPN
ejpam-3003	435	17	)	)	PUNCT
ejpam-3003	435	18	>	>	X
ejpam-3003	436	1	0	0	NUM
ejpam-3003	436	2	,	,	PUNCT
ejpam-3003	436	3	then	then	ADV
ejpam-3003	436	4	the	the	DET
ejpam-3003	436	5	functional	functional	ADJ
ejpam-3003	436	6	ψ(t	ψ(t	PROPN
ejpam-3003	436	7	)	)	PUNCT
ejpam-3003	436	8	=	=	SYM
ejpam-3003	436	9	ξ(t	ξ(t	PROPN
ejpam-3003	436	10	)	)	PUNCT
ejpam-3003	436	11	ρ	ρ	PROPN
ejpam-3003	436	12	∫	∫	PROPN
ejpam-3003	436	13	ω	ω	PROPN
ejpam-3003	436	14	|ut|	|ut|	NOUN
ejpam-3003	436	15	ρ−1utudx	ρ−1utudx	NOUN
ejpam-3003	436	16	satisfies	satisfy	VERB
ejpam-3003	436	17	the	the	DET
ejpam-3003	436	18	following	follow	VERB
ejpam-3003	436	19	inequality	inequality	NOUN
ejpam-3003	436	20	ψ′(t	ψ′(t	NOUN
ejpam-3003	436	21	)	)	PUNCT
ejpam-3003	436	22	≤	≤	NOUN
ejpam-3003	436	23	[	[	PUNCT
ejpam-3003	436	24	1	1	NUM
ejpam-3003	436	25	ρ	ρ	NUM
ejpam-3003	436	26	+	+	NUM
ejpam-3003	436	27	1	1	NUM
ejpam-3003	436	28	(	(	PUNCT
ejpam-3003	436	29	ρ+	ρ+	NOUN
ejpam-3003	437	1	1)ρα	1)ρα	PROPN
ejpam-3003	437	2	k	k	X
ejpam-3003	437	3	]	]	PUNCT
ejpam-3003	437	4	ξ(t)‖ut‖ρ+1	ξ(t)‖ut‖ρ+1	X
ejpam-3003	438	1	ρ+1	ρ+1	NUM
ejpam-3003	438	2	−	−	PROPN
ejpam-3003	438	3	[	[	PUNCT
ejpam-3003	438	4	b	b	NOUN
ejpam-3003	438	5	2	2	NUM
ejpam-3003	438	6	−	−	PROPN
ejpam-3003	438	7	α	α	PROPN
ejpam-3003	438	8	ρ+	ρ+	NUM
ejpam-3003	438	9	1	1	NUM
ejpam-3003	438	10	kbρ+1	kbρ+1	NOUN
ejpam-3003	438	11	ρ+1	ρ+1	NOUN
ejpam-3003	438	12	(	(	PUNCT
ejpam-3003	438	13	2(p+	2(p+	NUM
ejpam-3003	438	14	1)e(0	1)e(0	NOUN
ejpam-3003	438	15	)	)	PUNCT
ejpam-3003	438	16	(	(	PUNCT
ejpam-3003	438	17	p−	p−	NOUN
ejpam-3003	438	18	1)b	1)b	X
ejpam-3003	438	19	)	)	PUNCT
ejpam-3003	439	1	ρ−1	ρ−1	PROPN
ejpam-3003	439	2	2	2	NUM
ejpam-3003	439	3	h.f	h.f	PROPN
ejpam-3003	439	4	.	.	PROPN
ejpam-3003	439	5	di	di	PROPN
ejpam-3003	439	6	,	,	PUNCT
ejpam-3003	439	7	y.d	y.d	PROPN
ejpam-3003	439	8	.	.	PROPN
ejpam-3003	439	9	shang	shang	PROPN
ejpam-3003	439	10	/	/	SYM
ejpam-3003	439	11	eur	eur	PROPN
ejpam-3003	439	12	.	.	PUNCT
ejpam-3003	440	1	j.	j.	PROPN
ejpam-3003	440	2	pure	pure	PROPN
ejpam-3003	440	3	appl	appl	PROPN
ejpam-3003	440	4	.	.	PROPN
ejpam-3003	440	5	math	math	PROPN
ejpam-3003	440	6	,	,	PUNCT
ejpam-3003	440	7	10	10	NUM
ejpam-3003	440	8	(	(	PUNCT
ejpam-3003	440	9	4	4	NUM
ejpam-3003	440	10	)	)	PUNCT
ejpam-3003	440	11	(	(	PUNCT
ejpam-3003	440	12	2017	2017	NUM
ejpam-3003	440	13	)	)	PUNCT
ejpam-3003	440	14	,	,	PUNCT
ejpam-3003	440	15	668	668	NUM
ejpam-3003	440	16	-	-	SYM
ejpam-3003	440	17	701	701	NUM
ejpam-3003	440	18	687	687	NUM
ejpam-3003	440	19	−	−	NOUN
ejpam-3003	440	20	qα	qα	PROPN
ejpam-3003	440	21	q	q	PROPN
ejpam-3003	441	1	+	+	NUM
ejpam-3003	441	2	1	1	NUM
ejpam-3003	441	3	bq+1	bq+1	NUM
ejpam-3003	441	4	q+1	q+1	PROPN
ejpam-3003	441	5	(	(	PUNCT
ejpam-3003	441	6	2(p+	2(p+	NUM
ejpam-3003	441	7	1)e(0	1)e(0	NOUN
ejpam-3003	441	8	)	)	PUNCT
ejpam-3003	441	9	(	(	PUNCT
ejpam-3003	441	10	p−	p−	NOUN
ejpam-3003	441	11	1)b	1)b	X
ejpam-3003	441	12	)	)	PUNCT
ejpam-3003	442	1	q−1	q−1	PROPN
ejpam-3003	442	2	2	2	NUM
ejpam-3003	442	3	]	]	PUNCT
ejpam-3003	442	4	ξ(t)‖∇u‖22	ξ(t)‖∇u‖22	PUNCT
ejpam-3003	443	1	+	+	CCONJ
ejpam-3003	443	2	1−	1−	NUM
ejpam-3003	443	3	b	b	PROPN
ejpam-3003	443	4	2b	2b	NUM
ejpam-3003	443	5	ξ(t)(g	ξ(t)(g	ADP
ejpam-3003	443	6	◦	◦	PROPN
ejpam-3003	443	7	∇u)(t	∇u)(t	PROPN
ejpam-3003	443	8	)	)	PUNCT
ejpam-3003	444	1	+	+	NUM
ejpam-3003	445	1	ξ(t)‖u‖p+1	ξ(t)‖u‖p+1	INTJ
ejpam-3003	446	1	p+1	p+1	NOUN
ejpam-3003	447	1	+	+	NOUN
ejpam-3003	447	2	1	1	NUM
ejpam-3003	447	3	(	(	PUNCT
ejpam-3003	447	4	q	q	PROPN
ejpam-3003	447	5	+	+	NUM
ejpam-3003	447	6	1)α	1)α	NUM
ejpam-3003	447	7	ξ(t)‖ut‖q+1	ξ(t)‖ut‖q+1	PROPN
ejpam-3003	447	8	γ1,q+1	γ1,q+1	PROPN
ejpam-3003	447	9	.	.	PROPN
ejpam-3003	447	10	(	(	PUNCT
ejpam-3003	447	11	4.12	4.12	NUM
ejpam-3003	447	12	)	)	PUNCT
ejpam-3003	447	13	proof	proof	NOUN
ejpam-3003	447	14	.	.	PUNCT
ejpam-3003	448	1	by	by	ADP
ejpam-3003	448	2	using	use	VERB
ejpam-3003	448	3	the	the	DET
ejpam-3003	448	4	equation	equation	NOUN
ejpam-3003	448	5	of	of	ADP
ejpam-3003	448	6	(	(	PUNCT
ejpam-3003	448	7	1.1	1.1	NUM
ejpam-3003	448	8	)	)	PUNCT
ejpam-3003	448	9	,	,	PUNCT
ejpam-3003	448	10	we	we	PRON
ejpam-3003	448	11	deduce	deduce	VERB
ejpam-3003	448	12	that	that	PRON
ejpam-3003	448	13	ψ′(t	ψ′(t	PUNCT
ejpam-3003	448	14	)	)	PUNCT
ejpam-3003	448	15	=	=	SYM
ejpam-3003	448	16	ξ(t	ξ(t	PROPN
ejpam-3003	448	17	)	)	PUNCT
ejpam-3003	448	18	ρ	ρ	PROPN
ejpam-3003	448	19	‖ut‖ρ+1	‖ut‖ρ+1	PROPN
ejpam-3003	448	20	ρ+1	ρ+1	NOUN
ejpam-3003	448	21	+	+	NUM
ejpam-3003	448	22	ξ(t	ξ(t	NOUN
ejpam-3003	448	23	)	)	PUNCT
ejpam-3003	448	24	∫	∫	PROPN
ejpam-3003	448	25	ω	ω	NUM
ejpam-3003	448	26	|ut|ρ−1uttudx+	|ut|ρ−1uttudx+	NUM
ejpam-3003	448	27	ξ′(t	ξ′(t	SYM
ejpam-3003	448	28	)	)	PUNCT
ejpam-3003	448	29	ρ	ρ	PROPN
ejpam-3003	448	30	∫	∫	PROPN
ejpam-3003	448	31	ω	ω	NUM
ejpam-3003	448	32	|ut|ρ−1utudx	|ut|ρ−1utudx	NOUN
ejpam-3003	448	33	=	=	SYM
ejpam-3003	448	34	ξ(t	ξ(t	PROPN
ejpam-3003	448	35	)	)	PUNCT
ejpam-3003	448	36	ρ	ρ	PROPN
ejpam-3003	448	37	‖ut‖ρ+1	‖ut‖ρ+1	PROPN
ejpam-3003	449	1	ρ+1	ρ+1	NOUN
ejpam-3003	449	2	−	−	PUNCT
ejpam-3003	449	3	ξ(t)‖∇u‖	ξ(t)‖∇u‖	PROPN
ejpam-3003	449	4	2	2	NUM
ejpam-3003	449	5	2	2	NUM
ejpam-3003	449	6	+	+	NUM
ejpam-3003	449	7	ξ(t	ξ(t	NOUN
ejpam-3003	449	8	)	)	PUNCT
ejpam-3003	449	9	∫	∫	PROPN
ejpam-3003	449	10	ω	ω	PROPN
ejpam-3003	449	11	∇u(t	∇u(t	PROPN
ejpam-3003	449	12	)	)	PUNCT
ejpam-3003	449	13	·	·	PUNCT
ejpam-3003	450	1	∫	∫	PROPN
ejpam-3003	451	1	t	t	PROPN
ejpam-3003	451	2	0	0	NUM
ejpam-3003	451	3	g(t−	g(t−	PROPN
ejpam-3003	451	4	s)∇u(s)dsdx	s)∇u(s)dsdx	PROPN
ejpam-3003	451	5	+	+	PROPN
ejpam-3003	452	1	ξ(t)‖u‖p+1	ξ(t)‖u‖p+1	PROPN
ejpam-3003	452	2	p+1	p+1	NOUN
ejpam-3003	452	3	+	+	PUNCT
ejpam-3003	452	4	ξ′(t	ξ′(t	X
ejpam-3003	452	5	)	)	PUNCT
ejpam-3003	452	6	ρ	ρ	PROPN
ejpam-3003	452	7	∫	∫	PROPN
ejpam-3003	452	8	ω	ω	NUM
ejpam-3003	452	9	|ut|ρ−1utudx−	|ut|ρ−1utudx−	X
ejpam-3003	452	10	ξ(t	ξ(t	NOUN
ejpam-3003	452	11	)	)	PUNCT
ejpam-3003	452	12	∫	∫	PROPN
ejpam-3003	452	13	γ1	γ1	PROPN
ejpam-3003	452	14	u|ut|q−1utdγ	u|ut|q−1utdγ	NOUN
ejpam-3003	452	15	.	.	PUNCT
ejpam-3003	453	1	(	(	PUNCT
ejpam-3003	453	2	4.13	4.13	NUM
ejpam-3003	453	3	)	)	PUNCT
ejpam-3003	453	4	from	from	ADP
ejpam-3003	453	5	the	the	DET
ejpam-3003	453	6	young	young	ADJ
ejpam-3003	453	7	inequality	inequality	NOUN
ejpam-3003	453	8	and	and	CCONJ
ejpam-3003	453	9	the	the	DET
ejpam-3003	453	10	fact	fact	NOUN
ejpam-3003	453	11	that	that	SCONJ
ejpam-3003	453	12	∫	∫	PROPN
ejpam-3003	453	13	t	t	NOUN
ejpam-3003	453	14	0	0	NUM
ejpam-3003	453	15	g(s)ds	g(s)ds	PROPN
ejpam-3003	453	16	≤	≤	PROPN
ejpam-3003	453	17	∫∞	∫∞	NOUN
ejpam-3003	453	18	0	0	PUNCT
ejpam-3003	454	1	g(s)ds	g(s)ds	PROPN
ejpam-3003	454	2	=	=	SYM
ejpam-3003	454	3	1−	1−	NUM
ejpam-3003	454	4	b	b	NOUN
ejpam-3003	454	5	,	,	PUNCT
ejpam-3003	454	6	we	we	PRON
ejpam-3003	454	7	have∫	have∫	VERB
ejpam-3003	454	8	ω	ω	NUM
ejpam-3003	454	9	∇u(t	∇u(t	PROPN
ejpam-3003	454	10	)	)	PUNCT
ejpam-3003	454	11	·	·	PUNCT
ejpam-3003	455	1	∫	∫	PROPN
ejpam-3003	455	2	t	t	PROPN
ejpam-3003	455	3	0	0	NUM
ejpam-3003	455	4	g(t−	g(t−	PROPN
ejpam-3003	455	5	s)∇u(s)dsdx	s)∇u(s)dsdx	NOUN
ejpam-3003	455	6	≤	≤	ADV
ejpam-3003	455	7	1	1	NUM
ejpam-3003	455	8	2	2	NUM
ejpam-3003	455	9	‖∇u‖22	‖∇u‖22	NOUN
ejpam-3003	455	10	+	+	CCONJ
ejpam-3003	455	11	1	1	NUM
ejpam-3003	455	12	2	2	NUM
ejpam-3003	455	13	∫	∫	NOUN
ejpam-3003	455	14	ω	ω	PROPN
ejpam-3003	455	15	(	(	PUNCT
ejpam-3003	455	16	∫	∫	PROPN
ejpam-3003	455	17	t	t	PROPN
ejpam-3003	455	18	0	0	NUM
ejpam-3003	455	19	g(t−	g(t−	PROPN
ejpam-3003	455	20	s)(|∇u(s)−∇u(t)|+	s)(|∇u(s)−∇u(t)|+	PROPN
ejpam-3003	455	21	|∇u(t)|)ds	|∇u(t)|)ds	NUM
ejpam-3003	455	22	)	)	PUNCT
ejpam-3003	455	23	2	2	NUM
ejpam-3003	455	24	dx	dx	PROPN
ejpam-3003	455	25	≤	≤	NUM
ejpam-3003	455	26	1	1	NUM
ejpam-3003	455	27	2	2	NUM
ejpam-3003	455	28	‖∇u‖22	‖∇u‖22	NOUN
ejpam-3003	456	1	+	+	CCONJ
ejpam-3003	456	2	1	1	NUM
ejpam-3003	456	3	2	2	NUM
ejpam-3003	456	4	(	(	PUNCT
ejpam-3003	456	5	1	1	NUM
ejpam-3003	456	6	+	+	CCONJ
ejpam-3003	456	7	η	η	PROPN
ejpam-3003	457	1	)	)	PUNCT
ejpam-3003	457	2	∫	∫	PROPN
ejpam-3003	457	3	ω	ω	PROPN
ejpam-3003	457	4	(	(	PUNCT
ejpam-3003	457	5	∫	∫	PROPN
ejpam-3003	457	6	t	t	PROPN
ejpam-3003	457	7	0	0	NUM
ejpam-3003	457	8	g(t−	g(t−	PROPN
ejpam-3003	457	9	s)|∇u(t)|ds	s)|∇u(t)|ds	NOUN
ejpam-3003	457	10	)	)	PUNCT
ejpam-3003	457	11	2	2	NUM
ejpam-3003	457	12	dx	dx	NOUN
ejpam-3003	457	13	+	+	NOUN
ejpam-3003	457	14	1	1	NUM
ejpam-3003	457	15	2	2	NUM
ejpam-3003	457	16	(	(	PUNCT
ejpam-3003	457	17	1	1	NUM
ejpam-3003	457	18	+	+	SYM
ejpam-3003	457	19	1	1	NUM
ejpam-3003	457	20	η	η	NOUN
ejpam-3003	457	21	)	)	PUNCT
ejpam-3003	457	22	∫	∫	PROPN
ejpam-3003	457	23	ω	ω	PROPN
ejpam-3003	457	24	(	(	PUNCT
ejpam-3003	457	25	∫	∫	PROPN
ejpam-3003	457	26	t	t	PROPN
ejpam-3003	457	27	0	0	NUM
ejpam-3003	457	28	g(t−	g(t−	PROPN
ejpam-3003	457	29	s)|∇u(s)−∇u(t)|ds	s)|∇u(s)−∇u(t)|ds	ADJ
ejpam-3003	457	30	)	)	PUNCT
ejpam-3003	457	31	2	2	NUM
ejpam-3003	457	32	dx	dx	PROPN
ejpam-3003	457	33	≤	≤	NUM
ejpam-3003	457	34	1	1	NUM
ejpam-3003	457	35	2	2	NUM
ejpam-3003	457	36	‖∇u‖22	‖∇u‖22	NOUN
ejpam-3003	457	37	+	+	CCONJ
ejpam-3003	457	38	1	1	NUM
ejpam-3003	457	39	2	2	NUM
ejpam-3003	457	40	(	(	PUNCT
ejpam-3003	457	41	1	1	NUM
ejpam-3003	457	42	+	+	CCONJ
ejpam-3003	457	43	η)(1−	η)(1−	ADJ
ejpam-3003	457	44	b)2‖∇u‖22	b)2‖∇u‖22	NOUN
ejpam-3003	457	45	+	+	CCONJ
ejpam-3003	457	46	1	1	NUM
ejpam-3003	457	47	2	2	NUM
ejpam-3003	457	48	(	(	PUNCT
ejpam-3003	457	49	1	1	NUM
ejpam-3003	457	50	+	+	SYM
ejpam-3003	457	51	1	1	NUM
ejpam-3003	457	52	η	η	NOUN
ejpam-3003	457	53	)	)	PUNCT
ejpam-3003	457	54	(	(	PUNCT
ejpam-3003	457	55	1−	1−	NUM
ejpam-3003	457	56	b)(g	b)(g	NUM
ejpam-3003	457	57	◦	◦	PROPN
ejpam-3003	457	58	∇u)(t	∇u)(t	PROPN
ejpam-3003	457	59	)	)	PUNCT
ejpam-3003	457	60	(	(	PUNCT
ejpam-3003	457	61	4.14	4.14	NUM
ejpam-3003	457	62	)	)	PUNCT
ejpam-3003	457	63	for	for	ADP
ejpam-3003	457	64	any	any	DET
ejpam-3003	457	65	η	η	PROPN
ejpam-3003	457	66	>	>	X
ejpam-3003	457	67	0	0	NUM
ejpam-3003	457	68	.	.	PUNCT
ejpam-3003	458	1	we	we	PRON
ejpam-3003	458	2	choose	choose	VERB
ejpam-3003	458	3	η	η	PROPN
ejpam-3003	458	4	=	=	PROPN
ejpam-3003	458	5	b	b	PROPN
ejpam-3003	458	6	1−b	1−b	NUM
ejpam-3003	458	7	,	,	PUNCT
ejpam-3003	458	8	then	then	ADV
ejpam-3003	458	9	(	(	PUNCT
ejpam-3003	458	10	4.14	4.14	NUM
ejpam-3003	458	11	)	)	PUNCT
ejpam-3003	458	12	yields∫	yields∫	PROPN
ejpam-3003	458	13	ω	ω	PROPN
ejpam-3003	458	14	∇u(t	∇u(t	PROPN
ejpam-3003	458	15	)	)	PUNCT
ejpam-3003	458	16	·	·	PUNCT
ejpam-3003	459	1	∫	∫	PROPN
ejpam-3003	459	2	t	t	PROPN
ejpam-3003	459	3	0	0	NUM
ejpam-3003	459	4	g(t−	g(t−	PROPN
ejpam-3003	459	5	s)∇u(s)dsdx	s)∇u(s)dsdx	NOUN
ejpam-3003	459	6	≤	≤	ADV
ejpam-3003	459	7	2−	2−	NUM
ejpam-3003	459	8	b	b	SYM
ejpam-3003	459	9	2	2	NUM
ejpam-3003	459	10	‖∇u‖22	‖∇u‖22	NOUN
ejpam-3003	459	11	+	+	CCONJ
ejpam-3003	459	12	1−	1−	NUM
ejpam-3003	459	13	b	b	NOUN
ejpam-3003	459	14	2b	2b	NUM
ejpam-3003	459	15	(	(	PUNCT
ejpam-3003	459	16	g	g	PROPN
ejpam-3003	459	17	◦	◦	PROPN
ejpam-3003	459	18	∇u)(t	∇u)(t	PROPN
ejpam-3003	459	19	)	)	PUNCT
ejpam-3003	459	20	.	.	PUNCT
ejpam-3003	460	1	(	(	PUNCT
ejpam-3003	460	2	4.15	4.15	X
ejpam-3003	460	3	)	)	PUNCT
ejpam-3003	460	4	applying	apply	VERB
ejpam-3003	460	5	the	the	DET
ejpam-3003	460	6	young	young	ADJ
ejpam-3003	460	7	inequality	inequality	NOUN
ejpam-3003	460	8	,	,	PUNCT
ejpam-3003	460	9	hölder	hölder	NOUN
ejpam-3003	460	10	inequality	inequality	NOUN
ejpam-3003	460	11	and	and	CCONJ
ejpam-3003	460	12	(	(	PUNCT
ejpam-3003	460	13	4.5	4.5	NUM
ejpam-3003	460	14	)	)	PUNCT
ejpam-3003	460	15	,	,	PUNCT
ejpam-3003	460	16	it	it	PRON
ejpam-3003	460	17	is	be	AUX
ejpam-3003	460	18	easy	easy	ADJ
ejpam-3003	460	19	to	to	PART
ejpam-3003	460	20	see	see	VERB
ejpam-3003	460	21	that∫	that∫	PROPN
ejpam-3003	460	22	ω	ω	NUM
ejpam-3003	460	23	|ut|ρ−1utudx	|ut|ρ−1utudx	PROPN
ejpam-3003	460	24	≤	≤	PUNCT
ejpam-3003	460	25	‖ut‖ρρ+1‖u‖ρ+1	‖ut‖ρρ+1‖u‖ρ+1	ADV
ejpam-3003	460	26	≤	≤	PROPN
ejpam-3003	460	27	ρα	ρα	PROPN
ejpam-3003	460	28	ρ+	ρ+	NUM
ejpam-3003	460	29	1	1	NUM
ejpam-3003	460	30	‖u‖ρ+1	‖u‖ρ+1	SYM
ejpam-3003	460	31	ρ+1	ρ+1	NOUN
ejpam-3003	461	1	+	+	CCONJ
ejpam-3003	461	2	1	1	NUM
ejpam-3003	461	3	(	(	PUNCT
ejpam-3003	461	4	ρ+	ρ+	NUM
ejpam-3003	461	5	1)α	1)α	NUM
ejpam-3003	461	6	‖ut‖ρ+1	‖ut‖ρ+1	NUM
ejpam-3003	461	7	ρ+1	ρ+1	ADJ
ejpam-3003	461	8	≤	≤	NUM
ejpam-3003	461	9	ρα	ρα	PRON
ejpam-3003	461	10	ρ+	ρ+	NUM
ejpam-3003	461	11	1	1	NUM
ejpam-3003	461	12	bρ+1	bρ+1	NUM
ejpam-3003	461	13	ρ+1	ρ+1	NOUN
ejpam-3003	461	14	(	(	PUNCT
ejpam-3003	461	15	2(p+	2(p+	NUM
ejpam-3003	461	16	1)e(0	1)e(0	NOUN
ejpam-3003	461	17	)	)	PUNCT
ejpam-3003	461	18	(	(	PUNCT
ejpam-3003	461	19	p−	p−	NOUN
ejpam-3003	461	20	1)b	1)b	X
ejpam-3003	461	21	)	)	PUNCT
ejpam-3003	461	22	ρ−1	ρ−1	PROPN
ejpam-3003	461	23	2	2	NUM
ejpam-3003	461	24	‖∇u‖22	‖∇u‖22	NOUN
ejpam-3003	462	1	+	+	CCONJ
ejpam-3003	462	2	1	1	NUM
ejpam-3003	462	3	(	(	PUNCT
ejpam-3003	462	4	ρ+	ρ+	NUM
ejpam-3003	462	5	1)α	1)α	NUM
ejpam-3003	462	6	‖ut‖ρ+1	‖ut‖ρ+1	SYM
ejpam-3003	462	7	ρ+1	ρ+1	ADJ
ejpam-3003	462	8	,	,	PUNCT
ejpam-3003	462	9	(	(	PUNCT
ejpam-3003	462	10	4.16	4.16	NUM
ejpam-3003	462	11	)	)	PUNCT
ejpam-3003	462	12	for	for	ADP
ejpam-3003	462	13	any	any	DET
ejpam-3003	462	14	α	α	NOUN
ejpam-3003	462	15	>	>	X
ejpam-3003	462	16	0	0	NUM
ejpam-3003	462	17	.	.	PUNCT
ejpam-3003	463	1	by	by	ADP
ejpam-3003	463	2	the	the	DET
ejpam-3003	463	3	young	young	ADJ
ejpam-3003	463	4	inequality	inequality	NOUN
ejpam-3003	463	5	,	,	PUNCT
ejpam-3003	463	6	trace	trace	NOUN
ejpam-3003	463	7	theorem	theorem	NOUN
ejpam-3003	463	8	and	and	CCONJ
ejpam-3003	463	9	(	(	PUNCT
ejpam-3003	463	10	4.5	4.5	NUM
ejpam-3003	463	11	)	)	PUNCT
ejpam-3003	463	12	,	,	PUNCT
ejpam-3003	463	13	it	it	PRON
ejpam-3003	463	14	follows	follow	VERB
ejpam-3003	463	15	that∫	that∫	NOUN
ejpam-3003	463	16	γ1	γ1	PROPN
ejpam-3003	463	17	|ut|q−1utudγ	|ut|q−1utudγ	PROPN
ejpam-3003	463	18	h.f	h.f	PROPN
ejpam-3003	463	19	.	.	PROPN
ejpam-3003	463	20	di	di	PROPN
ejpam-3003	463	21	,	,	PUNCT
ejpam-3003	463	22	y.d	y.d	PROPN
ejpam-3003	463	23	.	.	PROPN
ejpam-3003	463	24	shang	shang	PROPN
ejpam-3003	463	25	/	/	SYM
ejpam-3003	463	26	eur	eur	PROPN
ejpam-3003	463	27	.	.	PUNCT
ejpam-3003	464	1	j.	j.	PROPN
ejpam-3003	464	2	pure	pure	PROPN
ejpam-3003	464	3	appl	appl	PROPN
ejpam-3003	464	4	.	.	PROPN
ejpam-3003	464	5	math	math	PROPN
ejpam-3003	464	6	,	,	PUNCT
ejpam-3003	464	7	10	10	NUM
ejpam-3003	464	8	(	(	PUNCT
ejpam-3003	464	9	4	4	NUM
ejpam-3003	464	10	)	)	PUNCT
ejpam-3003	464	11	(	(	PUNCT
ejpam-3003	464	12	2017	2017	NUM
ejpam-3003	464	13	)	)	PUNCT
ejpam-3003	464	14	,	,	PUNCT
ejpam-3003	464	15	668	668	NUM
ejpam-3003	464	16	-	-	SYM
ejpam-3003	464	17	701	701	NUM
ejpam-3003	464	18	688	688	NUM
ejpam-3003	464	19	≤	≤	NUM
ejpam-3003	464	20	qα	qα	PROPN
ejpam-3003	465	1	q	q	PROPN
ejpam-3003	466	1	+	+	PROPN
ejpam-3003	466	2	1	1	NUM
ejpam-3003	466	3	‖u‖q+1	‖u‖q+1	PROPN
ejpam-3003	466	4	γ1,q+1	γ1,q+1	PUNCT
ejpam-3003	467	1	+	+	CCONJ
ejpam-3003	467	2	1	1	NUM
ejpam-3003	467	3	(	(	PUNCT
ejpam-3003	467	4	q	q	NOUN
ejpam-3003	467	5	+	+	NUM
ejpam-3003	467	6	1)α	1)α	NUM
ejpam-3003	467	7	‖ut‖q+1	‖ut‖q+1	INTJ
ejpam-3003	467	8	γ1,q+1	γ1,q+1	PUNCT
ejpam-3003	467	9	≤	≤	PROPN
ejpam-3003	468	1	qα	qα	PROPN
ejpam-3003	468	2	q	q	PROPN
ejpam-3003	469	1	+	+	NUM
ejpam-3003	469	2	1	1	NUM
ejpam-3003	469	3	bq+1	bq+1	NUM
ejpam-3003	469	4	q+1	q+1	PROPN
ejpam-3003	469	5	(	(	PUNCT
ejpam-3003	469	6	2(p+	2(p+	NUM
ejpam-3003	469	7	1)e(0	1)e(0	NOUN
ejpam-3003	469	8	)	)	PUNCT
ejpam-3003	469	9	(	(	PUNCT
ejpam-3003	469	10	p−	p−	NOUN
ejpam-3003	469	11	1)b	1)b	X
ejpam-3003	469	12	)	)	PUNCT
ejpam-3003	470	1	q−1	q−1	PROPN
ejpam-3003	470	2	2	2	NUM
ejpam-3003	470	3	‖∇u‖22	‖∇u‖22	NOUN
ejpam-3003	471	1	+	+	CCONJ
ejpam-3003	471	2	1	1	NUM
ejpam-3003	471	3	(	(	PUNCT
ejpam-3003	471	4	q	q	NOUN
ejpam-3003	471	5	+	+	NUM
ejpam-3003	471	6	1)α	1)α	NUM
ejpam-3003	471	7	‖ut‖q+1	‖ut‖q+1	INTJ
ejpam-3003	471	8	γ1,q+1	γ1,q+1	PROPN
ejpam-3003	471	9	.	.	PROPN
ejpam-3003	472	1	(	(	PUNCT
ejpam-3003	472	2	4.17	4.17	NUM
ejpam-3003	472	3	)	)	PUNCT
ejpam-3003	472	4	where	where	SCONJ
ejpam-3003	472	5	bq+1	bq+1	PROPN
ejpam-3003	472	6	is	be	AUX
ejpam-3003	472	7	the	the	DET
ejpam-3003	472	8	optimal	optimal	ADJ
ejpam-3003	472	9	constant	constant	ADJ
ejpam-3003	472	10	satisfying	satisfy	VERB
ejpam-3003	472	11	the	the	DET
ejpam-3003	472	12	inequality	inequality	NOUN
ejpam-3003	472	13	‖u‖γ1,q+1	‖u‖γ1,q+1	PUNCT
ejpam-3003	472	14	≤	≤	NUM
ejpam-3003	472	15	bq+1‖∇u‖2	bq+1‖∇u‖2	X
ejpam-3003	472	16	.	.	PUNCT
ejpam-3003	473	1	inserting	insert	VERB
ejpam-3003	473	2	(	(	PUNCT
ejpam-3003	473	3	4.15)-(4.17	4.15)-(4.17	NUM
ejpam-3003	473	4	)	)	PUNCT
ejpam-3003	473	5	into	into	ADP
ejpam-3003	473	6	(	(	PUNCT
ejpam-3003	473	7	4.13	4.13	NUM
ejpam-3003	473	8	)	)	PUNCT
ejpam-3003	473	9	and	and	CCONJ
ejpam-3003	473	10	applying	apply	VERB
ejpam-3003	473	11	the	the	DET
ejpam-3003	473	12	conditions	condition	NOUN
ejpam-3003	473	13	(	(	PUNCT
ejpam-3003	473	14	a2	a2	PROPN
ejpam-3003	473	15	)	)	PUNCT
ejpam-3003	473	16	,	,	PUNCT
ejpam-3003	473	17	we	we	PRON
ejpam-3003	473	18	deduce	deduce	VERB
ejpam-3003	473	19	that	that	PRON
ejpam-3003	473	20	ψ′(t	ψ′(t	NOUN
ejpam-3003	473	21	)	)	PUNCT
ejpam-3003	473	22	≤	≤	NUM
ejpam-3003	473	23	ξ(t	ξ(t	NOUN
ejpam-3003	473	24	)	)	PUNCT
ejpam-3003	473	25	ρ	ρ	PROPN
ejpam-3003	473	26	‖ut‖ρ+1	‖ut‖ρ+1	PROPN
ejpam-3003	474	1	ρ+1	ρ+1	NOUN
ejpam-3003	474	2	−	−	PUNCT
ejpam-3003	474	3	ξ(t)‖∇u‖	ξ(t)‖∇u‖	PROPN
ejpam-3003	474	4	2	2	NUM
ejpam-3003	474	5	2	2	NUM
ejpam-3003	474	6	+	+	CCONJ
ejpam-3003	474	7	2−	2−	NUM
ejpam-3003	474	8	b	b	SYM
ejpam-3003	474	9	2	2	NUM
ejpam-3003	474	10	ξ(t)‖∇u‖22	ξ(t)‖∇u‖22	PUNCT
ejpam-3003	474	11	+	+	CCONJ
ejpam-3003	474	12	1−	1−	NUM
ejpam-3003	474	13	b	b	PROPN
ejpam-3003	474	14	2b	2b	NUM
ejpam-3003	474	15	ξ(t)(g	ξ(t)(g	ADP
ejpam-3003	474	16	◦	◦	PROPN
ejpam-3003	474	17	∇u)(t	∇u)(t	PROPN
ejpam-3003	474	18	)	)	PUNCT
ejpam-3003	474	19	+	+	NUM
ejpam-3003	475	1	ξ(t)‖u‖p+1	ξ(t)‖u‖p+1	INTJ
ejpam-3003	476	1	p+1	p+1	NOUN
ejpam-3003	477	1	+	+	NUM
ejpam-3003	477	2	α	α	NOUN
ejpam-3003	477	3	ρ+	ρ+	NOUN
ejpam-3003	477	4	1	1	NUM
ejpam-3003	477	5	kξ(t)bρ+1	kξ(t)bρ+1	PROPN
ejpam-3003	477	6	ρ+1	ρ+1	NUM
ejpam-3003	477	7	(	(	PUNCT
ejpam-3003	477	8	2(p+	2(p+	NUM
ejpam-3003	477	9	1)e(0	1)e(0	NOUN
ejpam-3003	477	10	)	)	PUNCT
ejpam-3003	477	11	(	(	PUNCT
ejpam-3003	477	12	p−	p−	NOUN
ejpam-3003	477	13	1)b	1)b	X
ejpam-3003	477	14	)	)	PUNCT
ejpam-3003	477	15	ρ−1	ρ−1	PROPN
ejpam-3003	477	16	2	2	NUM
ejpam-3003	477	17	‖∇u‖22	‖∇u‖22	NOUN
ejpam-3003	477	18	+	+	CCONJ
ejpam-3003	477	19	1	1	NUM
ejpam-3003	477	20	(	(	PUNCT
ejpam-3003	477	21	q	q	PROPN
ejpam-3003	477	22	+	+	NUM
ejpam-3003	477	23	1)α	1)α	NUM
ejpam-3003	477	24	ξ(t)‖ut‖q+1	ξ(t)‖ut‖q+1	PROPN
ejpam-3003	477	25	γ1,q+1	γ1,q+1	PUNCT
ejpam-3003	478	1	+	+	CCONJ
ejpam-3003	478	2	1	1	NUM
ejpam-3003	478	3	(	(	PUNCT
ejpam-3003	478	4	ρ+	ρ+	NUM
ejpam-3003	478	5	1)ρα	1)ρα	NUM
ejpam-3003	478	6	kξ(t)‖ut‖ρ+1	kξ(t)‖ut‖ρ+1	NOUN
ejpam-3003	478	7	ρ+1	ρ+1	X
ejpam-3003	478	8	+	+	CCONJ
ejpam-3003	478	9	qα	qα	PROPN
ejpam-3003	478	10	q	q	NOUN
ejpam-3003	479	1	+	+	NUM
ejpam-3003	479	2	1	1	NUM
ejpam-3003	479	3	bq+1	bq+1	NUM
ejpam-3003	479	4	q+1	q+1	PROPN
ejpam-3003	479	5	(	(	PUNCT
ejpam-3003	479	6	2(p+	2(p+	NUM
ejpam-3003	479	7	1)e(0	1)e(0	NOUN
ejpam-3003	479	8	)	)	PUNCT
ejpam-3003	479	9	(	(	PUNCT
ejpam-3003	479	10	p−	p−	NOUN
ejpam-3003	479	11	1)b	1)b	X
ejpam-3003	479	12	)	)	PUNCT
ejpam-3003	480	1	q−1	q−1	PROPN
ejpam-3003	480	2	2	2	NUM
ejpam-3003	480	3	ξ(t)‖∇u‖22	ξ(t)‖∇u‖22	X
ejpam-3003	481	1	=	=	SYM
ejpam-3003	481	2	[	[	PUNCT
ejpam-3003	481	3	1	1	NUM
ejpam-3003	481	4	ρ	ρ	NUM
ejpam-3003	481	5	+	+	NUM
ejpam-3003	481	6	1	1	NUM
ejpam-3003	481	7	(	(	PUNCT
ejpam-3003	481	8	ρ+	ρ+	NOUN
ejpam-3003	481	9	1)ρα	1)ρα	PROPN
ejpam-3003	481	10	k	k	X
ejpam-3003	481	11	]	]	PUNCT
ejpam-3003	481	12	ξ(t)‖ut‖ρ+1	ξ(t)‖ut‖ρ+1	X
ejpam-3003	482	1	ρ+1	ρ+1	NUM
ejpam-3003	482	2	−	−	PROPN
ejpam-3003	482	3	[	[	PUNCT
ejpam-3003	482	4	b	b	NOUN
ejpam-3003	482	5	2	2	NUM
ejpam-3003	482	6	−	−	PROPN
ejpam-3003	482	7	α	α	PROPN
ejpam-3003	482	8	ρ+	ρ+	NUM
ejpam-3003	482	9	1	1	NUM
ejpam-3003	482	10	kbρ+1	kbρ+1	NOUN
ejpam-3003	482	11	ρ+1	ρ+1	NOUN
ejpam-3003	482	12	(	(	PUNCT
ejpam-3003	482	13	2(p+	2(p+	NUM
ejpam-3003	482	14	1)e(0	1)e(0	NOUN
ejpam-3003	482	15	)	)	PUNCT
ejpam-3003	482	16	(	(	PUNCT
ejpam-3003	482	17	p−	p−	NOUN
ejpam-3003	482	18	1)b	1)b	X
ejpam-3003	482	19	)	)	PUNCT
ejpam-3003	483	1	ρ−1	ρ−1	PROPN
ejpam-3003	483	2	2	2	NUM
ejpam-3003	483	3	−	−	NOUN
ejpam-3003	483	4	qα	qα	PROPN
ejpam-3003	483	5	q	q	PROPN
ejpam-3003	484	1	+	+	NUM
ejpam-3003	484	2	1	1	NUM
ejpam-3003	484	3	bq+1	bq+1	NUM
ejpam-3003	484	4	q+1	q+1	PROPN
ejpam-3003	484	5	(	(	PUNCT
ejpam-3003	484	6	2(p+	2(p+	NUM
ejpam-3003	484	7	1)e(0	1)e(0	NOUN
ejpam-3003	484	8	)	)	PUNCT
ejpam-3003	484	9	(	(	PUNCT
ejpam-3003	484	10	p−	p−	NOUN
ejpam-3003	484	11	1)b	1)b	X
ejpam-3003	484	12	)	)	PUNCT
ejpam-3003	485	1	q−1	q−1	PROPN
ejpam-3003	485	2	2	2	NUM
ejpam-3003	485	3	]	]	PUNCT
ejpam-3003	485	4	ξ(t)‖∇u‖22	ξ(t)‖∇u‖22	PUNCT
ejpam-3003	486	1	+	+	CCONJ
ejpam-3003	486	2	1−	1−	NUM
ejpam-3003	486	3	b	b	PROPN
ejpam-3003	486	4	2b	2b	NUM
ejpam-3003	486	5	ξ(t)(g	ξ(t)(g	ADP
ejpam-3003	486	6	◦	◦	PROPN
ejpam-3003	486	7	∇u)(t	∇u)(t	PROPN
ejpam-3003	486	8	)	)	PUNCT
ejpam-3003	487	1	+	+	NUM
ejpam-3003	488	1	ξ(t)‖u‖p+1	ξ(t)‖u‖p+1	INTJ
ejpam-3003	489	1	p+1	p+1	NOUN
ejpam-3003	490	1	+	+	NOUN
ejpam-3003	490	2	1	1	NUM
ejpam-3003	490	3	(	(	PUNCT
ejpam-3003	490	4	q	q	PROPN
ejpam-3003	490	5	+	+	NUM
ejpam-3003	490	6	1)α	1)α	NUM
ejpam-3003	490	7	ξ(t)‖ut‖q+1	ξ(t)‖ut‖q+1	PROPN
ejpam-3003	490	8	γ1,q+1	γ1,q+1	PROPN
ejpam-3003	490	9	.	.	PROPN
ejpam-3003	490	10	lemma	lemma	PROPN
ejpam-3003	490	11	10	10	NUM
ejpam-3003	490	12	.	.	PUNCT
ejpam-3003	491	1	let	let	VERB
ejpam-3003	491	2	the	the	DET
ejpam-3003	491	3	assumptions	assumption	NOUN
ejpam-3003	491	4	(	(	PUNCT
ejpam-3003	491	5	a1)-(a3	a1)-(a3	NOUN
ejpam-3003	491	6	)	)	PUNCT
ejpam-3003	491	7	hold	hold	NOUN
ejpam-3003	491	8	and	and	CCONJ
ejpam-3003	491	9	1	1	NUM
ejpam-3003	491	10	<	<	X
ejpam-3003	491	11	ρ	ρ	X
ejpam-3003	491	12	<	<	X
ejpam-3003	491	13	∞	∞	PROPN
ejpam-3003	491	14	if	if	SCONJ
ejpam-3003	491	15	n	n	NOUN
ejpam-3003	491	16	≤	≤	ADV
ejpam-3003	491	17	2	2	NUM
ejpam-3003	491	18	,	,	PUNCT
ejpam-3003	491	19	1	1	NUM
ejpam-3003	492	1	<	<	X
ejpam-3003	492	2	ρ	ρ	X
ejpam-3003	492	3	≤	≤	PROPN
ejpam-3003	492	4	n+2	n+2	NUM
ejpam-3003	493	1	n−2	n−2	PROPN
ejpam-3003	493	2	if	if	SCONJ
ejpam-3003	493	3	n	n	PRON
ejpam-3003	493	4	≥	≥	NOUN
ejpam-3003	493	5	3	3	NUM
ejpam-3003	493	6	.	.	PUNCT
ejpam-3003	493	7	furthermore	furthermore	ADV
ejpam-3003	493	8	assume	assume	VERB
ejpam-3003	493	9	that	that	SCONJ
ejpam-3003	493	10	e(0	e(0	NOUN
ejpam-3003	493	11	)	)	PUNCT
ejpam-3003	493	12	<	<	X
ejpam-3003	493	13	d̃	d̃	PROPN
ejpam-3003	493	14	and	and	CCONJ
ejpam-3003	493	15	i(u0	i(u0	PROPN
ejpam-3003	493	16	)	)	PUNCT
ejpam-3003	493	17	>	>	X
ejpam-3003	494	1	0	0	NUM
ejpam-3003	494	2	,	,	PUNCT
ejpam-3003	494	3	then	then	ADV
ejpam-3003	494	4	the	the	DET
ejpam-3003	494	5	functional	functional	ADJ
ejpam-3003	494	6	φ(t	φ(t	PROPN
ejpam-3003	494	7	)	)	PUNCT
ejpam-3003	494	8	=	=	SYM
ejpam-3003	495	1	−	−	NOUN
ejpam-3003	495	2	ξ(t	ξ(t	NOUN
ejpam-3003	495	3	)	)	PUNCT
ejpam-3003	495	4	ρ	ρ	PROPN
ejpam-3003	495	5	∫	∫	PROPN
ejpam-3003	495	6	ω	ω	PROPN
ejpam-3003	495	7	|ut|	|ut|	PROPN
ejpam-3003	495	8	ρ−1ut	ρ−1ut	PROPN
ejpam-3003	495	9	∫	∫	PROPN
ejpam-3003	495	10	t	t	PROPN
ejpam-3003	495	11	0	0	NUM
ejpam-3003	496	1	g(t−	g(t−	PROPN
ejpam-3003	496	2	s)[u(t)−	s)[u(t)−	PROPN
ejpam-3003	496	3	u(s)]dsdx	u(s)]dsdx	PROPN
ejpam-3003	496	4	satisfies	satisfy	VERB
ejpam-3003	496	5	the	the	DET
ejpam-3003	496	6	following	follow	VERB
ejpam-3003	496	7	inequality	inequality	NOUN
ejpam-3003	496	8	φ′(t	φ′(t	NOUN
ejpam-3003	496	9	)	)	PUNCT
ejpam-3003	497	1	≤	≤	NUM
ejpam-3003	497	2	δ	δ	PROPN
ejpam-3003	497	3	[	[	PUNCT
ejpam-3003	497	4	1	1	NUM
ejpam-3003	497	5	+	+	CCONJ
ejpam-3003	497	6	2(1−	2(1−	NUM
ejpam-3003	497	7	b)2	b)2	ADJ
ejpam-3003	497	8	+	+	CCONJ
ejpam-3003	497	9	p	p	X
ejpam-3003	497	10	p+	p+	VERB
ejpam-3003	497	11	1	1	NUM
ejpam-3003	497	12	bp+1	bp+1	NOUN
ejpam-3003	497	13	p+1	p+1	PROPN
ejpam-3003	497	14	(	(	PUNCT
ejpam-3003	497	15	2(p+	2(p+	NUM
ejpam-3003	497	16	1)e(0	1)e(0	NOUN
ejpam-3003	497	17	)	)	PUNCT
ejpam-3003	497	18	(	(	PUNCT
ejpam-3003	497	19	p−	p−	NOUN
ejpam-3003	497	20	1)b	1)b	X
ejpam-3003	497	21	)	)	PUNCT
ejpam-3003	497	22	p−1	p−1	PROPN
ejpam-3003	497	23	2	2	NUM
ejpam-3003	497	24	]	]	PUNCT
ejpam-3003	497	25	ξ(t)‖∇u‖22	ξ(t)‖∇u‖22	PUNCT
ejpam-3003	498	1	+	+	CCONJ
ejpam-3003	498	2	[	[	PUNCT
ejpam-3003	498	3	δ	δ	NOUN
ejpam-3003	498	4	ρ+	ρ+	NOUN
ejpam-3003	498	5	1	1	NUM
ejpam-3003	498	6	+	+	CCONJ
ejpam-3003	498	7	kδ	kδ	PART
ejpam-3003	498	8	ρ+	ρ+	NUM
ejpam-3003	498	9	1	1	NUM
ejpam-3003	498	10	−	−	NOUN
ejpam-3003	498	11	∫	∫	PROPN
ejpam-3003	498	12	t	t	PROPN
ejpam-3003	498	13	0	0	NUM
ejpam-3003	498	14	g(s)ds	g(s)ds	PROPN
ejpam-3003	498	15	ρ	ρ	PROPN
ejpam-3003	498	16	]	]	PUNCT
ejpam-3003	498	17	ξ(t)‖ut‖ρ+1	ξ(t)‖ut‖ρ+1	X
ejpam-3003	499	1	ρ+1	ρ+1	NOUN
ejpam-3003	500	1	+	+	CCONJ
ejpam-3003	500	2	[	[	PUNCT
ejpam-3003	500	3	(	(	PUNCT
ejpam-3003	500	4	2δ	2δ	NUM
ejpam-3003	500	5	+	+	CCONJ
ejpam-3003	500	6	1	1	NUM
ejpam-3003	500	7	2δ	2δ	NUM
ejpam-3003	500	8	)	)	PUNCT
ejpam-3003	500	9	(	(	PUNCT
ejpam-3003	500	10	1−	1−	NUM
ejpam-3003	500	11	b	b	NOUN
ejpam-3003	500	12	)	)	PUNCT
ejpam-3003	501	1	+	+	NUM
ejpam-3003	501	2	bp+1	bp+1	PROPN
ejpam-3003	501	3	p+1(1−	p+1(1−	ADJ
ejpam-3003	501	4	b)p	b)p	NOUN
ejpam-3003	501	5	(	(	PUNCT
ejpam-3003	501	6	p+	p+	NOUN
ejpam-3003	501	7	1)δ	1)δ	NUM
ejpam-3003	501	8	(	(	PUNCT
ejpam-3003	501	9	4(p+	4(p+	NOUN
ejpam-3003	501	10	1)e(0	1)e(0	NOUN
ejpam-3003	501	11	)	)	PUNCT
ejpam-3003	501	12	(	(	PUNCT
ejpam-3003	501	13	p−	p−	NOUN
ejpam-3003	501	14	1)b	1)b	X
ejpam-3003	501	15	)	)	PUNCT
ejpam-3003	501	16	p−1	p−1	PROPN
ejpam-3003	501	17	2	2	NUM
ejpam-3003	501	18	+	+	CCONJ
ejpam-3003	501	19	bq+1	bq+1	PROPN
ejpam-3003	501	20	q+1(1−	q+1(1−	NUM
ejpam-3003	501	21	b)q	b)q	PUNCT
ejpam-3003	501	22	(	(	PUNCT
ejpam-3003	501	23	q	q	X
ejpam-3003	502	1	+	+	NUM
ejpam-3003	502	2	1)δ	1)δ	NUM
ejpam-3003	502	3	(	(	PUNCT
ejpam-3003	502	4	4(p+	4(p+	NOUN
ejpam-3003	502	5	1)e(0	1)e(0	NOUN
ejpam-3003	502	6	)	)	PUNCT
ejpam-3003	502	7	(	(	PUNCT
ejpam-3003	502	8	p−	p−	NOUN
ejpam-3003	502	9	1)b	1)b	X
ejpam-3003	502	10	)	)	PUNCT
ejpam-3003	503	1	q−1	q−1	PROPN
ejpam-3003	503	2	2	2	NUM
ejpam-3003	504	1	+	+	CCONJ
ejpam-3003	504	2	kbρ+1	kbρ+1	X
ejpam-3003	504	3	ρ+1(1−	ρ+1(1−	PRON
ejpam-3003	504	4	b)ρ	b)ρ	NUM
ejpam-3003	504	5	ρ(ρ+	ρ(ρ+	NOUN
ejpam-3003	504	6	1)δ	1)δ	NUM
ejpam-3003	504	7	(	(	PUNCT
ejpam-3003	504	8	4(p+	4(p+	NOUN
ejpam-3003	504	9	1)e(0	1)e(0	NOUN
ejpam-3003	504	10	)	)	PUNCT
ejpam-3003	504	11	(	(	PUNCT
ejpam-3003	504	12	p−	p−	NOUN
ejpam-3003	504	13	1)b	1)b	X
ejpam-3003	504	14	)	)	PUNCT
ejpam-3003	504	15	ρ−1	ρ−1	PROPN
ejpam-3003	504	16	2	2	NUM
ejpam-3003	504	17	]	]	PUNCT
ejpam-3003	504	18	ξ(t)(g	ξ(t)(g	ADP
ejpam-3003	504	19	◦	◦	PROPN
ejpam-3003	504	20	∇u)(t	∇u)(t	PROPN
ejpam-3003	504	21	)	)	PUNCT
ejpam-3003	505	1	+	+	CCONJ
ejpam-3003	505	2	qδ	qδ	PRON
ejpam-3003	505	3	q	q	PROPN
ejpam-3003	506	1	+	+	NUM
ejpam-3003	506	2	1	1	NUM
ejpam-3003	506	3	ξ(t)‖ut‖q+1	ξ(t)‖ut‖q+1	PROPN
ejpam-3003	506	4	γ1,q+1	γ1,q+1	PUNCT
ejpam-3003	507	1	−	−	PROPN
ejpam-3003	507	2	g(0)ρbρ+1	g(0)ρbρ+1	NOUN
ejpam-3003	507	3	ρ+1	ρ+1	NUM
ejpam-3003	507	4	ρ(ρ+	ρ(ρ+	NOUN
ejpam-3003	507	5	1)δ	1)δ	NUM
ejpam-3003	507	6	(	(	PUNCT
ejpam-3003	507	7	4(p+	4(p+	NOUN
ejpam-3003	507	8	1)e(0	1)e(0	NOUN
ejpam-3003	507	9	)	)	PUNCT
ejpam-3003	507	10	(	(	PUNCT
ejpam-3003	507	11	p−	p−	NOUN
ejpam-3003	507	12	1)b	1)b	X
ejpam-3003	507	13	)	)	PUNCT
ejpam-3003	507	14	ρ−1	ρ−1	PROPN
ejpam-3003	507	15	2	2	NUM
ejpam-3003	507	16	ξ(t)(g′	ξ(t)(g′	PUNCT
ejpam-3003	507	17	◦	◦	NOUN
ejpam-3003	507	18	∇u)(t	∇u)(t	PROPN
ejpam-3003	507	19	)	)	PUNCT
ejpam-3003	507	20	.	.	PUNCT
ejpam-3003	508	1	(	(	PUNCT
ejpam-3003	508	2	4.18	4.18	NUM
ejpam-3003	508	3	)	)	PUNCT
ejpam-3003	508	4	proof	proof	NOUN
ejpam-3003	508	5	.	.	PUNCT
ejpam-3003	509	1	applying	apply	VERB
ejpam-3003	509	2	the	the	DET
ejpam-3003	509	3	equation	equation	NOUN
ejpam-3003	509	4	of	of	ADP
ejpam-3003	509	5	(	(	PUNCT
ejpam-3003	509	6	1.1	1.1	NUM
ejpam-3003	509	7	)	)	PUNCT
ejpam-3003	509	8	and	and	CCONJ
ejpam-3003	509	9	integrating	integrate	VERB
ejpam-3003	509	10	by	by	ADP
ejpam-3003	509	11	parts	part	NOUN
ejpam-3003	509	12	,	,	PUNCT
ejpam-3003	509	13	we	we	PRON
ejpam-3003	509	14	deduce	deduce	VERB
ejpam-3003	509	15	that	that	SCONJ
ejpam-3003	509	16	φ′(t	φ′(t	VERB
ejpam-3003	509	17	)	)	PUNCT
ejpam-3003	509	18	=	=	SYM
ejpam-3003	509	19	−ξ(t	−ξ(t	NOUN
ejpam-3003	509	20	)	)	PUNCT
ejpam-3003	509	21	∫	∫	PROPN
ejpam-3003	510	1	ω	ω	NUM
ejpam-3003	510	2	|ut|ρ−1utt	|ut|ρ−1utt	PROPN
ejpam-3003	510	3	∫	∫	PROPN
ejpam-3003	510	4	t	t	PROPN
ejpam-3003	510	5	0	0	NUM
ejpam-3003	511	1	g(t−	g(t−	PROPN
ejpam-3003	511	2	s)[u(t)−	s)[u(t)−	PROPN
ejpam-3003	511	3	u(s)]dsdx	u(s)]dsdx	PROPN
ejpam-3003	511	4	h.f	h.f	PROPN
ejpam-3003	511	5	.	.	PROPN
ejpam-3003	511	6	di	di	PROPN
ejpam-3003	511	7	,	,	PUNCT
ejpam-3003	511	8	y.d	y.d	PROPN
ejpam-3003	511	9	.	.	PROPN
ejpam-3003	511	10	shang	shang	PROPN
ejpam-3003	511	11	/	/	SYM
ejpam-3003	511	12	eur	eur	PROPN
ejpam-3003	511	13	.	.	PUNCT
ejpam-3003	512	1	j.	j.	PROPN
ejpam-3003	512	2	pure	pure	PROPN
ejpam-3003	512	3	appl	appl	PROPN
ejpam-3003	512	4	.	.	PROPN
ejpam-3003	512	5	math	math	PROPN
ejpam-3003	512	6	,	,	PUNCT
ejpam-3003	512	7	10	10	NUM
ejpam-3003	512	8	(	(	PUNCT
ejpam-3003	512	9	4	4	NUM
ejpam-3003	512	10	)	)	PUNCT
ejpam-3003	512	11	(	(	PUNCT
ejpam-3003	512	12	2017	2017	NUM
ejpam-3003	512	13	)	)	PUNCT
ejpam-3003	512	14	,	,	PUNCT
ejpam-3003	513	1	668	668	NUM
ejpam-3003	513	2	-	-	SYM
ejpam-3003	513	3	701	701	NUM
ejpam-3003	513	4	689	689	NUM
ejpam-3003	513	5	−	−	NOUN
ejpam-3003	513	6	ξ′(t	ξ′(t	X
ejpam-3003	513	7	)	)	PUNCT
ejpam-3003	513	8	ρ	ρ	PROPN
ejpam-3003	513	9	∫	∫	PROPN
ejpam-3003	513	10	ω	ω	PROPN
ejpam-3003	513	11	|ut|ρ−1ut	|ut|ρ−1ut	PROPN
ejpam-3003	513	12	∫	∫	PROPN
ejpam-3003	513	13	t	t	PROPN
ejpam-3003	513	14	0	0	NUM
ejpam-3003	513	15	g(t−	g(t−	PROPN
ejpam-3003	513	16	s)[u(t)−	s)[u(t)−	PROPN
ejpam-3003	513	17	u(s)]dsdx	u(s)]dsdx	PROPN
ejpam-3003	513	18	−	−	PROPN
ejpam-3003	513	19	ξ(t	ξ(t	PROPN
ejpam-3003	513	20	)	)	PUNCT
ejpam-3003	513	21	ρ	ρ	PROPN
ejpam-3003	513	22	∫	∫	PROPN
ejpam-3003	513	23	ω	ω	PROPN
ejpam-3003	513	24	|ut|ρ−1ut	|ut|ρ−1ut	PROPN
ejpam-3003	513	25	∫	∫	PROPN
ejpam-3003	513	26	t	t	PROPN
ejpam-3003	513	27	0	0	NUM
ejpam-3003	514	1	g′(t−	g′(t−	PROPN
ejpam-3003	514	2	s)[u(t)−	s)[u(t)−	PROPN
ejpam-3003	514	3	u(s)]dsdx	u(s)]dsdx	PROPN
ejpam-3003	514	4	−	−	PROPN
ejpam-3003	514	5	ξ(t	ξ(t	PROPN
ejpam-3003	514	6	)	)	PUNCT
ejpam-3003	515	1	ρ	ρ	PROPN
ejpam-3003	515	2	∫	∫	PROPN
ejpam-3003	515	3	t	t	PROPN
ejpam-3003	515	4	0	0	NUM
ejpam-3003	516	1	g(s)ds	g(s)ds	PROPN
ejpam-3003	516	2	∫	∫	PROPN
ejpam-3003	516	3	ω	ω	PROPN
ejpam-3003	516	4	|ut|ρ+1dx	|ut|ρ+1dx	PROPN
ejpam-3003	516	5	=	=	SYM
ejpam-3003	516	6	ξ(t	ξ(t	PROPN
ejpam-3003	516	7	)	)	PUNCT
ejpam-3003	516	8	∫	∫	PROPN
ejpam-3003	516	9	ω	ω	PROPN
ejpam-3003	516	10	∇u(t	∇u(t	PROPN
ejpam-3003	516	11	)	)	PUNCT
ejpam-3003	516	12	∫	∫	PROPN
ejpam-3003	517	1	t	t	PROPN
ejpam-3003	517	2	0	0	NUM
ejpam-3003	517	3	g(t−	g(t−	PROPN
ejpam-3003	517	4	s)[∇u(t)−∇u(s)]dsdx	s)[∇u(t)−∇u(s)]dsdx	ADP
ejpam-3003	517	5	−	−	PROPN
ejpam-3003	517	6	ξ(t	ξ(t	NOUN
ejpam-3003	517	7	)	)	PUNCT
ejpam-3003	517	8	∫	∫	PROPN
ejpam-3003	518	1	ω	ω	NUM
ejpam-3003	518	2	∫	∫	PROPN
ejpam-3003	518	3	t	t	PROPN
ejpam-3003	518	4	0	0	NUM
ejpam-3003	518	5	g(t−	g(t−	PROPN
ejpam-3003	518	6	s)∇u(s)ds	s)∇u(s)ds	ADJ
ejpam-3003	519	1	∫	∫	PROPN
ejpam-3003	519	2	t	t	PROPN
ejpam-3003	519	3	0	0	NUM
ejpam-3003	519	4	g(t−	g(t−	PROPN
ejpam-3003	519	5	s)[∇u(t)−∇u(s)]dsdx	s)[∇u(t)−∇u(s)]dsdx	ADP
ejpam-3003	519	6	−	−	PROPN
ejpam-3003	519	7	ξ(t	ξ(t	NOUN
ejpam-3003	519	8	)	)	PUNCT
ejpam-3003	519	9	∫	∫	PROPN
ejpam-3003	520	1	ω	ω	NUM
ejpam-3003	520	2	|u|p−1u	|u|p−1u	INTJ
ejpam-3003	520	3	∫	∫	PROPN
ejpam-3003	520	4	t	t	PROPN
ejpam-3003	520	5	0	0	NUM
ejpam-3003	521	1	g(t−	g(t−	PROPN
ejpam-3003	521	2	s)[u(t)−	s)[u(t)−	PROPN
ejpam-3003	521	3	u(s)]dsdx	u(s)]dsdx	PROPN
ejpam-3003	521	4	+	+	CCONJ
ejpam-3003	521	5	ξ(t	ξ(t	PROPN
ejpam-3003	521	6	)	)	PUNCT
ejpam-3003	521	7	∫	∫	PROPN
ejpam-3003	521	8	γ1	γ1	PROPN
ejpam-3003	521	9	|ut|q−1ut	|ut|q−1ut	PROPN
ejpam-3003	521	10	∫	∫	PROPN
ejpam-3003	521	11	t	t	PROPN
ejpam-3003	521	12	0	0	NUM
ejpam-3003	522	1	g(t−	g(t−	PROPN
ejpam-3003	522	2	s)[u(t)−	s)[u(t)−	PROPN
ejpam-3003	522	3	u(s)]dsdγ	u(s)]dsdγ	PROPN
ejpam-3003	522	4	−	−	PROPN
ejpam-3003	522	5	ξ′(t	ξ′(t	SYM
ejpam-3003	522	6	)	)	PUNCT
ejpam-3003	522	7	ρ	ρ	PROPN
ejpam-3003	522	8	∫	∫	PROPN
ejpam-3003	522	9	ω	ω	PROPN
ejpam-3003	522	10	|ut|ρ−1ut	|ut|ρ−1ut	PROPN
ejpam-3003	522	11	∫	∫	PROPN
ejpam-3003	522	12	t	t	PROPN
ejpam-3003	522	13	0	0	NUM
ejpam-3003	522	14	g(t−	g(t−	PROPN
ejpam-3003	522	15	s)[u(t)−	s)[u(t)−	PROPN
ejpam-3003	522	16	u(s)]dsdx	u(s)]dsdx	PROPN
ejpam-3003	522	17	−	−	PROPN
ejpam-3003	522	18	ξ(t	ξ(t	PROPN
ejpam-3003	522	19	)	)	PUNCT
ejpam-3003	522	20	ρ	ρ	PROPN
ejpam-3003	522	21	∫	∫	PROPN
ejpam-3003	522	22	ω	ω	PROPN
ejpam-3003	523	1	|ut|ρ−1ut	|ut|ρ−1ut	PROPN
ejpam-3003	523	2	∫	∫	PROPN
ejpam-3003	523	3	t	t	PROPN
ejpam-3003	523	4	0	0	NUM
ejpam-3003	524	1	g′(t−	g′(t−	PROPN
ejpam-3003	524	2	s)[u(t)−	s)[u(t)−	PROPN
ejpam-3003	524	3	u(s)]dsdx	u(s)]dsdx	PROPN
ejpam-3003	524	4	−	−	PROPN
ejpam-3003	524	5	ξ(t	ξ(t	PROPN
ejpam-3003	524	6	)	)	PUNCT
ejpam-3003	525	1	ρ	ρ	PROPN
ejpam-3003	525	2	∫	∫	PROPN
ejpam-3003	525	3	t	t	PROPN
ejpam-3003	525	4	0	0	NUM
ejpam-3003	526	1	g(s)ds	g(s)ds	PROPN
ejpam-3003	526	2	∫	∫	PROPN
ejpam-3003	526	3	ω	ω	PROPN
ejpam-3003	526	4	|ut|ρ+1dx	|ut|ρ+1dx	PROPN
ejpam-3003	526	5	.	.	PUNCT
ejpam-3003	526	6	(	(	PUNCT
ejpam-3003	526	7	4.19	4.19	NUM
ejpam-3003	526	8	)	)	PUNCT
ejpam-3003	526	9	from	from	ADP
ejpam-3003	526	10	the	the	DET
ejpam-3003	526	11	young	young	ADJ
ejpam-3003	526	12	inequality	inequality	NOUN
ejpam-3003	526	13	and	and	CCONJ
ejpam-3003	526	14	hölder	hölder	NOUN
ejpam-3003	526	15	inequality	inequality	NOUN
ejpam-3003	526	16	,	,	PUNCT
ejpam-3003	526	17	for	for	ADP
ejpam-3003	526	18	any	any	DET
ejpam-3003	526	19	δ	δ	PROPN
ejpam-3003	526	20	>	>	X
ejpam-3003	526	21	0	0	PROPN
ejpam-3003	526	22	,	,	PUNCT
ejpam-3003	526	23	we	we	PRON
ejpam-3003	526	24	have∫	have∫	VERB
ejpam-3003	526	25	ω	ω	NUM
ejpam-3003	526	26	∇u(t	∇u(t	PROPN
ejpam-3003	526	27	)	)	PUNCT
ejpam-3003	527	1	∫	∫	PROPN
ejpam-3003	527	2	t	t	PROPN
ejpam-3003	527	3	0	0	NUM
ejpam-3003	528	1	g(t−	g(t−	PROPN
ejpam-3003	528	2	s)[∇u(t)−∇u(s)]dsdx	s)[∇u(t)−∇u(s)]dsdx	NOUN
ejpam-3003	528	3	≤	≤	NOUN
ejpam-3003	528	4	δ‖∇u‖22	δ‖∇u‖22	PROPN
ejpam-3003	528	5	+	+	CCONJ
ejpam-3003	528	6	1−	1−	NUM
ejpam-3003	528	7	b	b	NOUN
ejpam-3003	528	8	4δ	4δ	NOUN
ejpam-3003	528	9	(	(	PUNCT
ejpam-3003	528	10	g	g	PROPN
ejpam-3003	528	11	◦	◦	NOUN
ejpam-3003	528	12	∇u)(t	∇u)(t	PROPN
ejpam-3003	528	13	)	)	PUNCT
ejpam-3003	528	14	.	.	PUNCT
ejpam-3003	529	1	(	(	PUNCT
ejpam-3003	529	2	4.20	4.20	NUM
ejpam-3003	529	3	)	)	PUNCT
ejpam-3003	529	4	by	by	ADP
ejpam-3003	529	5	the	the	DET
ejpam-3003	529	6	calculation	calculation	NOUN
ejpam-3003	529	7	similar	similar	ADJ
ejpam-3003	529	8	to	to	ADP
ejpam-3003	529	9	(	(	PUNCT
ejpam-3003	529	10	4.14	4.14	NUM
ejpam-3003	529	11	)	)	PUNCT
ejpam-3003	529	12	,	,	PUNCT
ejpam-3003	529	13	we	we	PRON
ejpam-3003	529	14	get	get	VERB
ejpam-3003	529	15	−	−	PROPN
ejpam-3003	529	16	∫	∫	PROPN
ejpam-3003	529	17	ω	ω	NUM
ejpam-3003	529	18	∫	∫	PROPN
ejpam-3003	529	19	t	t	PROPN
ejpam-3003	529	20	0	0	NUM
ejpam-3003	529	21	g(t−	g(t−	PROPN
ejpam-3003	530	1	s)∇u(s)ds	s)∇u(s)ds	ADJ
ejpam-3003	530	2	∫	∫	PROPN
ejpam-3003	530	3	t	t	PROPN
ejpam-3003	530	4	0	0	NUM
ejpam-3003	530	5	g(t−	g(t−	PROPN
ejpam-3003	530	6	s)[∇u(t)−∇u(s)]dsdx	s)[∇u(t)−∇u(s)]dsdx	NOUN
ejpam-3003	530	7	≤	≤	NUM
ejpam-3003	531	1	δ	δ	PROPN
ejpam-3003	531	2	∫	∫	PROPN
ejpam-3003	531	3	ω	ω	PROPN
ejpam-3003	531	4	(	(	PUNCT
ejpam-3003	531	5	∫	∫	PROPN
ejpam-3003	531	6	t	t	PROPN
ejpam-3003	531	7	0	0	NUM
ejpam-3003	531	8	g(t−	g(t−	PROPN
ejpam-3003	531	9	s)[|∇u(s)−∇u(t)|+	s)[|∇u(s)−∇u(t)|+	PROPN
ejpam-3003	531	10	|∇u(t)|]ds	|∇u(t)|]ds	PROPN
ejpam-3003	531	11	)	)	PUNCT
ejpam-3003	531	12	2	2	NUM
ejpam-3003	531	13	dx	dx	NOUN
ejpam-3003	531	14	+	+	NOUN
ejpam-3003	531	15	1	1	NUM
ejpam-3003	531	16	4δ	4δ	NOUN
ejpam-3003	531	17	∫	∫	PROPN
ejpam-3003	531	18	ω	ω	PROPN
ejpam-3003	531	19	(	(	PUNCT
ejpam-3003	531	20	∫	∫	PROPN
ejpam-3003	531	21	t	t	PROPN
ejpam-3003	531	22	0	0	NUM
ejpam-3003	531	23	g(t−	g(t−	PROPN
ejpam-3003	531	24	s)|∇u(t)−∇u(s)|ds	s)|∇u(t)−∇u(s)|ds	NOUN
ejpam-3003	531	25	)	)	PUNCT
ejpam-3003	531	26	2	2	NUM
ejpam-3003	531	27	dx	dx	PROPN
ejpam-3003	531	28	≤	≤	NUM
ejpam-3003	531	29	(	(	PUNCT
ejpam-3003	531	30	2δ	2δ	NUM
ejpam-3003	531	31	+	+	CCONJ
ejpam-3003	531	32	1	1	NUM
ejpam-3003	531	33	4δ	4δ	NOUN
ejpam-3003	531	34	)	)	PUNCT
ejpam-3003	531	35	∫	∫	PROPN
ejpam-3003	532	1	ω	ω	INTJ
ejpam-3003	532	2	(	(	PUNCT
ejpam-3003	532	3	∫	∫	PROPN
ejpam-3003	532	4	t	t	PROPN
ejpam-3003	532	5	0	0	NUM
ejpam-3003	532	6	g(t−	g(t−	PROPN
ejpam-3003	532	7	s)|∇u(s)−∇u(t)|ds	s)|∇u(s)−∇u(t)|ds	ADJ
ejpam-3003	532	8	)	)	PUNCT
ejpam-3003	532	9	2	2	NUM
ejpam-3003	532	10	dx+	dx+	NOUN
ejpam-3003	532	11	2δ(1−	2δ(1−	NUM
ejpam-3003	532	12	b)2‖∇u‖22	b)2‖∇u‖22	NOUN
ejpam-3003	532	13	≤	≤	NOUN
ejpam-3003	532	14	(	(	PUNCT
ejpam-3003	532	15	2δ	2δ	NUM
ejpam-3003	532	16	+	+	CCONJ
ejpam-3003	532	17	1	1	NUM
ejpam-3003	532	18	4δ	4δ	NOUN
ejpam-3003	532	19	)	)	PUNCT
ejpam-3003	532	20	(	(	PUNCT
ejpam-3003	532	21	1−	1−	NUM
ejpam-3003	532	22	b)(g	b)(g	NUM
ejpam-3003	532	23	◦	◦	PROPN
ejpam-3003	532	24	∇u)(t	∇u)(t	PROPN
ejpam-3003	532	25	)	)	PUNCT
ejpam-3003	532	26	+	+	NUM
ejpam-3003	532	27	2δ(1−	2δ(1−	NUM
ejpam-3003	532	28	b)2‖∇u‖22	b)2‖∇u‖22	NOUN
ejpam-3003	532	29	.	.	PUNCT
ejpam-3003	533	1	(	(	PUNCT
ejpam-3003	533	2	4.21	4.21	NUM
ejpam-3003	533	3	)	)	PUNCT
ejpam-3003	533	4	using	use	VERB
ejpam-3003	533	5	the	the	DET
ejpam-3003	533	6	young	young	ADJ
ejpam-3003	533	7	inequality	inequality	NOUN
ejpam-3003	533	8	and	and	CCONJ
ejpam-3003	533	9	sobolev	sobolev	NOUN
ejpam-3003	533	10	inequality	inequality	NOUN
ejpam-3003	533	11	,	,	PUNCT
ejpam-3003	533	12	it	it	PRON
ejpam-3003	533	13	follows	follow	VERB
ejpam-3003	533	14	that	that	SCONJ
ejpam-3003	533	15	−	−	PROPN
ejpam-3003	534	1	∫	∫	PROPN
ejpam-3003	534	2	ω	ω	NUM
ejpam-3003	534	3	|u|p−1u	|u|p−1u	INTJ
ejpam-3003	534	4	∫	∫	PROPN
ejpam-3003	534	5	t	t	PROPN
ejpam-3003	534	6	0	0	NUM
ejpam-3003	535	1	g(t−	g(t−	PROPN
ejpam-3003	535	2	s)[u(t)−	s)[u(t)−	PROPN
ejpam-3003	535	3	u(s)]dsdx	u(s)]dsdx	PROPN
ejpam-3003	535	4	h.f	h.f	PROPN
ejpam-3003	535	5	.	.	PROPN
ejpam-3003	535	6	di	di	PROPN
ejpam-3003	535	7	,	,	PUNCT
ejpam-3003	535	8	y.d	y.d	PROPN
ejpam-3003	535	9	.	.	PROPN
ejpam-3003	535	10	shang	shang	PROPN
ejpam-3003	535	11	/	/	SYM
ejpam-3003	535	12	eur	eur	PROPN
ejpam-3003	535	13	.	.	PUNCT
ejpam-3003	536	1	j.	j.	PROPN
ejpam-3003	536	2	pure	pure	PROPN
ejpam-3003	536	3	appl	appl	PROPN
ejpam-3003	536	4	.	.	PROPN
ejpam-3003	536	5	math	math	PROPN
ejpam-3003	536	6	,	,	PUNCT
ejpam-3003	536	7	10	10	NUM
ejpam-3003	536	8	(	(	PUNCT
ejpam-3003	536	9	4	4	NUM
ejpam-3003	536	10	)	)	PUNCT
ejpam-3003	536	11	(	(	PUNCT
ejpam-3003	536	12	2017	2017	NUM
ejpam-3003	536	13	)	)	PUNCT
ejpam-3003	536	14	,	,	PUNCT
ejpam-3003	536	15	668	668	NUM
ejpam-3003	536	16	-	-	SYM
ejpam-3003	536	17	701	701	NUM
ejpam-3003	536	18	690	690	NUM
ejpam-3003	536	19	≤	≤	NUM
ejpam-3003	536	20	pδ	pδ	ADP
ejpam-3003	536	21	p+	p+	NOUN
ejpam-3003	536	22	1	1	NUM
ejpam-3003	536	23	‖u‖p+1	‖u‖p+1	NOUN
ejpam-3003	536	24	p+1	p+1	NOUN
ejpam-3003	536	25	+	+	NOUN
ejpam-3003	536	26	1	1	NUM
ejpam-3003	536	27	(	(	PUNCT
ejpam-3003	536	28	p+	p+	NOUN
ejpam-3003	536	29	1)δ	1)δ	NUM
ejpam-3003	536	30	∫	∫	PROPN
ejpam-3003	536	31	ω	ω	PROPN
ejpam-3003	536	32	(	(	PUNCT
ejpam-3003	536	33	∫	∫	PROPN
ejpam-3003	536	34	t	t	PROPN
ejpam-3003	536	35	0	0	NUM
ejpam-3003	536	36	g(t−	g(t−	PROPN
ejpam-3003	536	37	s)[u(t)−	s)[u(t)−	PROPN
ejpam-3003	536	38	u(s)]ds	u(s)]ds	NOUN
ejpam-3003	536	39	)	)	PUNCT
ejpam-3003	537	1	p+1	p+1	PROPN
ejpam-3003	537	2	dx	dx	PROPN
ejpam-3003	537	3	≤	≤	PROPN
ejpam-3003	537	4	pδ	pδ	ADP
ejpam-3003	537	5	p+	p+	NOUN
ejpam-3003	537	6	1	1	NUM
ejpam-3003	537	7	‖u‖p+1	‖u‖p+1	NOUN
ejpam-3003	537	8	p+1	p+1	NOUN
ejpam-3003	537	9	+	+	NOUN
ejpam-3003	537	10	bp+1	bp+1	PROPN
ejpam-3003	537	11	p+1(1−	p+1(1−	ADJ
ejpam-3003	537	12	b)p	b)p	NOUN
ejpam-3003	537	13	(	(	PUNCT
ejpam-3003	537	14	p+	p+	NOUN
ejpam-3003	537	15	1)δ	1)δ	NUM
ejpam-3003	537	16	(	(	PUNCT
ejpam-3003	537	17	4(p+	4(p+	NOUN
ejpam-3003	537	18	1)e(0	1)e(0	NOUN
ejpam-3003	537	19	)	)	PUNCT
ejpam-3003	537	20	(	(	PUNCT
ejpam-3003	537	21	p−	p−	NOUN
ejpam-3003	537	22	1)b	1)b	X
ejpam-3003	537	23	)	)	PUNCT
ejpam-3003	537	24	p−1	p−1	PROPN
ejpam-3003	537	25	2	2	NUM
ejpam-3003	537	26	(	(	PUNCT
ejpam-3003	537	27	g	g	PROPN
ejpam-3003	537	28	◦	◦	PROPN
ejpam-3003	537	29	∇u)(t	∇u)(t	PROPN
ejpam-3003	537	30	)	)	PUNCT
ejpam-3003	537	31	.	.	PUNCT
ejpam-3003	538	1	(	(	PUNCT
ejpam-3003	538	2	4.22	4.22	X
ejpam-3003	538	3	)	)	PUNCT
ejpam-3003	538	4	taking	take	VERB
ejpam-3003	538	5	the	the	DET
ejpam-3003	538	6	young	young	ADJ
ejpam-3003	538	7	inequality	inequality	NOUN
ejpam-3003	538	8	and	and	CCONJ
ejpam-3003	538	9	trace	trace	NOUN
ejpam-3003	538	10	theorem	theorem	VERB
ejpam-3003	538	11	into	into	ADP
ejpam-3003	538	12	account	account	NOUN
ejpam-3003	538	13	,	,	PUNCT
ejpam-3003	538	14	we	we	PRON
ejpam-3003	538	15	deduce∫	deduce∫	VERB
ejpam-3003	538	16	γ1	γ1	PROPN
ejpam-3003	538	17	|ut|q−1ut	|ut|q−1ut	PROPN
ejpam-3003	538	18	∫	∫	PROPN
ejpam-3003	538	19	t	t	PROPN
ejpam-3003	538	20	0	0	NUM
ejpam-3003	539	1	g(t−	g(t−	PROPN
ejpam-3003	539	2	s)[u(t)−	s)[u(t)−	PROPN
ejpam-3003	539	3	u(s)]dsdγ	u(s)]dsdγ	PROPN
ejpam-3003	539	4	≤	≤	PUNCT
ejpam-3003	540	1	qδ	qδ	ADP
ejpam-3003	540	2	q	q	PROPN
ejpam-3003	541	1	+	+	NUM
ejpam-3003	541	2	1	1	NUM
ejpam-3003	541	3	‖ut‖q+1	‖ut‖q+1	PUNCT
ejpam-3003	541	4	γ1,q+1	γ1,q+1	PUNCT
ejpam-3003	542	1	+	+	CCONJ
ejpam-3003	542	2	1	1	NUM
ejpam-3003	542	3	(	(	PUNCT
ejpam-3003	542	4	q	q	PROPN
ejpam-3003	542	5	+	+	NUM
ejpam-3003	542	6	1)δ	1)δ	NUM
ejpam-3003	542	7	∫	∫	PROPN
ejpam-3003	542	8	γ1	γ1	PROPN
ejpam-3003	542	9	(	(	PUNCT
ejpam-3003	542	10	∫	∫	PROPN
ejpam-3003	542	11	t	t	PROPN
ejpam-3003	542	12	0	0	NUM
ejpam-3003	542	13	g(t−	g(t−	PROPN
ejpam-3003	542	14	s)[u(t)−	s)[u(t)−	PROPN
ejpam-3003	542	15	u(s)]ds	u(s)]ds	PROPN
ejpam-3003	542	16	)	)	PUNCT
ejpam-3003	542	17	q+1	q+1	PROPN
ejpam-3003	542	18	dγ	dγ	ADP
ejpam-3003	542	19	≤	≤	NUM
ejpam-3003	542	20	qδ	qδ	NOUN
ejpam-3003	542	21	q	q	PROPN
ejpam-3003	543	1	+	+	NUM
ejpam-3003	543	2	1	1	NUM
ejpam-3003	543	3	‖ut‖q+1	‖ut‖q+1	PUNCT
ejpam-3003	543	4	γ1,q+1	γ1,q+1	PUNCT
ejpam-3003	544	1	+	+	CCONJ
ejpam-3003	544	2	bq+1	bq+1	PROPN
ejpam-3003	544	3	q+1(1−	q+1(1−	NUM
ejpam-3003	544	4	b)q	b)q	PUNCT
ejpam-3003	544	5	(	(	PUNCT
ejpam-3003	544	6	q	q	X
ejpam-3003	544	7	+	+	NUM
ejpam-3003	544	8	1)δ	1)δ	NUM
ejpam-3003	544	9	(	(	PUNCT
ejpam-3003	544	10	4(p+	4(p+	NOUN
ejpam-3003	544	11	1)e(0	1)e(0	NOUN
ejpam-3003	544	12	)	)	PUNCT
ejpam-3003	544	13	(	(	PUNCT
ejpam-3003	544	14	p−	p−	NOUN
ejpam-3003	544	15	1)b	1)b	X
ejpam-3003	544	16	)	)	PUNCT
ejpam-3003	545	1	q−1	q−1	PROPN
ejpam-3003	545	2	2	2	NUM
ejpam-3003	545	3	(	(	PUNCT
ejpam-3003	545	4	g	g	PROPN
ejpam-3003	545	5	◦	◦	PROPN
ejpam-3003	545	6	∇u)(t	∇u)(t	PROPN
ejpam-3003	545	7	)	)	PUNCT
ejpam-3003	545	8	.	.	PUNCT
ejpam-3003	546	1	(	(	PUNCT
ejpam-3003	546	2	4.23	4.23	X
ejpam-3003	546	3	)	)	PUNCT
ejpam-3003	546	4	making	make	VERB
ejpam-3003	546	5	use	use	NOUN
ejpam-3003	546	6	of	of	ADP
ejpam-3003	546	7	the	the	DET
ejpam-3003	546	8	young	young	ADJ
ejpam-3003	546	9	inequality	inequality	NOUN
ejpam-3003	546	10	and	and	CCONJ
ejpam-3003	546	11	lemma	lemma	PROPN
ejpam-3003	546	12	5	5	NUM
ejpam-3003	546	13	,	,	PUNCT
ejpam-3003	546	14	we	we	PRON
ejpam-3003	546	15	have	have	VERB
ejpam-3003	546	16	−1	−1	NOUN
ejpam-3003	546	17	ρ	ρ	PROPN
ejpam-3003	546	18	∫	∫	PROPN
ejpam-3003	546	19	ω	ω	PROPN
ejpam-3003	547	1	|ut|ρ−1ut	|ut|ρ−1ut	PROPN
ejpam-3003	547	2	∫	∫	PROPN
ejpam-3003	547	3	t	t	PROPN
ejpam-3003	547	4	0	0	NUM
ejpam-3003	548	1	g(t−	g(t−	PROPN
ejpam-3003	548	2	s)[u(t)−	s)[u(t)−	PROPN
ejpam-3003	548	3	u(s)]dsdx	u(s)]dsdx	PROPN
ejpam-3003	548	4	≤	≤	PROPN
ejpam-3003	548	5	δ	δ	PROPN
ejpam-3003	548	6	ρ+	ρ+	NUM
ejpam-3003	548	7	1	1	NUM
ejpam-3003	548	8	‖ut‖ρ+1	‖ut‖ρ+1	SYM
ejpam-3003	548	9	ρ+1	ρ+1	NUM
ejpam-3003	548	10	+	+	CCONJ
ejpam-3003	548	11	1	1	NUM
ejpam-3003	548	12	ρ(ρ+	ρ(ρ+	NUM
ejpam-3003	548	13	1)δ	1)δ	NUM
ejpam-3003	548	14	∫	∫	PROPN
ejpam-3003	548	15	ω	ω	PROPN
ejpam-3003	548	16	(	(	PUNCT
ejpam-3003	548	17	∫	∫	PROPN
ejpam-3003	548	18	t	t	PROPN
ejpam-3003	548	19	0	0	NUM
ejpam-3003	548	20	g(t−	g(t−	PROPN
ejpam-3003	548	21	s)[u(t)−	s)[u(t)−	PROPN
ejpam-3003	548	22	u(s)]ds	u(s)]ds	NOUN
ejpam-3003	548	23	)	)	PUNCT
ejpam-3003	549	1	ρ+1	ρ+1	NUM
ejpam-3003	549	2	dx	dx	PROPN
ejpam-3003	549	3	≤	≤	PROPN
ejpam-3003	549	4	δ	δ	PROPN
ejpam-3003	549	5	ρ+	ρ+	NUM
ejpam-3003	549	6	1	1	NUM
ejpam-3003	549	7	‖ut‖ρ+1	‖ut‖ρ+1	SYM
ejpam-3003	549	8	ρ+1	ρ+1	NOUN
ejpam-3003	549	9	+	+	CCONJ
ejpam-3003	549	10	bρ+1	bρ+1	SYM
ejpam-3003	549	11	ρ+1(1−	ρ+1(1−	NUM
ejpam-3003	549	12	b)ρ	b)ρ	NUM
ejpam-3003	549	13	ρ(ρ+	ρ(ρ+	NOUN
ejpam-3003	549	14	1)δ	1)δ	NUM
ejpam-3003	549	15	(	(	PUNCT
ejpam-3003	549	16	4(p+	4(p+	NOUN
ejpam-3003	549	17	1)e(0	1)e(0	NOUN
ejpam-3003	549	18	)	)	PUNCT
ejpam-3003	549	19	(	(	PUNCT
ejpam-3003	549	20	p−	p−	NOUN
ejpam-3003	549	21	1)b	1)b	X
ejpam-3003	549	22	)	)	PUNCT
ejpam-3003	549	23	ρ−1	ρ−1	PROPN
ejpam-3003	549	24	2	2	NUM
ejpam-3003	549	25	(	(	PUNCT
ejpam-3003	549	26	g	g	PROPN
ejpam-3003	549	27	◦	◦	PROPN
ejpam-3003	549	28	∇u)(t	∇u)(t	PROPN
ejpam-3003	549	29	)	)	PUNCT
ejpam-3003	549	30	.	.	PUNCT
ejpam-3003	550	1	(	(	PUNCT
ejpam-3003	550	2	4.24	4.24	NUM
ejpam-3003	550	3	)	)	PUNCT
ejpam-3003	550	4	furthermore	furthermore	ADV
ejpam-3003	550	5	,	,	PUNCT
ejpam-3003	550	6	similar	similar	ADJ
ejpam-3003	550	7	calculation	calculation	NOUN
ejpam-3003	550	8	give	give	VERB
ejpam-3003	550	9	that	that	DET
ejpam-3003	550	10	−1	−1	NOUN
ejpam-3003	550	11	ρ	ρ	PROPN
ejpam-3003	550	12	∫	∫	PROPN
ejpam-3003	550	13	ω	ω	PROPN
ejpam-3003	550	14	|ut|ρ−1ut	|ut|ρ−1ut	PROPN
ejpam-3003	550	15	∫	∫	PROPN
ejpam-3003	550	16	t	t	PROPN
ejpam-3003	550	17	0	0	NUM
ejpam-3003	551	1	g′(t−	g′(t−	PROPN
ejpam-3003	551	2	s)[u(t)−	s)[u(t)−	PROPN
ejpam-3003	551	3	u(s)]dsdx	u(s)]dsdx	PROPN
ejpam-3003	551	4	≤	≤	PROPN
ejpam-3003	551	5	δ	δ	PROPN
ejpam-3003	551	6	ρ+	ρ+	NUM
ejpam-3003	551	7	1	1	NUM
ejpam-3003	551	8	‖ut‖ρ+1	‖ut‖ρ+1	SYM
ejpam-3003	551	9	ρ+1	ρ+1	NUM
ejpam-3003	551	10	+	+	CCONJ
ejpam-3003	551	11	1	1	NUM
ejpam-3003	551	12	ρ(ρ+	ρ(ρ+	NUM
ejpam-3003	551	13	1)δ	1)δ	NUM
ejpam-3003	551	14	∫	∫	PROPN
ejpam-3003	551	15	ω	ω	PROPN
ejpam-3003	551	16	(	(	PUNCT
ejpam-3003	551	17	∫	∫	PROPN
ejpam-3003	551	18	t	t	PROPN
ejpam-3003	551	19	0	0	NUM
ejpam-3003	552	1	g′(t−	g′(t−	ADJ
ejpam-3003	552	2	s)[u(t)−	s)[u(t)−	PROPN
ejpam-3003	552	3	u(s)]ds	u(s)]ds	NOUN
ejpam-3003	552	4	)	)	PUNCT
ejpam-3003	553	1	ρ+1	ρ+1	NUM
ejpam-3003	553	2	dx	dx	PROPN
ejpam-3003	553	3	≤	≤	PROPN
ejpam-3003	553	4	δ	δ	PROPN
ejpam-3003	553	5	ρ+	ρ+	NUM
ejpam-3003	553	6	1	1	NUM
ejpam-3003	553	7	‖ut‖ρ+1	‖ut‖ρ+1	SYM
ejpam-3003	553	8	ρ+1	ρ+1	ADJ
ejpam-3003	553	9	+	+	CCONJ
ejpam-3003	553	10	g(0)ρbρ+1	g(0)ρbρ+1	NOUN
ejpam-3003	553	11	ρ+1	ρ+1	NUM
ejpam-3003	553	12	ρ(ρ+	ρ(ρ+	NOUN
ejpam-3003	553	13	1)δ	1)δ	NUM
ejpam-3003	553	14	(	(	PUNCT
ejpam-3003	553	15	4(p+	4(p+	NOUN
ejpam-3003	553	16	1)e(0	1)e(0	NOUN
ejpam-3003	553	17	)	)	PUNCT
ejpam-3003	553	18	(	(	PUNCT
ejpam-3003	553	19	p−	p−	NOUN
ejpam-3003	553	20	1)b	1)b	X
ejpam-3003	553	21	)	)	PUNCT
ejpam-3003	553	22	ρ−1	ρ−1	PROPN
ejpam-3003	553	23	2	2	NUM
ejpam-3003	553	24	(	(	PUNCT
ejpam-3003	553	25	−g′	−g′	NOUN
ejpam-3003	553	26	◦	◦	NOUN
ejpam-3003	553	27	∇u)(t	∇u)(t	PROPN
ejpam-3003	553	28	)	)	PUNCT
ejpam-3003	553	29	.	.	PUNCT
ejpam-3003	554	1	(	(	PUNCT
ejpam-3003	554	2	4.25	4.25	NUM
ejpam-3003	554	3	)	)	PUNCT
ejpam-3003	554	4	finally	finally	ADV
ejpam-3003	554	5	,	,	PUNCT
ejpam-3003	554	6	inserting	insert	VERB
ejpam-3003	554	7	(	(	PUNCT
ejpam-3003	554	8	4.20)-(4.25	4.20)-(4.25	NUM
ejpam-3003	554	9	)	)	PUNCT
ejpam-3003	554	10	into	into	ADP
ejpam-3003	554	11	(	(	PUNCT
ejpam-3003	554	12	4.19	4.19	NUM
ejpam-3003	554	13	)	)	PUNCT
ejpam-3003	554	14	and	and	CCONJ
ejpam-3003	554	15	applying	apply	VERB
ejpam-3003	554	16	the	the	DET
ejpam-3003	554	17	conditions	condition	NOUN
ejpam-3003	554	18	(	(	PUNCT
ejpam-3003	554	19	a2	a2	PROPN
ejpam-3003	554	20	)	)	PUNCT
ejpam-3003	554	21	,	,	PUNCT
ejpam-3003	554	22	we	we	PRON
ejpam-3003	554	23	can	can	AUX
ejpam-3003	554	24	obtain	obtain	VERB
ejpam-3003	554	25	that	that	SCONJ
ejpam-3003	554	26	the	the	DET
ejpam-3003	554	27	conclusion	conclusion	NOUN
ejpam-3003	554	28	of	of	ADP
ejpam-3003	554	29	lemma	lemma	PROPN
ejpam-3003	554	30	holds	hold	VERB
ejpam-3003	554	31	.	.	PUNCT
ejpam-3003	555	1	now	now	ADV
ejpam-3003	555	2	,	,	PUNCT
ejpam-3003	555	3	we	we	PRON
ejpam-3003	555	4	are	be	AUX
ejpam-3003	555	5	ready	ready	ADJ
ejpam-3003	555	6	to	to	PART
ejpam-3003	555	7	give	give	VERB
ejpam-3003	555	8	the	the	DET
ejpam-3003	555	9	proof	proof	NOUN
ejpam-3003	555	10	of	of	ADP
ejpam-3003	555	11	the	the	DET
ejpam-3003	555	12	theorem	theorem	NOUN
ejpam-3003	555	13	2	2	NUM
ejpam-3003	555	14	.	.	PUNCT
ejpam-3003	555	15	proof	proof	NOUN
ejpam-3003	555	16	.	.	PUNCT
ejpam-3003	556	1	since	since	SCONJ
ejpam-3003	556	2	the	the	DET
ejpam-3003	556	3	function	function	NOUN
ejpam-3003	556	4	g	g	NOUN
ejpam-3003	556	5	is	be	AUX
ejpam-3003	556	6	positive	positive	ADJ
ejpam-3003	556	7	,	,	PUNCT
ejpam-3003	556	8	continuous	continuous	ADJ
ejpam-3003	556	9	and	and	CCONJ
ejpam-3003	556	10	g(0	g(0	NOUN
ejpam-3003	556	11	)	)	PUNCT
ejpam-3003	556	12	>	>	X
ejpam-3003	556	13	0	0	NUM
ejpam-3003	556	14	,	,	PUNCT
ejpam-3003	556	15	for	for	ADP
ejpam-3003	556	16	any	any	DET
ejpam-3003	556	17	t0	t0	PROPN
ejpam-3003	556	18	>	>	X
ejpam-3003	556	19	0	0	NUM
ejpam-3003	557	1	we	we	PRON
ejpam-3003	557	2	have	have	VERB
ejpam-3003	557	3	∫	∫	PROPN
ejpam-3003	557	4	t	t	PROPN
ejpam-3003	557	5	0	0	NUM
ejpam-3003	557	6	g(s)ds	g(s)ds	PROPN
ejpam-3003	557	7	≥	≥	NOUN
ejpam-3003	557	8	∫	∫	PROPN
ejpam-3003	557	9	t0	t0	PROPN
ejpam-3003	557	10	0	0	NUM
ejpam-3003	557	11	g(s)ds	g(s)ds	PROPN
ejpam-3003	557	12	=	=	SYM
ejpam-3003	557	13	g0	g0	PROPN
ejpam-3003	557	14	>	>	X
ejpam-3003	557	15	0	0	PROPN
ejpam-3003	557	16	,	,	PUNCT
ejpam-3003	557	17	∀	∀	X
ejpam-3003	557	18	t	t	PROPN
ejpam-3003	557	19	≥	≥	PROPN
ejpam-3003	557	20	t0	t0	PROPN
ejpam-3003	557	21	.	.	PUNCT
ejpam-3003	558	1	(	(	PUNCT
ejpam-3003	558	2	4.26	4.26	NUM
ejpam-3003	558	3	)	)	PUNCT
ejpam-3003	558	4	combining	combine	VERB
ejpam-3003	558	5	(	(	PUNCT
ejpam-3003	558	6	4.1),(4.12),(4.18	4.1),(4.12),(4.18	NUM
ejpam-3003	558	7	)	)	PUNCT
ejpam-3003	558	8	and	and	CCONJ
ejpam-3003	558	9	lemma	lemma	PROPN
ejpam-3003	558	10	4	4	NUM
ejpam-3003	558	11	,	,	PUNCT
ejpam-3003	558	12	by	by	ADP
ejpam-3003	558	13	a	a	DET
ejpam-3003	558	14	series	series	NOUN
ejpam-3003	558	15	of	of	ADP
ejpam-3003	558	16	computations	computation	NOUN
ejpam-3003	558	17	,	,	PUNCT
ejpam-3003	558	18	we	we	PRON
ejpam-3003	558	19	have	have	VERB
ejpam-3003	558	20	that	that	SCONJ
ejpam-3003	558	21	f	f	PROPN
ejpam-3003	558	22	′(t	′(t	PROPN
ejpam-3003	558	23	)	)	PUNCT
ejpam-3003	558	24	≤me′(t	≤me′(t	NOUN
ejpam-3003	558	25	)	)	PUNCT
ejpam-3003	559	1	+	+	CCONJ
ejpam-3003	559	2	ε	ε	PROPN
ejpam-3003	559	3	[	[	PUNCT
ejpam-3003	559	4	1	1	NUM
ejpam-3003	559	5	ρ	ρ	NUM
ejpam-3003	559	6	+	+	X
ejpam-3003	559	7	k	k	X
ejpam-3003	559	8	(	(	PUNCT
ejpam-3003	559	9	ρ+	ρ+	NUM
ejpam-3003	559	10	1)ρα	1)ρα	NOUN
ejpam-3003	559	11	]	]	PUNCT
ejpam-3003	559	12	ξ(t)‖ut‖ρ+1	ξ(t)‖ut‖ρ+1	PUNCT
ejpam-3003	560	1	ρ+1	ρ+1	NUM
ejpam-3003	560	2	−	−	PROPN
ejpam-3003	560	3	ε	ε	PROPN
ejpam-3003	560	4	[	[	PUNCT
ejpam-3003	560	5	b	b	PROPN
ejpam-3003	560	6	2	2	NUM
ejpam-3003	560	7	−	−	NOUN
ejpam-3003	560	8	αkbρ+1	αkbρ+1	NOUN
ejpam-3003	560	9	ρ+1	ρ+1	NOUN
ejpam-3003	560	10	ρ+	ρ+	NOUN
ejpam-3003	560	11	1	1	NUM
ejpam-3003	560	12	h.f	h.f	PROPN
ejpam-3003	560	13	.	.	PROPN
ejpam-3003	560	14	di	di	PROPN
ejpam-3003	560	15	,	,	PUNCT
ejpam-3003	560	16	y.d	y.d	PROPN
ejpam-3003	560	17	.	.	PROPN
ejpam-3003	560	18	shang	shang	PROPN
ejpam-3003	560	19	/	/	SYM
ejpam-3003	560	20	eur	eur	PROPN
ejpam-3003	560	21	.	.	PUNCT
ejpam-3003	561	1	j.	j.	PROPN
ejpam-3003	561	2	pure	pure	PROPN
ejpam-3003	561	3	appl	appl	PROPN
ejpam-3003	561	4	.	.	PROPN
ejpam-3003	561	5	math	math	PROPN
ejpam-3003	561	6	,	,	PUNCT
ejpam-3003	561	7	10	10	NUM
ejpam-3003	561	8	(	(	PUNCT
ejpam-3003	561	9	4	4	NUM
ejpam-3003	561	10	)	)	PUNCT
ejpam-3003	561	11	(	(	PUNCT
ejpam-3003	561	12	2017	2017	NUM
ejpam-3003	561	13	)	)	PUNCT
ejpam-3003	561	14	,	,	PUNCT
ejpam-3003	561	15	668	668	NUM
ejpam-3003	561	16	-	-	SYM
ejpam-3003	561	17	701	701	NUM
ejpam-3003	561	18	691	691	NUM
ejpam-3003	561	19	×	×	NOUN
ejpam-3003	561	20	(	(	PUNCT
ejpam-3003	561	21	2(p+	2(p+	NUM
ejpam-3003	561	22	1)e(0	1)e(0	NOUN
ejpam-3003	561	23	)	)	PUNCT
ejpam-3003	561	24	(	(	PUNCT
ejpam-3003	561	25	p−	p−	NOUN
ejpam-3003	561	26	1)b	1)b	X
ejpam-3003	561	27	)	)	PUNCT
ejpam-3003	561	28	ρ−1	ρ−1	PROPN
ejpam-3003	561	29	2	2	NUM
ejpam-3003	561	30	−	−	PROPN
ejpam-3003	561	31	qαbq+1	qαbq+1	PROPN
ejpam-3003	561	32	q+1	q+1	PROPN
ejpam-3003	561	33	q	q	NOUN
ejpam-3003	562	1	+	+	NUM
ejpam-3003	562	2	1	1	NUM
ejpam-3003	562	3	(	(	PUNCT
ejpam-3003	562	4	2(p+	2(p+	NUM
ejpam-3003	562	5	1)e(0	1)e(0	NOUN
ejpam-3003	562	6	)	)	PUNCT
ejpam-3003	562	7	(	(	PUNCT
ejpam-3003	562	8	p−	p−	NOUN
ejpam-3003	562	9	1)b	1)b	X
ejpam-3003	562	10	)	)	PUNCT
ejpam-3003	563	1	q−1	q−1	PROPN
ejpam-3003	563	2	2	2	NUM
ejpam-3003	563	3	]	]	PUNCT
ejpam-3003	563	4	ξ(t)‖∇u‖22	ξ(t)‖∇u‖22	PUNCT
ejpam-3003	564	1	+	+	CCONJ
ejpam-3003	564	2	ε	ε	PROPN
ejpam-3003	564	3	1−	1−	NUM
ejpam-3003	564	4	b	b	PROPN
ejpam-3003	564	5	2b	2b	NUM
ejpam-3003	564	6	ξ(t)(g	ξ(t)(g	ADP
ejpam-3003	564	7	◦	◦	PROPN
ejpam-3003	564	8	∇u)(t	∇u)(t	PROPN
ejpam-3003	564	9	)	)	PUNCT
ejpam-3003	564	10	+	+	NUM
ejpam-3003	564	11	εξ(t)‖u‖p+1	εξ(t)‖u‖p+1	ADJ
ejpam-3003	564	12	p+1	p+1	NOUN
ejpam-3003	565	1	+	+	CCONJ
ejpam-3003	565	2	ε	ε	PROPN
ejpam-3003	565	3	1	1	NUM
ejpam-3003	565	4	(	(	PUNCT
ejpam-3003	565	5	q	q	PROPN
ejpam-3003	565	6	+	+	NUM
ejpam-3003	565	7	1)α	1)α	NUM
ejpam-3003	565	8	ξ(t)‖ut‖q+1	ξ(t)‖ut‖q+1	PROPN
ejpam-3003	565	9	γ1,q+1	γ1,q+1	PUNCT
ejpam-3003	566	1	+	+	CCONJ
ejpam-3003	566	2	δ	δ	PROPN
ejpam-3003	566	3	[	[	PUNCT
ejpam-3003	566	4	1	1	NUM
ejpam-3003	566	5	+	+	CCONJ
ejpam-3003	566	6	2(1−	2(1−	NUM
ejpam-3003	566	7	b)2	b)2	ADJ
ejpam-3003	566	8	+	+	CCONJ
ejpam-3003	566	9	p	p	X
ejpam-3003	566	10	p+	p+	VERB
ejpam-3003	566	11	1	1	NUM
ejpam-3003	566	12	bp+1	bp+1	NOUN
ejpam-3003	566	13	p+1	p+1	PROPN
ejpam-3003	566	14	(	(	PUNCT
ejpam-3003	566	15	2(p+	2(p+	NUM
ejpam-3003	566	16	1)e(0	1)e(0	NOUN
ejpam-3003	566	17	)	)	PUNCT
ejpam-3003	566	18	(	(	PUNCT
ejpam-3003	566	19	p−	p−	NOUN
ejpam-3003	566	20	1)b	1)b	X
ejpam-3003	566	21	)	)	PUNCT
ejpam-3003	566	22	p−1	p−1	PROPN
ejpam-3003	566	23	2	2	NUM
ejpam-3003	566	24	]	]	PUNCT
ejpam-3003	566	25	ξ(t)‖∇u‖22	ξ(t)‖∇u‖22	PUNCT
ejpam-3003	567	1	+	+	CCONJ
ejpam-3003	567	2	[	[	PUNCT
ejpam-3003	567	3	δ	δ	NOUN
ejpam-3003	567	4	ρ+	ρ+	NOUN
ejpam-3003	567	5	1	1	NUM
ejpam-3003	567	6	+	+	CCONJ
ejpam-3003	567	7	kδ	kδ	PART
ejpam-3003	567	8	ρ+	ρ+	NUM
ejpam-3003	567	9	1	1	NUM
ejpam-3003	567	10	−	−	NOUN
ejpam-3003	567	11	∫	∫	PROPN
ejpam-3003	567	12	t	t	PROPN
ejpam-3003	567	13	0	0	NUM
ejpam-3003	567	14	g(s)ds	g(s)ds	PROPN
ejpam-3003	567	15	ρ	ρ	PROPN
ejpam-3003	567	16	]	]	PUNCT
ejpam-3003	567	17	ξ(t)‖ut‖ρ+1	ξ(t)‖ut‖ρ+1	X
ejpam-3003	568	1	ρ+1	ρ+1	NOUN
ejpam-3003	569	1	+	+	CCONJ
ejpam-3003	569	2	[	[	PUNCT
ejpam-3003	569	3	(	(	PUNCT
ejpam-3003	569	4	2δ	2δ	NUM
ejpam-3003	569	5	+	+	CCONJ
ejpam-3003	569	6	1	1	NUM
ejpam-3003	569	7	2δ	2δ	NUM
ejpam-3003	569	8	)	)	PUNCT
ejpam-3003	569	9	(	(	PUNCT
ejpam-3003	569	10	1−	1−	NUM
ejpam-3003	569	11	b	b	NOUN
ejpam-3003	569	12	)	)	PUNCT
ejpam-3003	570	1	+	+	NUM
ejpam-3003	570	2	bp+1	bp+1	PROPN
ejpam-3003	570	3	p+1(1−	p+1(1−	ADJ
ejpam-3003	570	4	b)p	b)p	NOUN
ejpam-3003	570	5	(	(	PUNCT
ejpam-3003	570	6	p+	p+	NOUN
ejpam-3003	570	7	1)δ	1)δ	NUM
ejpam-3003	570	8	(	(	PUNCT
ejpam-3003	570	9	4(p+	4(p+	NOUN
ejpam-3003	570	10	1)e(0	1)e(0	NOUN
ejpam-3003	570	11	)	)	PUNCT
ejpam-3003	570	12	(	(	PUNCT
ejpam-3003	570	13	p−	p−	NOUN
ejpam-3003	570	14	1)b	1)b	X
ejpam-3003	570	15	)	)	PUNCT
ejpam-3003	570	16	p−1	p−1	PROPN
ejpam-3003	570	17	2	2	NUM
ejpam-3003	570	18	+	+	CCONJ
ejpam-3003	570	19	bq+1	bq+1	PROPN
ejpam-3003	570	20	q+1(1−	q+1(1−	NUM
ejpam-3003	570	21	b)q	b)q	PUNCT
ejpam-3003	570	22	(	(	PUNCT
ejpam-3003	570	23	q	q	X
ejpam-3003	571	1	+	+	NUM
ejpam-3003	571	2	1)δ	1)δ	NUM
ejpam-3003	571	3	(	(	PUNCT
ejpam-3003	571	4	4(p+	4(p+	NOUN
ejpam-3003	571	5	1)e(0	1)e(0	NOUN
ejpam-3003	571	6	)	)	PUNCT
ejpam-3003	571	7	(	(	PUNCT
ejpam-3003	571	8	p−	p−	NOUN
ejpam-3003	571	9	1)b	1)b	X
ejpam-3003	571	10	)	)	PUNCT
ejpam-3003	572	1	q−1	q−1	PROPN
ejpam-3003	572	2	2	2	NUM
ejpam-3003	573	1	+	+	CCONJ
ejpam-3003	573	2	k	k	NOUN
ejpam-3003	573	3	ρ(ρ+	ρ(ρ+	NUM
ejpam-3003	573	4	1)δ	1)δ	NUM
ejpam-3003	573	5	bρ+1	bρ+1	X
ejpam-3003	573	6	ρ+1(1−	ρ+1(1−	NUM
ejpam-3003	573	7	b)ρ	b)ρ	NOUN
ejpam-3003	573	8	(	(	PUNCT
ejpam-3003	573	9	4(p+	4(p+	NUM
ejpam-3003	573	10	1)e(0	1)e(0	NOUN
ejpam-3003	573	11	)	)	PUNCT
ejpam-3003	573	12	(	(	PUNCT
ejpam-3003	573	13	p−	p−	NOUN
ejpam-3003	573	14	1)b	1)b	X
ejpam-3003	573	15	)	)	PUNCT
ejpam-3003	573	16	ρ−1	ρ−1	PROPN
ejpam-3003	573	17	2	2	NUM
ejpam-3003	573	18	]	]	PUNCT
ejpam-3003	573	19	ξ(t)(g	ξ(t)(g	ADP
ejpam-3003	573	20	◦	◦	PROPN
ejpam-3003	573	21	∇u)(t	∇u)(t	PROPN
ejpam-3003	573	22	)	)	PUNCT
ejpam-3003	573	23	−	−	NOUN
ejpam-3003	573	24	g(0)ρbρ+1	g(0)ρbρ+1	NOUN
ejpam-3003	573	25	ρ+1	ρ+1	NUM
ejpam-3003	573	26	ρ(ρ+	ρ(ρ+	NOUN
ejpam-3003	573	27	1)δ	1)δ	NUM
ejpam-3003	573	28	(	(	PUNCT
ejpam-3003	573	29	4(p+	4(p+	NOUN
ejpam-3003	573	30	1)e(0	1)e(0	NOUN
ejpam-3003	573	31	)	)	PUNCT
ejpam-3003	573	32	(	(	PUNCT
ejpam-3003	573	33	p−	p−	NOUN
ejpam-3003	573	34	1)b	1)b	X
ejpam-3003	573	35	)	)	PUNCT
ejpam-3003	573	36	ρ−1	ρ−1	PROPN
ejpam-3003	573	37	2	2	NUM
ejpam-3003	573	38	ξ(t)(g′	ξ(t)(g′	PUNCT
ejpam-3003	573	39	◦	◦	NOUN
ejpam-3003	573	40	∇u)(t	∇u)(t	PROPN
ejpam-3003	573	41	)	)	PUNCT
ejpam-3003	574	1	+	+	CCONJ
ejpam-3003	574	2	qδ	qδ	PRON
ejpam-3003	574	3	q	q	PROPN
ejpam-3003	575	1	+	+	NUM
ejpam-3003	576	1	1	1	NUM
ejpam-3003	576	2	ξ(t)‖ut‖q+1	ξ(t)‖ut‖q+1	PROPN
ejpam-3003	576	3	γ1,q+1	γ1,q+1	PUNCT
ejpam-3003	577	1	≤	≤	ADV
ejpam-3003	577	2	−	−	PROPN
ejpam-3003	577	3	{	{	PUNCT
ejpam-3003	577	4	ε	ε	PROPN
ejpam-3003	577	5	[	[	PUNCT
ejpam-3003	577	6	b	b	PROPN
ejpam-3003	577	7	2	2	NUM
ejpam-3003	577	8	−	−	NOUN
ejpam-3003	577	9	αkbρ+1	αkbρ+1	NOUN
ejpam-3003	577	10	ρ+1	ρ+1	NOUN
ejpam-3003	577	11	ρ+	ρ+	NOUN
ejpam-3003	577	12	1	1	NUM
ejpam-3003	577	13	(	(	PUNCT
ejpam-3003	577	14	2(p+	2(p+	NUM
ejpam-3003	577	15	1)e(0	1)e(0	NOUN
ejpam-3003	577	16	)	)	PUNCT
ejpam-3003	577	17	(	(	PUNCT
ejpam-3003	577	18	p−	p−	NOUN
ejpam-3003	577	19	1)b	1)b	X
ejpam-3003	577	20	)	)	PUNCT
ejpam-3003	578	1	ρ−1	ρ−1	PROPN
ejpam-3003	578	2	2	2	NUM
ejpam-3003	578	3	−	−	PROPN
ejpam-3003	578	4	qαbq+1	qαbq+1	PROPN
ejpam-3003	578	5	q+1	q+1	PROPN
ejpam-3003	578	6	q	q	NOUN
ejpam-3003	579	1	+	+	NUM
ejpam-3003	579	2	1	1	NUM
ejpam-3003	579	3	(	(	PUNCT
ejpam-3003	579	4	2(p+	2(p+	NUM
ejpam-3003	579	5	1)e(0	1)e(0	NOUN
ejpam-3003	579	6	)	)	PUNCT
ejpam-3003	579	7	(	(	PUNCT
ejpam-3003	579	8	p−	p−	NOUN
ejpam-3003	579	9	1)b	1)b	X
ejpam-3003	579	10	)	)	PUNCT
ejpam-3003	580	1	q−1	q−1	PROPN
ejpam-3003	580	2	2	2	NUM
ejpam-3003	580	3	]	]	PUNCT
ejpam-3003	580	4	−	−	PROPN
ejpam-3003	580	5	δ	δ	PROPN
ejpam-3003	580	6	[	[	PUNCT
ejpam-3003	580	7	1	1	NUM
ejpam-3003	580	8	+	+	CCONJ
ejpam-3003	580	9	2(1−	2(1−	NUM
ejpam-3003	580	10	b)2	b)2	ADJ
ejpam-3003	581	1	+	+	CCONJ
ejpam-3003	581	2	p	p	X
ejpam-3003	581	3	p+	p+	VERB
ejpam-3003	581	4	1	1	NUM
ejpam-3003	581	5	bp+1	bp+1	NOUN
ejpam-3003	581	6	p+1	p+1	PROPN
ejpam-3003	581	7	(	(	PUNCT
ejpam-3003	581	8	2(p+	2(p+	NUM
ejpam-3003	581	9	1)e(0	1)e(0	NOUN
ejpam-3003	581	10	)	)	PUNCT
ejpam-3003	581	11	(	(	PUNCT
ejpam-3003	581	12	p−	p−	NOUN
ejpam-3003	581	13	1)b	1)b	X
ejpam-3003	581	14	)	)	PUNCT
ejpam-3003	581	15	p−1	p−1	NOUN
ejpam-3003	581	16	2	2	NUM
ejpam-3003	581	17	]	]	PUNCT
ejpam-3003	581	18	}	}	PUNCT
ejpam-3003	581	19	ξ(t)‖∇u‖22	ξ(t)‖∇u‖22	PUNCT
ejpam-3003	582	1	−	−	PROPN
ejpam-3003	582	2	{	{	PUNCT
ejpam-3003	582	3	m	m	NOUN
ejpam-3003	582	4	2	2	NUM
ejpam-3003	582	5	−	−	NUM
ejpam-3003	582	6	1	1	NUM
ejpam-3003	582	7	ρ(ρ+	ρ(ρ+	NUM
ejpam-3003	582	8	1)δ	1)δ	NUM
ejpam-3003	582	9	g(0)ρbρ+1	g(0)ρbρ+1	NOUN
ejpam-3003	582	10	2	2	NUM
ejpam-3003	582	11	(	(	PUNCT
ejpam-3003	582	12	4(p+	4(p+	NOUN
ejpam-3003	582	13	1)e(0	1)e(0	NOUN
ejpam-3003	582	14	)	)	PUNCT
ejpam-3003	582	15	(	(	PUNCT
ejpam-3003	582	16	p−	p−	NOUN
ejpam-3003	582	17	1)b	1)b	X
ejpam-3003	582	18	)	)	PUNCT
ejpam-3003	582	19	ρ−1	ρ−1	PROPN
ejpam-3003	582	20	2	2	NUM
ejpam-3003	582	21	ξ(0	ξ(0	NOUN
ejpam-3003	582	22	)	)	PUNCT
ejpam-3003	582	23	}	}	PUNCT
ejpam-3003	582	24	(	(	PUNCT
ejpam-3003	582	25	−g′	−g′	NOUN
ejpam-3003	582	26	◦	◦	NOUN
ejpam-3003	582	27	∇u)(t	∇u)(t	PROPN
ejpam-3003	582	28	)	)	PUNCT
ejpam-3003	583	1	+	+	CCONJ
ejpam-3003	583	2	{	{	PUNCT
ejpam-3003	583	3	ε	ε	PROPN
ejpam-3003	583	4	1−	1−	NUM
ejpam-3003	583	5	b	b	PROPN
ejpam-3003	583	6	2b	2b	NUM
ejpam-3003	583	7	+	+	X
ejpam-3003	583	8	[	[	PUNCT
ejpam-3003	583	9	(	(	PUNCT
ejpam-3003	583	10	2δ	2δ	NUM
ejpam-3003	583	11	+	+	CCONJ
ejpam-3003	583	12	1	1	NUM
ejpam-3003	583	13	2δ	2δ	NUM
ejpam-3003	583	14	)	)	PUNCT
ejpam-3003	583	15	(	(	PUNCT
ejpam-3003	583	16	1−	1−	NUM
ejpam-3003	583	17	b	b	NOUN
ejpam-3003	583	18	)	)	PUNCT
ejpam-3003	583	19	+	+	NUM
ejpam-3003	583	20	bp+1	bp+1	PROPN
ejpam-3003	583	21	p+1(1−	p+1(1−	ADJ
ejpam-3003	583	22	b)p	b)p	NOUN
ejpam-3003	583	23	(	(	PUNCT
ejpam-3003	583	24	p+	p+	NOUN
ejpam-3003	583	25	1)δ	1)δ	NUM
ejpam-3003	583	26	(	(	PUNCT
ejpam-3003	583	27	4(p+	4(p+	NOUN
ejpam-3003	583	28	1)e(0	1)e(0	NOUN
ejpam-3003	583	29	)	)	PUNCT
ejpam-3003	583	30	(	(	PUNCT
ejpam-3003	583	31	p−	p−	NOUN
ejpam-3003	583	32	1)b	1)b	X
ejpam-3003	583	33	)	)	PUNCT
ejpam-3003	583	34	p−1	p−1	PROPN
ejpam-3003	583	35	2	2	NUM
ejpam-3003	583	36	+	+	CCONJ
ejpam-3003	583	37	bq+1	bq+1	PROPN
ejpam-3003	583	38	q+1(1−	q+1(1−	NUM
ejpam-3003	583	39	b)q	b)q	PUNCT
ejpam-3003	583	40	(	(	PUNCT
ejpam-3003	583	41	q	q	X
ejpam-3003	584	1	+	+	NUM
ejpam-3003	584	2	1)δ	1)δ	NUM
ejpam-3003	584	3	(	(	PUNCT
ejpam-3003	584	4	4(p+	4(p+	NOUN
ejpam-3003	584	5	1)e(0	1)e(0	NOUN
ejpam-3003	584	6	)	)	PUNCT
ejpam-3003	584	7	(	(	PUNCT
ejpam-3003	584	8	p−	p−	NOUN
ejpam-3003	584	9	1)b	1)b	X
ejpam-3003	584	10	)	)	PUNCT
ejpam-3003	585	1	q−1	q−1	PROPN
ejpam-3003	585	2	2	2	NUM
ejpam-3003	586	1	+	+	CCONJ
ejpam-3003	586	2	kbρ+1	kbρ+1	X
ejpam-3003	586	3	2	2	NUM
ejpam-3003	586	4	(	(	PUNCT
ejpam-3003	586	5	1−	1−	NUM
ejpam-3003	586	6	b)ρ	b)ρ	NUM
ejpam-3003	586	7	ρ(ρ+	ρ(ρ+	NOUN
ejpam-3003	586	8	1)δ	1)δ	NUM
ejpam-3003	586	9	×	×	NOUN
ejpam-3003	586	10	(	(	PUNCT
ejpam-3003	586	11	4(p+	4(p+	PROPN
ejpam-3003	586	12	1)e(0	1)e(0	NOUN
ejpam-3003	586	13	)	)	PUNCT
ejpam-3003	586	14	(	(	PUNCT
ejpam-3003	586	15	p−	p−	NOUN
ejpam-3003	586	16	1)b	1)b	X
ejpam-3003	586	17	)	)	PUNCT
ejpam-3003	586	18	ρ−1	ρ−1	PROPN
ejpam-3003	586	19	2	2	NUM
ejpam-3003	586	20	]	]	PUNCT
ejpam-3003	586	21	}	}	PUNCT
ejpam-3003	586	22	ξ(t)(g	ξ(t)(g	ADP
ejpam-3003	586	23	◦	◦	PROPN
ejpam-3003	586	24	∇u)(t	∇u)(t	PROPN
ejpam-3003	586	25	)	)	PUNCT
ejpam-3003	586	26	+	+	NUM
ejpam-3003	586	27	εξ(t)‖u‖p+1	εξ(t)‖u‖p+1	ADJ
ejpam-3003	586	28	p+1	p+1	NOUN
ejpam-3003	586	29	−	−	PROPN
ejpam-3003	586	30	{	{	PUNCT
ejpam-3003	586	31	m	m	NOUN
ejpam-3003	586	32	−	−	NOUN
ejpam-3003	586	33	ε	ε	PROPN
ejpam-3003	586	34	1	1	NUM
ejpam-3003	586	35	(	(	PUNCT
ejpam-3003	586	36	q	q	PROPN
ejpam-3003	587	1	+	+	NUM
ejpam-3003	587	2	1)α	1)α	NUM
ejpam-3003	587	3	ξ(0)−	ξ(0)−	NUM
ejpam-3003	588	1	qδ	qδ	PRON
ejpam-3003	588	2	q	q	PROPN
ejpam-3003	589	1	+	+	CCONJ
ejpam-3003	589	2	1	1	NUM
ejpam-3003	589	3	ξ(0	ξ(0	NOUN
ejpam-3003	589	4	)	)	PUNCT
ejpam-3003	589	5	}	}	PUNCT
ejpam-3003	590	1	‖ut‖q+1	‖ut‖q+1	PROPN
ejpam-3003	590	2	γ1,q+1	γ1,q+1	SYM
ejpam-3003	591	1	−	−	PROPN
ejpam-3003	591	2	{	{	PUNCT
ejpam-3003	591	3	g0	g0	PROPN
ejpam-3003	591	4	ρ	ρ	PROPN
ejpam-3003	591	5	−	−	PROPN
ejpam-3003	591	6	ε	ε	PROPN
ejpam-3003	591	7	[	[	PUNCT
ejpam-3003	591	8	1	1	NUM
ejpam-3003	591	9	ρ	ρ	NUM
ejpam-3003	592	1	+	+	X
ejpam-3003	592	2	k	k	X
ejpam-3003	592	3	(	(	PUNCT
ejpam-3003	592	4	ρ+	ρ+	NUM
ejpam-3003	592	5	1)ρα	1)ρα	NOUN
ejpam-3003	592	6	]	]	X
ejpam-3003	592	7	−	−	PROPN
ejpam-3003	593	1	[	[	PUNCT
ejpam-3003	593	2	δ	δ	PROPN
ejpam-3003	593	3	ρ+	ρ+	NOUN
ejpam-3003	593	4	1	1	NUM
ejpam-3003	593	5	+	+	CCONJ
ejpam-3003	593	6	kδ	kδ	PART
ejpam-3003	593	7	ρ+	ρ+	NUM
ejpam-3003	593	8	1	1	NUM
ejpam-3003	593	9	]	]	PUNCT
ejpam-3003	593	10	}	}	PUNCT
ejpam-3003	593	11	ξ(t)‖ut‖ρ+1	ξ(t)‖ut‖ρ+1	PROPN
ejpam-3003	593	12	ρ+1	ρ+1	NOUN
ejpam-3003	593	13	,	,	PUNCT
ejpam-3003	593	14	(	(	PUNCT
ejpam-3003	593	15	4.27	4.27	NUM
ejpam-3003	593	16	)	)	PUNCT
ejpam-3003	593	17	for	for	ADP
ejpam-3003	593	18	all	all	DET
ejpam-3003	593	19	t	t	PROPN
ejpam-3003	593	20	≥	≥	PROPN
ejpam-3003	593	21	t0	t0	PROPN
ejpam-3003	593	22	.	.	PUNCT
ejpam-3003	594	1	at	at	ADP
ejpam-3003	594	2	this	this	DET
ejpam-3003	594	3	point	point	NOUN
ejpam-3003	594	4	,	,	PUNCT
ejpam-3003	594	5	we	we	PRON
ejpam-3003	594	6	choose	choose	VERB
ejpam-3003	594	7	α	α	PRON
ejpam-3003	594	8	>	>	X
ejpam-3003	594	9	0	0	PUNCT
ejpam-3003	595	1	so	so	ADV
ejpam-3003	595	2	small	small	ADJ
ejpam-3003	595	3	that	that	SCONJ
ejpam-3003	595	4	b	b	X
ejpam-3003	595	5	2	2	NUM
ejpam-3003	595	6	−	−	NOUN
ejpam-3003	595	7	αkbρ+1	αkbρ+1	NOUN
ejpam-3003	595	8	ρ+1	ρ+1	NOUN
ejpam-3003	595	9	ρ+	ρ+	NOUN
ejpam-3003	595	10	1	1	NUM
ejpam-3003	595	11	(	(	PUNCT
ejpam-3003	595	12	2(p+	2(p+	NUM
ejpam-3003	595	13	1)e(0	1)e(0	NOUN
ejpam-3003	595	14	)	)	PUNCT
ejpam-3003	595	15	(	(	PUNCT
ejpam-3003	595	16	p−	p−	NOUN
ejpam-3003	595	17	1)b	1)b	X
ejpam-3003	595	18	)	)	PUNCT
ejpam-3003	596	1	ρ−1	ρ−1	PROPN
ejpam-3003	596	2	2	2	NUM
ejpam-3003	597	1	−	−	PROPN
ejpam-3003	597	2	αqbq+1	αqbq+1	NUM
ejpam-3003	597	3	q+1	q+1	NUM
ejpam-3003	597	4	q	q	NOUN
ejpam-3003	598	1	+	+	NUM
ejpam-3003	598	2	1	1	NUM
ejpam-3003	598	3	(	(	PUNCT
ejpam-3003	598	4	2(p+	2(p+	NUM
ejpam-3003	598	5	1)e(0	1)e(0	NOUN
ejpam-3003	598	6	)	)	PUNCT
ejpam-3003	598	7	(	(	PUNCT
ejpam-3003	598	8	p−	p−	NOUN
ejpam-3003	598	9	1)b	1)b	X
ejpam-3003	598	10	)	)	PUNCT
ejpam-3003	599	1	q−1	q−1	PROPN
ejpam-3003	599	2	2	2	NUM
ejpam-3003	599	3	>	>	SYM
ejpam-3003	599	4	0	0	NUM
ejpam-3003	599	5	.	.	PUNCT
ejpam-3003	600	1	(	(	PUNCT
ejpam-3003	600	2	4.28	4.28	NUM
ejpam-3003	600	3	)	)	PUNCT
ejpam-3003	600	4	h.f	h.f	PROPN
ejpam-3003	600	5	.	.	PROPN
ejpam-3003	600	6	di	di	PROPN
ejpam-3003	600	7	,	,	PUNCT
ejpam-3003	600	8	y.d	y.d	PROPN
ejpam-3003	600	9	.	.	PROPN
ejpam-3003	600	10	shang	shang	PROPN
ejpam-3003	600	11	/	/	SYM
ejpam-3003	600	12	eur	eur	PROPN
ejpam-3003	600	13	.	.	PUNCT
ejpam-3003	601	1	j.	j.	PROPN
ejpam-3003	601	2	pure	pure	PROPN
ejpam-3003	601	3	appl	appl	PROPN
ejpam-3003	601	4	.	.	PROPN
ejpam-3003	601	5	math	math	PROPN
ejpam-3003	601	6	,	,	PUNCT
ejpam-3003	601	7	10	10	NUM
ejpam-3003	601	8	(	(	PUNCT
ejpam-3003	601	9	4	4	NUM
ejpam-3003	601	10	)	)	PUNCT
ejpam-3003	601	11	(	(	PUNCT
ejpam-3003	601	12	2017	2017	NUM
ejpam-3003	601	13	)	)	PUNCT
ejpam-3003	601	14	,	,	PUNCT
ejpam-3003	601	15	668	668	NUM
ejpam-3003	601	16	-	-	SYM
ejpam-3003	601	17	701	701	NUM
ejpam-3003	601	18	692	692	NUM
ejpam-3003	601	19	when	when	SCONJ
ejpam-3003	601	20	α	α	PROPN
ejpam-3003	601	21	is	be	AUX
ejpam-3003	601	22	fixed	fix	VERB
ejpam-3003	602	1	,	,	PUNCT
ejpam-3003	602	2	we	we	PRON
ejpam-3003	602	3	choose	choose	VERB
ejpam-3003	602	4	ε	ε	PROPN
ejpam-3003	602	5	>	>	X
ejpam-3003	602	6	0	0	PUNCT
ejpam-3003	602	7	small	small	ADJ
ejpam-3003	602	8	enough	enough	ADV
ejpam-3003	602	9	so	so	SCONJ
ejpam-3003	602	10	that	that	SCONJ
ejpam-3003	602	11	lemma	lemma	PROPN
ejpam-3003	602	12	9	9	NUM
ejpam-3003	602	13	holds	hold	NOUN
ejpam-3003	602	14	and	and	CCONJ
ejpam-3003	602	15	that	that	SCONJ
ejpam-3003	602	16	ε	ε	PROPN
ejpam-3003	602	17	<	<	X
ejpam-3003	602	18	g0(ρ+	g0(ρ+	PROPN
ejpam-3003	602	19	1)α	1)α	NUM
ejpam-3003	602	20	(	(	PUNCT
ejpam-3003	602	21	ρ+	ρ+	NUM
ejpam-3003	602	22	1)α+	1)α+	NUM
ejpam-3003	602	23	k	k	X
ejpam-3003	602	24	.	.	PUNCT
ejpam-3003	603	1	(	(	PUNCT
ejpam-3003	603	2	4.29	4.29	NUM
ejpam-3003	603	3	)	)	PUNCT
ejpam-3003	603	4	once	once	SCONJ
ejpam-3003	603	5	α	α	PRON
ejpam-3003	603	6	and	and	CCONJ
ejpam-3003	603	7	ε	ε	PROPN
ejpam-3003	603	8	are	be	AUX
ejpam-3003	603	9	fixed	fix	VERB
ejpam-3003	603	10	,	,	PUNCT
ejpam-3003	603	11	we	we	PRON
ejpam-3003	603	12	choose	choose	VERB
ejpam-3003	603	13	a	a	DET
ejpam-3003	603	14	positive	positive	ADJ
ejpam-3003	603	15	constant	constant	ADJ
ejpam-3003	603	16	δ	δ	NOUN
ejpam-3003	603	17	small	small	ADJ
ejpam-3003	603	18	enough	enough	ADV
ejpam-3003	603	19	such	such	ADJ
ejpam-3003	603	20	that	that	DET
ejpam-3003	603	21	ε	ε	PROPN
ejpam-3003	603	22	[	[	PUNCT
ejpam-3003	603	23	b	b	PROPN
ejpam-3003	603	24	2	2	NUM
ejpam-3003	603	25	−	−	NOUN
ejpam-3003	603	26	αkbρ+1	αkbρ+1	NOUN
ejpam-3003	603	27	ρ+1	ρ+1	NOUN
ejpam-3003	603	28	ρ+	ρ+	NOUN
ejpam-3003	603	29	1	1	NUM
ejpam-3003	603	30	(	(	PUNCT
ejpam-3003	603	31	2(p+	2(p+	NUM
ejpam-3003	603	32	1)e(0	1)e(0	NOUN
ejpam-3003	603	33	)	)	PUNCT
ejpam-3003	603	34	(	(	PUNCT
ejpam-3003	603	35	p−	p−	NOUN
ejpam-3003	603	36	1)b	1)b	X
ejpam-3003	603	37	)	)	PUNCT
ejpam-3003	603	38	ρ−1	ρ−1	PROPN
ejpam-3003	603	39	2	2	NUM
ejpam-3003	603	40	−	−	PROPN
ejpam-3003	603	41	αqbq+1	αqbq+1	NUM
ejpam-3003	603	42	q+1	q+1	NUM
ejpam-3003	603	43	q	q	NOUN
ejpam-3003	604	1	+	+	NUM
ejpam-3003	604	2	1	1	NUM
ejpam-3003	604	3	(	(	PUNCT
ejpam-3003	604	4	2(p+	2(p+	NUM
ejpam-3003	604	5	1)e(0	1)e(0	NOUN
ejpam-3003	604	6	)	)	PUNCT
ejpam-3003	604	7	(	(	PUNCT
ejpam-3003	604	8	p−	p−	NOUN
ejpam-3003	604	9	1)b	1)b	X
ejpam-3003	604	10	)	)	PUNCT
ejpam-3003	605	1	q−1	q−1	PROPN
ejpam-3003	605	2	2	2	NUM
ejpam-3003	605	3	]	]	PUNCT
ejpam-3003	605	4	−	−	PROPN
ejpam-3003	605	5	δ	δ	PROPN
ejpam-3003	605	6	[	[	PUNCT
ejpam-3003	605	7	1	1	NUM
ejpam-3003	605	8	+	+	CCONJ
ejpam-3003	605	9	2(1−	2(1−	NUM
ejpam-3003	605	10	b)2	b)2	ADJ
ejpam-3003	605	11	+	+	NUM
ejpam-3003	605	12	pbp+1	pbp+1	NOUN
ejpam-3003	605	13	p+1	p+1	PRON
ejpam-3003	605	14	p+	p+	VERB
ejpam-3003	605	15	1	1	NUM
ejpam-3003	605	16	(	(	PUNCT
ejpam-3003	605	17	2(p+	2(p+	NUM
ejpam-3003	605	18	1)e(0	1)e(0	NOUN
ejpam-3003	605	19	)	)	PUNCT
ejpam-3003	605	20	(	(	PUNCT
ejpam-3003	605	21	p−	p−	NOUN
ejpam-3003	605	22	1)b	1)b	X
ejpam-3003	605	23	)	)	PUNCT
ejpam-3003	605	24	p−1	p−1	PROPN
ejpam-3003	605	25	2	2	NUM
ejpam-3003	605	26	]	]	PUNCT
ejpam-3003	605	27	>	>	X
ejpam-3003	605	28	0	0	NUM
ejpam-3003	605	29	,	,	PUNCT
ejpam-3003	605	30	(	(	PUNCT
ejpam-3003	605	31	4.30	4.30	NUM
ejpam-3003	605	32	)	)	PUNCT
ejpam-3003	605	33	and	and	CCONJ
ejpam-3003	605	34	g0	g0	ADJ
ejpam-3003	605	35	ρ	ρ	PROPN
ejpam-3003	605	36	−	−	PROPN
ejpam-3003	605	37	ε	ε	PROPN
ejpam-3003	605	38	[	[	PUNCT
ejpam-3003	605	39	1	1	NUM
ejpam-3003	605	40	ρ	ρ	NUM
ejpam-3003	605	41	+	+	X
ejpam-3003	605	42	k	k	X
ejpam-3003	605	43	(	(	PUNCT
ejpam-3003	605	44	ρ+	ρ+	NUM
ejpam-3003	605	45	1)ρα	1)ρα	NOUN
ejpam-3003	605	46	]	]	X
ejpam-3003	605	47	−	−	PROPN
ejpam-3003	606	1	[	[	PUNCT
ejpam-3003	606	2	δ	δ	PROPN
ejpam-3003	606	3	ρ+	ρ+	NOUN
ejpam-3003	606	4	1	1	NUM
ejpam-3003	606	5	+	+	CCONJ
ejpam-3003	606	6	kδ	kδ	PART
ejpam-3003	606	7	ρ+	ρ+	NUM
ejpam-3003	606	8	1	1	X
ejpam-3003	606	9	]	]	PUNCT
ejpam-3003	606	10	>	>	X
ejpam-3003	606	11	0	0	X
ejpam-3003	606	12	.	.	PUNCT
ejpam-3003	607	1	(	(	PUNCT
ejpam-3003	607	2	4.31	4.31	NUM
ejpam-3003	607	3	)	)	PUNCT
ejpam-3003	607	4	then	then	ADV
ejpam-3003	607	5	,	,	PUNCT
ejpam-3003	607	6	we	we	PRON
ejpam-3003	607	7	pick	pick	VERB
ejpam-3003	607	8	m	m	PRON
ejpam-3003	607	9	sufficiently	sufficiently	ADV
ejpam-3003	607	10	large	large	ADJ
ejpam-3003	607	11	such	such	ADJ
ejpam-3003	607	12	that	that	SCONJ
ejpam-3003	607	13	lemma	lemma	PROPN
ejpam-3003	607	14	9	9	NUM
ejpam-3003	607	15	holds	hold	NOUN
ejpam-3003	607	16	and	and	CCONJ
ejpam-3003	607	17	that	that	SCONJ
ejpam-3003	607	18	{	{	PUNCT
ejpam-3003	607	19	m	m	VERB
ejpam-3003	607	20	2	2	NUM
ejpam-3003	607	21	−	−	NOUN
ejpam-3003	607	22	g(0)ρbρ+1	g(0)ρbρ+1	NOUN
ejpam-3003	607	23	ρ+1	ρ+1	NOUN
ejpam-3003	607	24	ρ(ρ+	ρ(ρ+	NOUN
ejpam-3003	607	25	1)δ	1)δ	NUM
ejpam-3003	607	26	(	(	PUNCT
ejpam-3003	607	27	4(p+	4(p+	NOUN
ejpam-3003	607	28	1)e(0	1)e(0	NOUN
ejpam-3003	607	29	)	)	PUNCT
ejpam-3003	607	30	(	(	PUNCT
ejpam-3003	607	31	p−	p−	NOUN
ejpam-3003	607	32	1)b	1)b	X
ejpam-3003	607	33	)	)	PUNCT
ejpam-3003	608	1	ρ−1	ρ−1	PROPN
ejpam-3003	608	2	2	2	NUM
ejpam-3003	608	3	ξ(0	ξ(0	NOUN
ejpam-3003	608	4	)	)	PUNCT
ejpam-3003	608	5	}	}	PUNCT
ejpam-3003	608	6	−	−	PROPN
ejpam-3003	608	7	{	{	PUNCT
ejpam-3003	608	8	ε	ε	PROPN
ejpam-3003	608	9	1−	1−	NUM
ejpam-3003	608	10	b	b	PROPN
ejpam-3003	608	11	2b	2b	NUM
ejpam-3003	608	12	+	+	X
ejpam-3003	608	13	[	[	PUNCT
ejpam-3003	608	14	(	(	PUNCT
ejpam-3003	608	15	2δ	2δ	NUM
ejpam-3003	608	16	+	+	CCONJ
ejpam-3003	608	17	1	1	NUM
ejpam-3003	608	18	2δ	2δ	NUM
ejpam-3003	608	19	)	)	PUNCT
ejpam-3003	608	20	(	(	PUNCT
ejpam-3003	608	21	1−	1−	NUM
ejpam-3003	608	22	b	b	NOUN
ejpam-3003	608	23	)	)	PUNCT
ejpam-3003	608	24	+	+	NUM
ejpam-3003	608	25	bp+1	bp+1	PROPN
ejpam-3003	608	26	p+1(1−	p+1(1−	ADJ
ejpam-3003	608	27	b)p	b)p	NOUN
ejpam-3003	608	28	(	(	PUNCT
ejpam-3003	608	29	p+	p+	NOUN
ejpam-3003	608	30	1)δ	1)δ	NUM
ejpam-3003	608	31	(	(	PUNCT
ejpam-3003	608	32	4(p+	4(p+	NOUN
ejpam-3003	608	33	1)e(0	1)e(0	NOUN
ejpam-3003	608	34	)	)	PUNCT
ejpam-3003	608	35	(	(	PUNCT
ejpam-3003	608	36	p−	p−	NOUN
ejpam-3003	608	37	1)b	1)b	X
ejpam-3003	608	38	)	)	PUNCT
ejpam-3003	609	1	p−1	p−1	PROPN
ejpam-3003	609	2	2	2	NUM
ejpam-3003	609	3	+	+	CCONJ
ejpam-3003	609	4	bq+1	bq+1	PROPN
ejpam-3003	609	5	q+1(1−	q+1(1−	NUM
ejpam-3003	609	6	b)q	b)q	PUNCT
ejpam-3003	609	7	(	(	PUNCT
ejpam-3003	609	8	q	q	X
ejpam-3003	610	1	+	+	NUM
ejpam-3003	610	2	1)δ	1)δ	NUM
ejpam-3003	610	3	(	(	PUNCT
ejpam-3003	610	4	4(p+	4(p+	NOUN
ejpam-3003	610	5	1)e(0	1)e(0	NOUN
ejpam-3003	610	6	)	)	PUNCT
ejpam-3003	610	7	(	(	PUNCT
ejpam-3003	610	8	p−	p−	NOUN
ejpam-3003	610	9	1)b	1)b	X
ejpam-3003	610	10	)	)	PUNCT
ejpam-3003	611	1	q−1	q−1	PROPN
ejpam-3003	611	2	2	2	NUM
ejpam-3003	612	1	+	+	CCONJ
ejpam-3003	612	2	kbρ+1	kbρ+1	X
ejpam-3003	612	3	ρ+1(1−	ρ+1(1−	PRON
ejpam-3003	612	4	b)ρ	b)ρ	NUM
ejpam-3003	612	5	ρ(ρ+	ρ(ρ+	NOUN
ejpam-3003	612	6	1)δ	1)δ	NUM
ejpam-3003	612	7	(	(	PUNCT
ejpam-3003	612	8	4(p+	4(p+	NOUN
ejpam-3003	612	9	1)e(0	1)e(0	NOUN
ejpam-3003	612	10	)	)	PUNCT
ejpam-3003	612	11	(	(	PUNCT
ejpam-3003	612	12	p−	p−	NOUN
ejpam-3003	612	13	1)b	1)b	X
ejpam-3003	612	14	)	)	PUNCT
ejpam-3003	612	15	ρ−1	ρ−1	PROPN
ejpam-3003	612	16	2	2	NUM
ejpam-3003	612	17	]	]	PUNCT
ejpam-3003	612	18	}	}	PUNCT
ejpam-3003	612	19	>	>	X
ejpam-3003	612	20	0	0	NUM
ejpam-3003	612	21	,	,	PUNCT
ejpam-3003	612	22	(	(	PUNCT
ejpam-3003	612	23	4.32	4.32	NUM
ejpam-3003	612	24	)	)	PUNCT
ejpam-3003	612	25	and	and	CCONJ
ejpam-3003	612	26	m	m	PRON
ejpam-3003	612	27	−	−	PROPN
ejpam-3003	612	28	ε	ε	PROPN
ejpam-3003	612	29	(	(	PUNCT
ejpam-3003	612	30	q	q	PROPN
ejpam-3003	613	1	+	+	NUM
ejpam-3003	613	2	1)α	1)α	NUM
ejpam-3003	613	3	ξ(0)−	ξ(0)−	NUM
ejpam-3003	614	1	qδ	qδ	PRON
ejpam-3003	614	2	q	q	PROPN
ejpam-3003	615	1	+	+	CCONJ
ejpam-3003	615	2	1	1	NUM
ejpam-3003	615	3	ξ(0	ξ(0	NOUN
ejpam-3003	615	4	)	)	PUNCT
ejpam-3003	615	5	>	>	X
ejpam-3003	615	6	0	0	X
ejpam-3003	615	7	.	.	PUNCT
ejpam-3003	616	1	(	(	PUNCT
ejpam-3003	616	2	4.33	4.33	NUM
ejpam-3003	616	3	)	)	PUNCT
ejpam-3003	616	4	therefore	therefore	ADV
ejpam-3003	616	5	,	,	PUNCT
ejpam-3003	616	6	from	from	ADP
ejpam-3003	616	7	the	the	DET
ejpam-3003	616	8	conditions	condition	NOUN
ejpam-3003	616	9	(	(	PUNCT
ejpam-3003	616	10	a2	a2	PROPN
ejpam-3003	616	11	)	)	PUNCT
ejpam-3003	616	12	,	,	PUNCT
ejpam-3003	616	13	we	we	PRON
ejpam-3003	616	14	obtain	obtain	VERB
ejpam-3003	616	15	that	that	SCONJ
ejpam-3003	616	16	there	there	PRON
ejpam-3003	616	17	exists	exist	VERB
ejpam-3003	616	18	a	a	DET
ejpam-3003	616	19	positive	positive	ADJ
ejpam-3003	616	20	constant	constant	ADJ
ejpam-3003	616	21	β1	β1	NOUN
ejpam-3003	616	22	>	>	X
ejpam-3003	616	23	0	0	NUM
ejpam-3003	617	1	such	such	ADJ
ejpam-3003	617	2	that	that	SCONJ
ejpam-3003	617	3	{	{	PUNCT
ejpam-3003	617	4	m	m	PROPN
ejpam-3003	617	5	2	2	NUM
ejpam-3003	617	6	−	−	NOUN
ejpam-3003	617	7	g(0)ρbρ+1	g(0)ρbρ+1	NOUN
ejpam-3003	617	8	ρ+1	ρ+1	NOUN
ejpam-3003	617	9	ρ(ρ+	ρ(ρ+	NOUN
ejpam-3003	617	10	1)δ	1)δ	NUM
ejpam-3003	617	11	(	(	PUNCT
ejpam-3003	617	12	4(p+	4(p+	NOUN
ejpam-3003	617	13	1)e(0	1)e(0	NOUN
ejpam-3003	617	14	)	)	PUNCT
ejpam-3003	617	15	(	(	PUNCT
ejpam-3003	617	16	p−	p−	NOUN
ejpam-3003	617	17	1)b	1)b	X
ejpam-3003	617	18	)	)	PUNCT
ejpam-3003	617	19	ρ−1	ρ−1	PROPN
ejpam-3003	617	20	2	2	NUM
ejpam-3003	617	21	ξ(0	ξ(0	NOUN
ejpam-3003	617	22	)	)	PUNCT
ejpam-3003	617	23	}	}	PUNCT
ejpam-3003	617	24	(	(	PUNCT
ejpam-3003	617	25	−g′	−g′	PROPN
ejpam-3003	617	26	◦	◦	NOUN
ejpam-3003	617	27	∇u)(t)−	∇u)(t)−	PROPN
ejpam-3003	617	28	{	{	PUNCT
ejpam-3003	617	29	ε	ε	PROPN
ejpam-3003	617	30	1−	1−	NUM
ejpam-3003	617	31	b	b	PROPN
ejpam-3003	617	32	2b	2b	NUM
ejpam-3003	617	33	+	+	X
ejpam-3003	617	34	[	[	PUNCT
ejpam-3003	617	35	(	(	PUNCT
ejpam-3003	617	36	2δ	2δ	NUM
ejpam-3003	617	37	+	+	CCONJ
ejpam-3003	617	38	1	1	NUM
ejpam-3003	617	39	2δ	2δ	NUM
ejpam-3003	617	40	)	)	PUNCT
ejpam-3003	617	41	(	(	PUNCT
ejpam-3003	617	42	1−	1−	NUM
ejpam-3003	617	43	b	b	NOUN
ejpam-3003	617	44	)	)	PUNCT
ejpam-3003	617	45	+	+	NUM
ejpam-3003	617	46	bp+1	bp+1	PROPN
ejpam-3003	617	47	p+1(1−	p+1(1−	ADJ
ejpam-3003	617	48	b)p	b)p	NOUN
ejpam-3003	617	49	(	(	PUNCT
ejpam-3003	617	50	p+	p+	NOUN
ejpam-3003	617	51	1)δ	1)δ	NUM
ejpam-3003	617	52	(	(	PUNCT
ejpam-3003	617	53	4(p+	4(p+	NOUN
ejpam-3003	617	54	1)e(0	1)e(0	NOUN
ejpam-3003	617	55	)	)	PUNCT
ejpam-3003	617	56	(	(	PUNCT
ejpam-3003	617	57	p−	p−	NOUN
ejpam-3003	617	58	1)b	1)b	X
ejpam-3003	617	59	)	)	PUNCT
ejpam-3003	617	60	p−1	p−1	PROPN
ejpam-3003	617	61	2	2	NUM
ejpam-3003	617	62	+	+	CCONJ
ejpam-3003	617	63	bq+1	bq+1	PROPN
ejpam-3003	617	64	q+1(1−	q+1(1−	NUM
ejpam-3003	617	65	b)q	b)q	PUNCT
ejpam-3003	617	66	(	(	PUNCT
ejpam-3003	617	67	q	q	X
ejpam-3003	617	68	+	+	NUM
ejpam-3003	617	69	1)δ	1)δ	NUM
ejpam-3003	617	70	(	(	PUNCT
ejpam-3003	617	71	4(p+	4(p+	NOUN
ejpam-3003	617	72	1)e(0	1)e(0	NOUN
ejpam-3003	617	73	)	)	PUNCT
ejpam-3003	617	74	(	(	PUNCT
ejpam-3003	617	75	p−	p−	NOUN
ejpam-3003	617	76	1)b	1)b	X
ejpam-3003	617	77	)	)	PUNCT
ejpam-3003	617	78	q−1	q−1	PROPN
ejpam-3003	617	79	2	2	NUM
ejpam-3003	617	80	+	+	CCONJ
ejpam-3003	617	81	kbρ+1	kbρ+1	X
ejpam-3003	617	82	ρ+1(1−	ρ+1(1−	PRON
ejpam-3003	617	83	b)ρ	b)ρ	NUM
ejpam-3003	617	84	ρ(ρ+	ρ(ρ+	NOUN
ejpam-3003	617	85	1)δ	1)δ	NUM
ejpam-3003	617	86	(	(	PUNCT
ejpam-3003	617	87	4(p+	4(p+	NOUN
ejpam-3003	617	88	1)e(0	1)e(0	NOUN
ejpam-3003	617	89	)	)	PUNCT
ejpam-3003	617	90	(	(	PUNCT
ejpam-3003	617	91	p−	p−	NOUN
ejpam-3003	617	92	1)b	1)b	X
ejpam-3003	617	93	)	)	PUNCT
ejpam-3003	617	94	ρ−1	ρ−1	PROPN
ejpam-3003	617	95	2	2	NUM
ejpam-3003	617	96	]	]	PUNCT
ejpam-3003	617	97	}	}	PUNCT
ejpam-3003	617	98	ξ(t)(g	ξ(t)(g	ADP
ejpam-3003	617	99	◦	◦	PROPN
ejpam-3003	617	100	∇u)(t	∇u)(t	PROPN
ejpam-3003	617	101	)	)	PUNCT
ejpam-3003	617	102	>	>	PUNCT
ejpam-3003	617	103	β1ξ(t)(g	β1ξ(t)(g	PROPN
ejpam-3003	617	104	◦	◦	PROPN
ejpam-3003	617	105	∇u)(t	∇u)(t	PROPN
ejpam-3003	617	106	)	)	PUNCT
ejpam-3003	617	107	.	.	PUNCT
ejpam-3003	618	1	(	(	PUNCT
ejpam-3003	618	2	4.34	4.34	X
ejpam-3003	618	3	)	)	PUNCT
ejpam-3003	618	4	combining	combine	VERB
ejpam-3003	618	5	(	(	PUNCT
ejpam-3003	618	6	4.27)-(4.34	4.27)-(4.34	NUM
ejpam-3003	618	7	)	)	PUNCT
ejpam-3003	618	8	,	,	PUNCT
ejpam-3003	618	9	the	the	DET
ejpam-3003	618	10	definition	definition	NOUN
ejpam-3003	618	11	of	of	ADP
ejpam-3003	618	12	e(t	e(t	PROPN
ejpam-3003	618	13	)	)	PUNCT
ejpam-3003	618	14	and	and	CCONJ
ejpam-3003	618	15	lemma	lemma	PROPN
ejpam-3003	618	16	8	8	NUM
ejpam-3003	618	17	,	,	PUNCT
ejpam-3003	618	18	we	we	PRON
ejpam-3003	618	19	deduce	deduce	VERB
ejpam-3003	618	20	that	that	SCONJ
ejpam-3003	618	21	there	there	PRON
ejpam-3003	618	22	exists	exist	VERB
ejpam-3003	618	23	a	a	DET
ejpam-3003	618	24	positive	positive	ADJ
ejpam-3003	618	25	constant	constant	ADJ
ejpam-3003	618	26	β2	β2	NOUN
ejpam-3003	618	27	>	>	X
ejpam-3003	618	28	0	0	NUM
ejpam-3003	619	1	such	such	ADJ
ejpam-3003	619	2	that	that	SCONJ
ejpam-3003	619	3	f	f	PROPN
ejpam-3003	619	4	′(t	′(t	PROPN
ejpam-3003	619	5	)	)	PUNCT
ejpam-3003	619	6	≤	≤	NUM
ejpam-3003	619	7	−β2ξ(t)e(t	−β2ξ(t)e(t	PROPN
ejpam-3003	619	8	)	)	PUNCT
ejpam-3003	619	9	≤	≤	NUM
ejpam-3003	619	10	−c1β2ξ(t)f	−c1β2ξ(t)f	SYM
ejpam-3003	619	11	(	(	PUNCT
ejpam-3003	619	12	t	t	PROPN
ejpam-3003	619	13	)	)	PUNCT
ejpam-3003	619	14	,	,	PUNCT
ejpam-3003	619	15	∀	∀	X
ejpam-3003	619	16	t	t	PROPN
ejpam-3003	619	17	≥	≥	PROPN
ejpam-3003	619	18	t0	t0	PROPN
ejpam-3003	619	19	.	.	PUNCT
ejpam-3003	620	1	(	(	PUNCT
ejpam-3003	620	2	4.35	4.35	NUM
ejpam-3003	620	3	)	)	PUNCT
ejpam-3003	620	4	h.f	h.f	PROPN
ejpam-3003	620	5	.	.	PROPN
ejpam-3003	620	6	di	di	PROPN
ejpam-3003	620	7	,	,	PUNCT
ejpam-3003	620	8	y.d	y.d	PROPN
ejpam-3003	620	9	.	.	PROPN
ejpam-3003	620	10	shang	shang	PROPN
ejpam-3003	620	11	/	/	SYM
ejpam-3003	620	12	eur	eur	PROPN
ejpam-3003	620	13	.	.	PUNCT
ejpam-3003	621	1	j.	j.	PROPN
ejpam-3003	621	2	pure	pure	PROPN
ejpam-3003	621	3	appl	appl	PROPN
ejpam-3003	621	4	.	.	PROPN
ejpam-3003	621	5	math	math	PROPN
ejpam-3003	621	6	,	,	PUNCT
ejpam-3003	621	7	10	10	NUM
ejpam-3003	621	8	(	(	PUNCT
ejpam-3003	621	9	4	4	NUM
ejpam-3003	621	10	)	)	PUNCT
ejpam-3003	621	11	(	(	PUNCT
ejpam-3003	621	12	2017	2017	NUM
ejpam-3003	621	13	)	)	PUNCT
ejpam-3003	621	14	,	,	PUNCT
ejpam-3003	621	15	668	668	NUM
ejpam-3003	621	16	-	-	SYM
ejpam-3003	621	17	701	701	NUM
ejpam-3003	621	18	693	693	NUM
ejpam-3003	621	19	a	a	DET
ejpam-3003	621	20	simple	simple	ADJ
ejpam-3003	621	21	integration	integration	NOUN
ejpam-3003	621	22	of	of	ADP
ejpam-3003	621	23	(	(	PUNCT
ejpam-3003	621	24	4.35	4.35	NUM
ejpam-3003	621	25	)	)	PUNCT
ejpam-3003	621	26	over	over	ADP
ejpam-3003	621	27	(	(	PUNCT
ejpam-3003	621	28	t0	t0	PROPN
ejpam-3003	621	29	,	,	PUNCT
ejpam-3003	621	30	t	t	PROPN
ejpam-3003	621	31	)	)	PUNCT
ejpam-3003	622	1	,	,	PUNCT
ejpam-3003	622	2	it	it	PRON
ejpam-3003	622	3	follows	follow	VERB
ejpam-3003	622	4	that	that	SCONJ
ejpam-3003	622	5	f	f	PROPN
ejpam-3003	622	6	(	(	PUNCT
ejpam-3003	622	7	t	t	PROPN
ejpam-3003	622	8	)	)	PUNCT
ejpam-3003	622	9	≤	≤	NUM
ejpam-3003	622	10	f	f	X
ejpam-3003	622	11	(	(	PUNCT
ejpam-3003	622	12	t0)e	t0)e	NOUN
ejpam-3003	622	13	−c1β2	−c1β2	NOUN
ejpam-3003	622	14	∫	∫	PROPN
ejpam-3003	622	15	t	t	PROPN
ejpam-3003	622	16	t0	t0	PROPN
ejpam-3003	622	17	ξ(s)ds	ξ(s)ds	PROPN
ejpam-3003	622	18	,	,	PUNCT
ejpam-3003	622	19	∀	∀	X
ejpam-3003	622	20	t	t	PROPN
ejpam-3003	622	21	≥	≥	PROPN
ejpam-3003	622	22	t0	t0	PROPN
ejpam-3003	622	23	.	.	PUNCT
ejpam-3003	623	1	(	(	PUNCT
ejpam-3003	623	2	4.36	4.36	NUM
ejpam-3003	623	3	)	)	PUNCT
ejpam-3003	623	4	furthermore	furthermore	ADV
ejpam-3003	623	5	,	,	PUNCT
ejpam-3003	623	6	by	by	ADP
ejpam-3003	623	7	lemma	lemma	PROPN
ejpam-3003	623	8	6	6	NUM
ejpam-3003	623	9	and	and	CCONJ
ejpam-3003	623	10	(	(	PUNCT
ejpam-3003	623	11	4.36	4.36	NUM
ejpam-3003	623	12	)	)	PUNCT
ejpam-3003	623	13	,	,	PUNCT
ejpam-3003	623	14	we	we	PRON
ejpam-3003	623	15	obtain	obtain	VERB
ejpam-3003	623	16	e(t	e(t	NOUN
ejpam-3003	623	17	)	)	PUNCT
ejpam-3003	623	18	≤	≤	NOUN
ejpam-3003	623	19	c2f	c2f	NOUN
ejpam-3003	623	20	(	(	PUNCT
ejpam-3003	623	21	t0)e	t0)e	NOUN
ejpam-3003	623	22	−c1β2	−c1β2	NOUN
ejpam-3003	623	23	∫	∫	PROPN
ejpam-3003	623	24	t	t	PROPN
ejpam-3003	623	25	t0	t0	PROPN
ejpam-3003	623	26	ξ(s)ds	ξ(s)ds	PROPN
ejpam-3003	623	27	=	=	SYM
ejpam-3003	623	28	le	le	X
ejpam-3003	623	29	−η	−η	PROPN
ejpam-3003	623	30	∫	∫	PROPN
ejpam-3003	623	31	t	t	PROPN
ejpam-3003	623	32	t0	t0	PROPN
ejpam-3003	623	33	ξ(s)ds	ξ(s)ds	PROPN
ejpam-3003	623	34	,	,	PUNCT
ejpam-3003	623	35	∀	∀	X
ejpam-3003	623	36	t	t	PROPN
ejpam-3003	623	37	≥	≥	PROPN
ejpam-3003	623	38	t0	t0	PROPN
ejpam-3003	623	39	.	.	PUNCT
ejpam-3003	624	1	(	(	PUNCT
ejpam-3003	624	2	4.37	4.37	NUM
ejpam-3003	624	3	)	)	PUNCT
ejpam-3003	624	4	where	where	SCONJ
ejpam-3003	624	5	l	l	NOUN
ejpam-3003	624	6	=	=	X
ejpam-3003	624	7	c2f	c2f	NOUN
ejpam-3003	624	8	(	(	PUNCT
ejpam-3003	624	9	t0	t0	NOUN
ejpam-3003	624	10	)	)	PUNCT
ejpam-3003	624	11	and	and	CCONJ
ejpam-3003	624	12	η	η	PROPN
ejpam-3003	624	13	=	=	SYM
ejpam-3003	624	14	c1β2	c1β2	PROPN
ejpam-3003	624	15	.	.	PUNCT
ejpam-3003	625	1	this	this	PRON
ejpam-3003	625	2	completes	complete	VERB
ejpam-3003	625	3	the	the	DET
ejpam-3003	625	4	proof	proof	NOUN
ejpam-3003	625	5	.	.	PUNCT
ejpam-3003	626	1	5	5	X
ejpam-3003	626	2	.	.	X
ejpam-3003	626	3	finite	finite	PROPN
ejpam-3003	626	4	time	time	NOUN
ejpam-3003	626	5	blow	blow	VERB
ejpam-3003	626	6	up	up	ADP
ejpam-3003	626	7	of	of	ADP
ejpam-3003	626	8	the	the	DET
ejpam-3003	626	9	solutions	solution	NOUN
ejpam-3003	626	10	to	to	PART
ejpam-3003	626	11	prove	prove	VERB
ejpam-3003	626	12	the	the	DET
ejpam-3003	626	13	blow	blow	NOUN
ejpam-3003	626	14	up	up	ADP
ejpam-3003	626	15	result	result	NOUN
ejpam-3003	626	16	for	for	ADP
ejpam-3003	626	17	certain	certain	ADJ
ejpam-3003	626	18	solutions	solution	NOUN
ejpam-3003	626	19	with	with	ADP
ejpam-3003	626	20	nonpositive	nonpositive	ADJ
ejpam-3003	626	21	initial	initial	ADJ
ejpam-3003	626	22	energy	energy	NOUN
ejpam-3003	626	23	as	as	ADV
ejpam-3003	626	24	well	well	ADV
ejpam-3003	626	25	as	as	ADP
ejpam-3003	626	26	positive	positive	ADJ
ejpam-3003	626	27	initial	initial	ADJ
ejpam-3003	626	28	energy	energy	NOUN
ejpam-3003	626	29	,	,	PUNCT
ejpam-3003	626	30	we	we	PRON
ejpam-3003	626	31	modified	modify	VERB
ejpam-3003	626	32	and	and	CCONJ
ejpam-3003	626	33	improved	improve	VERB
ejpam-3003	626	34	the	the	DET
ejpam-3003	626	35	methods	method	NOUN
ejpam-3003	626	36	of	of	ADP
ejpam-3003	626	37	[	[	X
ejpam-3003	626	38	9,21	9,21	NUM
ejpam-3003	626	39	]	]	PUNCT
ejpam-3003	626	40	.	.	PUNCT
ejpam-3003	627	1	theorem	theorem	NOUN
ejpam-3003	627	2	11	11	NUM
ejpam-3003	627	3	.	.	PUNCT
ejpam-3003	628	1	let	let	VERB
ejpam-3003	628	2	the	the	DET
ejpam-3003	628	3	assumptions	assumption	NOUN
ejpam-3003	628	4	(	(	PUNCT
ejpam-3003	628	5	a1	a1	NOUN
ejpam-3003	628	6	)	)	PUNCT
ejpam-3003	628	7	,	,	PUNCT
ejpam-3003	628	8	(	(	PUNCT
ejpam-3003	628	9	a3	a3	NOUN
ejpam-3003	628	10	)	)	PUNCT
ejpam-3003	628	11	hold	hold	VERB
ejpam-3003	628	12	.	.	PUNCT
ejpam-3003	629	1	for	for	ADP
ejpam-3003	629	2	any	any	DET
ejpam-3003	629	3	fixed	fix	VERB
ejpam-3003	629	4	positive	positive	ADJ
ejpam-3003	629	5	number	number	NOUN
ejpam-3003	629	6	β	β	X
ejpam-3003	629	7	<	<	X
ejpam-3003	629	8	1	1	NUM
ejpam-3003	629	9	,	,	PUNCT
ejpam-3003	629	10	assume	assume	VERB
ejpam-3003	629	11	that	that	SCONJ
ejpam-3003	629	12	u0(x	u0(x	NOUN
ejpam-3003	629	13	)	)	PUNCT
ejpam-3003	629	14	∈	∈	PROPN
ejpam-3003	629	15	h1	h1	PROPN
ejpam-3003	629	16	γ0	γ0	PROPN
ejpam-3003	629	17	(	(	PUNCT
ejpam-3003	629	18	ω	ω	NOUN
ejpam-3003	629	19	)	)	PUNCT
ejpam-3003	629	20	,	,	PUNCT
ejpam-3003	629	21	u1(x	u1(x	NOUN
ejpam-3003	629	22	)	)	PUNCT
ejpam-3003	629	23	∈	∈	PROPN
ejpam-3003	629	24	lρ+1(ω	lρ+1(ω	X
ejpam-3003	629	25	)	)	PUNCT
ejpam-3003	629	26	∩	∩	NOUN
ejpam-3003	629	27	lq+1(γ1	lq+1(γ1	NOUN
ejpam-3003	629	28	)	)	PUNCT
ejpam-3003	629	29	,	,	PUNCT
ejpam-3003	629	30	and	and	CCONJ
ejpam-3003	629	31	satisfy	satisfy	VERB
ejpam-3003	629	32	i(u0	i(u0	PROPN
ejpam-3003	629	33	)	)	PUNCT
ejpam-3003	629	34	<	<	X
ejpam-3003	629	35	0	0	NUM
ejpam-3003	629	36	,	,	PUNCT
ejpam-3003	629	37	e(0	e(0	NOUN
ejpam-3003	629	38	)	)	PUNCT
ejpam-3003	629	39	<	<	X
ejpam-3003	629	40	βd̃.	βd̃.	X
ejpam-3003	629	41	(	(	PUNCT
ejpam-3003	629	42	5.1	5.1	NUM
ejpam-3003	629	43	)	)	PUNCT
ejpam-3003	629	44	further	far	ADV
ejpam-3003	629	45	assume	assume	VERB
ejpam-3003	629	46	that	that	SCONJ
ejpam-3003	629	47	ρ	ρ	PROPN
ejpam-3003	629	48	<	<	X
ejpam-3003	629	49	p	p	NOUN
ejpam-3003	629	50	and	and	CCONJ
ejpam-3003	629	51	the	the	DET
ejpam-3003	629	52	relaxation	relaxation	NOUN
ejpam-3003	629	53	function	function	NOUN
ejpam-3003	629	54	g	g	PROPN
ejpam-3003	629	55	satisfies∫	satisfies∫	NOUN
ejpam-3003	629	56	∞	∞	PROPN
ejpam-3003	629	57	0	0	NUM
ejpam-3003	630	1	g(s)ds	g(s)ds	X
ejpam-3003	630	2	<	<	X
ejpam-3003	630	3	[	[	X
ejpam-3003	630	4	(	(	PUNCT
ejpam-3003	630	5	p−	p−	NOUN
ejpam-3003	630	6	1)(1−	1)(1−	NUM
ejpam-3003	630	7	β)−	β)−	PUNCT
ejpam-3003	630	8	γ]2	γ]2	PROPN
ejpam-3003	630	9	+	+	CCONJ
ejpam-3003	630	10	2[(p−	2[(p−	NUM
ejpam-3003	630	11	1)(1−	1)(1−	NUM
ejpam-3003	630	12	β)−	β)−	SCONJ
ejpam-3003	630	13	γ	γ	X
ejpam-3003	630	14	]	]	X
ejpam-3003	630	15	[	[	X
ejpam-3003	630	16	(	(	PUNCT
ejpam-3003	630	17	p−	p−	NOUN
ejpam-3003	630	18	1)(1−	1)(1−	NUM
ejpam-3003	630	19	β)−	β)−	SCONJ
ejpam-3003	630	20	γ	γ	X
ejpam-3003	630	21	+	+	CCONJ
ejpam-3003	630	22	2]2	2]2	NUM
ejpam-3003	630	23	+	+	CCONJ
ejpam-3003	630	24	1	1	NUM
ejpam-3003	630	25	,	,	PUNCT
ejpam-3003	630	26	(	(	PUNCT
ejpam-3003	630	27	5.2	5.2	NUM
ejpam-3003	630	28	)	)	PUNCT
ejpam-3003	630	29	where	where	SCONJ
ejpam-3003	630	30	0	0	PUNCT
ejpam-3003	630	31	<	<	X
ejpam-3003	630	32	γ	γ	X
ejpam-3003	630	33	<	<	X
ejpam-3003	630	34	(	(	PUNCT
ejpam-3003	630	35	p−1)(1−β	p−1)(1−β	NOUN
ejpam-3003	630	36	)	)	PUNCT
ejpam-3003	630	37	.	.	PUNCT
ejpam-3003	631	1	then	then	ADV
ejpam-3003	631	2	,	,	PUNCT
ejpam-3003	631	3	the	the	DET
ejpam-3003	631	4	solutions	solution	NOUN
ejpam-3003	631	5	of	of	ADP
ejpam-3003	631	6	problem	problem	NOUN
ejpam-3003	631	7	(	(	PUNCT
ejpam-3003	631	8	1.1	1.1	NUM
ejpam-3003	631	9	)	)	PUNCT
ejpam-3003	631	10	blows	blow	VERB
ejpam-3003	631	11	up	up	ADP
ejpam-3003	631	12	in	in	ADP
ejpam-3003	631	13	finite	finite	ADJ
ejpam-3003	631	14	time	time	NOUN
ejpam-3003	631	15	,	,	PUNCT
ejpam-3003	631	16	that	that	ADV
ejpam-3003	631	17	is	is	ADV
ejpam-3003	631	18	,	,	PUNCT
ejpam-3003	631	19	the	the	DET
ejpam-3003	631	20	maximum	maximum	ADJ
ejpam-3003	631	21	existence	existence	NOUN
ejpam-3003	631	22	time	time	NOUN
ejpam-3003	631	23	tmax	tmax	ADP
ejpam-3003	631	24	of	of	ADP
ejpam-3003	631	25	u(t	u(t	NOUN
ejpam-3003	631	26	)	)	PUNCT
ejpam-3003	631	27	is	be	AUX
ejpam-3003	631	28	finite	finite	ADJ
ejpam-3003	631	29	and	and	CCONJ
ejpam-3003	632	1	lim	lim	PROPN
ejpam-3003	632	2	t→tmax	t→tmax	ADV
ejpam-3003	632	3	(	(	PUNCT
ejpam-3003	632	4	‖ut‖ρ+1	‖ut‖ρ+1	PROPN
ejpam-3003	632	5	ρ+1	ρ+1	NOUN
ejpam-3003	632	6	+	+	CCONJ
ejpam-3003	632	7	‖∇u‖22	‖∇u‖22	NOUN
ejpam-3003	633	1	+	+	CCONJ
ejpam-3003	633	2	‖u‖p+1	‖u‖p+1	NOUN
ejpam-3003	633	3	p+1	p+1	NOUN
ejpam-3003	633	4	)	)	PUNCT
ejpam-3003	634	1	=	=	PUNCT
ejpam-3003	635	1	+	+	NUM
ejpam-3003	635	2	∞.	∞.	PROPN
ejpam-3003	635	3	(	(	PUNCT
ejpam-3003	635	4	5.3	5.3	NUM
ejpam-3003	635	5	)	)	PUNCT
ejpam-3003	635	6	first	first	ADV
ejpam-3003	635	7	of	of	ADP
ejpam-3003	635	8	all	all	PRON
ejpam-3003	635	9	,	,	PUNCT
ejpam-3003	635	10	we	we	PRON
ejpam-3003	635	11	introduce	introduce	VERB
ejpam-3003	635	12	the	the	DET
ejpam-3003	635	13	following	follow	VERB
ejpam-3003	635	14	lemma	lemma	PROPN
ejpam-3003	635	15	which	which	PRON
ejpam-3003	635	16	will	will	AUX
ejpam-3003	635	17	be	be	AUX
ejpam-3003	635	18	needed	need	VERB
ejpam-3003	635	19	in	in	ADP
ejpam-3003	635	20	the	the	DET
ejpam-3003	635	21	course	course	NOUN
ejpam-3003	635	22	of	of	ADP
ejpam-3003	635	23	this	this	DET
ejpam-3003	635	24	section	section	NOUN
ejpam-3003	635	25	.	.	PUNCT
ejpam-3003	636	1	lemma	lemma	PROPN
ejpam-3003	636	2	12	12	NUM
ejpam-3003	636	3	.	.	PUNCT
ejpam-3003	637	1	let	let	VERB
ejpam-3003	637	2	the	the	DET
ejpam-3003	637	3	assumptions	assumption	NOUN
ejpam-3003	637	4	(	(	PUNCT
ejpam-3003	637	5	a3	a3	NOUN
ejpam-3003	637	6	)	)	PUNCT
ejpam-3003	637	7	hold	hold	NOUN
ejpam-3003	637	8	.	.	PUNCT
ejpam-3003	638	1	then	then	ADV
ejpam-3003	638	2	there	there	PRON
ejpam-3003	638	3	exists	exist	VERB
ejpam-3003	638	4	a	a	DET
ejpam-3003	638	5	positive	positive	ADJ
ejpam-3003	638	6	constant	constant	ADJ
ejpam-3003	638	7	c	c	NOUN
ejpam-3003	638	8	>	>	X
ejpam-3003	638	9	1	1	NUM
ejpam-3003	638	10	depending	depend	VERB
ejpam-3003	638	11	on	on	ADP
ejpam-3003	638	12	ω	ω	NUM
ejpam-3003	638	13	only	only	ADV
ejpam-3003	638	14	such	such	ADJ
ejpam-3003	638	15	that	that	SCONJ
ejpam-3003	638	16	‖u‖sp+1	‖u‖sp+1	PROPN
ejpam-3003	638	17	≤	≤	PUNCT
ejpam-3003	638	18	c(‖∇u‖22	c(‖∇u‖22	PROPN
ejpam-3003	639	1	+	+	NUM
ejpam-3003	639	2	‖u‖p+1	‖u‖p+1	PROPN
ejpam-3003	639	3	p+1	p+1	NOUN
ejpam-3003	639	4	)	)	PUNCT
ejpam-3003	639	5	(	(	PUNCT
ejpam-3003	639	6	5.4	5.4	NUM
ejpam-3003	639	7	)	)	PUNCT
ejpam-3003	639	8	for	for	ADP
ejpam-3003	639	9	any	any	DET
ejpam-3003	639	10	u	u	PROPN
ejpam-3003	639	11	∈	∈	PROPN
ejpam-3003	639	12	h1	h1	PROPN
ejpam-3003	639	13	γ0	γ0	PROPN
ejpam-3003	639	14	(	(	PUNCT
ejpam-3003	639	15	ω	ω	NOUN
ejpam-3003	639	16	)	)	PUNCT
ejpam-3003	639	17	and	and	CCONJ
ejpam-3003	639	18	2	2	NUM
ejpam-3003	639	19	≤	≤	NOUN
ejpam-3003	639	20	s	s	PART
ejpam-3003	639	21	≤	≤	NOUN
ejpam-3003	639	22	p+	p+	VERB
ejpam-3003	639	23	1	1	NUM
ejpam-3003	639	24	.	.	PUNCT
ejpam-3003	640	1	now	now	ADV
ejpam-3003	640	2	,	,	PUNCT
ejpam-3003	640	3	we	we	PRON
ejpam-3003	640	4	are	be	AUX
ejpam-3003	640	5	ready	ready	ADJ
ejpam-3003	640	6	to	to	PART
ejpam-3003	640	7	prove	prove	VERB
ejpam-3003	640	8	blow	blow	VERB
ejpam-3003	640	9	up	up	ADP
ejpam-3003	640	10	result	result	NOUN
ejpam-3003	640	11	of	of	ADP
ejpam-3003	640	12	the	the	DET
ejpam-3003	640	13	solutions	solution	NOUN
ejpam-3003	640	14	for	for	ADP
ejpam-3003	640	15	the	the	DET
ejpam-3003	640	16	problem	problem	NOUN
ejpam-3003	640	17	(	(	PUNCT
ejpam-3003	640	18	1.1	1.1	NUM
ejpam-3003	640	19	)	)	PUNCT
ejpam-3003	640	20	.	.	PUNCT
ejpam-3003	641	1	proof	proof	NOUN
ejpam-3003	641	2	.	.	PUNCT
ejpam-3003	642	1	in	in	ADP
ejpam-3003	642	2	lemma	lemma	PROPN
ejpam-3003	642	3	3	3	NUM
ejpam-3003	642	4	(	(	PUNCT
ejpam-3003	642	5	2	2	NUM
ejpam-3003	642	6	)	)	PUNCT
ejpam-3003	642	7	,	,	PUNCT
ejpam-3003	642	8	we	we	PRON
ejpam-3003	642	9	have	have	AUX
ejpam-3003	642	10	proved	prove	VERB
ejpam-3003	642	11	that	that	SCONJ
ejpam-3003	642	12	if	if	SCONJ
ejpam-3003	642	13	i(u0	i(u0	PROPN
ejpam-3003	642	14	)	)	PUNCT
ejpam-3003	642	15	<	<	X
ejpam-3003	642	16	0	0	X
ejpam-3003	642	17	then	then	ADV
ejpam-3003	642	18	i(u	i(u	PROPN
ejpam-3003	642	19	)	)	PUNCT
ejpam-3003	642	20	<	<	X
ejpam-3003	642	21	0	0	NUM
ejpam-3003	642	22	for	for	ADP
ejpam-3003	642	23	any	any	DET
ejpam-3003	642	24	t	t	NOUN
ejpam-3003	642	25	∈	∈	PROPN
ejpam-3003	643	1	[	[	X
ejpam-3003	643	2	0	0	NUM
ejpam-3003	643	3	,	,	PUNCT
ejpam-3003	643	4	tmax	tmax	NUM
ejpam-3003	643	5	)	)	PUNCT
ejpam-3003	643	6	in	in	ADP
ejpam-3003	643	7	the	the	DET
ejpam-3003	643	8	case	case	NOUN
ejpam-3003	643	9	of	of	ADP
ejpam-3003	643	10	e(0	e(0	NOUN
ejpam-3003	643	11	)	)	PUNCT
ejpam-3003	643	12	<	<	X
ejpam-3003	643	13	βd̃.	βd̃.	PUNCT
ejpam-3003	643	14	by	by	ADP
ejpam-3003	643	15	contradiction	contradiction	NOUN
ejpam-3003	643	16	,	,	PUNCT
ejpam-3003	643	17	we	we	PRON
ejpam-3003	643	18	assume	assume	VERB
ejpam-3003	643	19	that	that	SCONJ
ejpam-3003	643	20	the	the	DET
ejpam-3003	643	21	solution	solution	NOUN
ejpam-3003	643	22	of	of	ADP
ejpam-3003	643	23	problem	problem	NOUN
ejpam-3003	643	24	(	(	PUNCT
ejpam-3003	643	25	1.1	1.1	NUM
ejpam-3003	643	26	)	)	PUNCT
ejpam-3003	643	27	is	be	AUX
ejpam-3003	643	28	global	global	ADJ
ejpam-3003	643	29	.	.	PUNCT
ejpam-3003	644	1	then	then	ADV
ejpam-3003	644	2	,	,	PUNCT
ejpam-3003	644	3	for	for	ADP
ejpam-3003	644	4	any	any	DET
ejpam-3003	644	5	t	t	NOUN
ejpam-3003	644	6	>	>	X
ejpam-3003	644	7	0	0	PUNCT
ejpam-3003	645	1	we	we	PRON
ejpam-3003	645	2	may	may	AUX
ejpam-3003	645	3	consider	consider	VERB
ejpam-3003	645	4	functional	functional	ADJ
ejpam-3003	645	5	θ	θ	NOUN
ejpam-3003	645	6	:	:	PUNCT
ejpam-3003	646	1	[	[	X
ejpam-3003	646	2	0	0	NUM
ejpam-3003	646	3	,	,	PUNCT
ejpam-3003	646	4	t	t	X
ejpam-3003	646	5	]	]	PUNCT
ejpam-3003	646	6	→	→	SYM
ejpam-3003	646	7	r+	r+	PRON
ejpam-3003	646	8	defined	define	VERB
ejpam-3003	646	9	by	by	ADP
ejpam-3003	646	10	θ(t	θ(t	NOUN
ejpam-3003	646	11	)	)	PUNCT
ejpam-3003	647	1	=	=	PUNCT
ejpam-3003	648	1	‖ut‖ρ+1	‖ut‖ρ+1	PUNCT
ejpam-3003	648	2	ρ+1	ρ+1	NOUN
ejpam-3003	648	3	+	+	CCONJ
ejpam-3003	648	4	‖∇u‖22	‖∇u‖22	NOUN
ejpam-3003	649	1	+	+	CCONJ
ejpam-3003	649	2	‖u‖p+1	‖u‖p+1	NOUN
ejpam-3003	649	3	p+1	p+1	NOUN
ejpam-3003	649	4	.	.	PUNCT
ejpam-3003	650	1	(	(	PUNCT
ejpam-3003	650	2	5.5	5.5	NUM
ejpam-3003	650	3	)	)	PUNCT
ejpam-3003	650	4	h.f	h.f	PROPN
ejpam-3003	650	5	.	.	PROPN
ejpam-3003	650	6	di	di	PROPN
ejpam-3003	650	7	,	,	PUNCT
ejpam-3003	650	8	y.d	y.d	PROPN
ejpam-3003	650	9	.	.	PROPN
ejpam-3003	650	10	shang	shang	PROPN
ejpam-3003	650	11	/	/	SYM
ejpam-3003	650	12	eur	eur	PROPN
ejpam-3003	650	13	.	.	PUNCT
ejpam-3003	651	1	j.	j.	PROPN
ejpam-3003	651	2	pure	pure	PROPN
ejpam-3003	651	3	appl	appl	PROPN
ejpam-3003	651	4	.	.	PROPN
ejpam-3003	651	5	math	math	PROPN
ejpam-3003	651	6	,	,	PUNCT
ejpam-3003	651	7	10	10	NUM
ejpam-3003	651	8	(	(	PUNCT
ejpam-3003	651	9	4	4	NUM
ejpam-3003	651	10	)	)	PUNCT
ejpam-3003	651	11	(	(	PUNCT
ejpam-3003	651	12	2017	2017	NUM
ejpam-3003	651	13	)	)	PUNCT
ejpam-3003	651	14	,	,	PUNCT
ejpam-3003	651	15	668	668	NUM
ejpam-3003	651	16	-	-	SYM
ejpam-3003	651	17	701	701	NUM
ejpam-3003	651	18	694	694	NUM
ejpam-3003	651	19	as	as	ADP
ejpam-3003	651	20	θ(t	θ(t	NOUN
ejpam-3003	651	21	)	)	PUNCT
ejpam-3003	651	22	is	be	AUX
ejpam-3003	651	23	continuous	continuous	ADJ
ejpam-3003	651	24	on	on	ADP
ejpam-3003	651	25	[	[	X
ejpam-3003	651	26	0	0	NUM
ejpam-3003	651	27	,	,	PUNCT
ejpam-3003	651	28	t	t	X
ejpam-3003	651	29	]	]	PUNCT
ejpam-3003	651	30	,	,	PUNCT
ejpam-3003	651	31	there	there	PRON
ejpam-3003	651	32	exist	exist	VERB
ejpam-3003	651	33	δ1	δ1	NOUN
ejpam-3003	651	34	,	,	PUNCT
ejpam-3003	651	35	δ2	δ2	VERB
ejpam-3003	651	36	>	>	X
ejpam-3003	651	37	0	0	NUM
ejpam-3003	652	1	such	such	ADJ
ejpam-3003	652	2	that	that	DET
ejpam-3003	652	3	δ1	δ1	NOUN
ejpam-3003	652	4	≤	≤	NUM
ejpam-3003	652	5	θ(t	θ(t	NOUN
ejpam-3003	652	6	)	)	PUNCT
ejpam-3003	652	7	≤	≤	NOUN
ejpam-3003	652	8	δ2	δ2	VERB
ejpam-3003	652	9	.	.	PUNCT
ejpam-3003	653	1	first	first	ADV
ejpam-3003	653	2	,	,	PUNCT
ejpam-3003	653	3	we	we	PRON
ejpam-3003	653	4	set	set	VERB
ejpam-3003	653	5	n(t	n(t	PRON
ejpam-3003	653	6	)	)	PUNCT
ejpam-3003	653	7	=	=	PUNCT
ejpam-3003	653	8	βd̃−	βd̃−	VERB
ejpam-3003	653	9	e(t	e(t	NOUN
ejpam-3003	653	10	)	)	PUNCT
ejpam-3003	653	11	(	(	PUNCT
ejpam-3003	653	12	5.6	5.6	NUM
ejpam-3003	653	13	)	)	PUNCT
ejpam-3003	653	14	for	for	ADP
ejpam-3003	653	15	all	all	DET
ejpam-3003	653	16	t	t	NOUN
ejpam-3003	653	17	∈	∈	PROPN
ejpam-3003	654	1	[	[	X
ejpam-3003	654	2	0	0	NUM
ejpam-3003	654	3	,	,	PUNCT
ejpam-3003	654	4	t	t	X
ejpam-3003	654	5	]	]	PUNCT
ejpam-3003	654	6	.	.	PUNCT
ejpam-3003	655	1	differentiating	differentiate	VERB
ejpam-3003	655	2	the	the	DET
ejpam-3003	655	3	identity	identity	NOUN
ejpam-3003	655	4	(	(	PUNCT
ejpam-3003	655	5	5.6	5.6	NUM
ejpam-3003	655	6	)	)	PUNCT
ejpam-3003	655	7	with	with	ADP
ejpam-3003	655	8	respect	respect	NOUN
ejpam-3003	655	9	to	to	ADP
ejpam-3003	655	10	t	t	PROPN
ejpam-3003	655	11	,	,	PUNCT
ejpam-3003	655	12	we	we	PRON
ejpam-3003	655	13	have	have	VERB
ejpam-3003	655	14	n	n	NUM
ejpam-3003	655	15	′(t	′(t	NOUN
ejpam-3003	655	16	)	)	PUNCT
ejpam-3003	655	17	=	=	PUNCT
ejpam-3003	656	1	−e′(t	−e′(t	PROPN
ejpam-3003	656	2	)	)	PUNCT
ejpam-3003	656	3	=	=	PUNCT
ejpam-3003	657	1	‖ut‖q+1	‖ut‖q+1	PUNCT
ejpam-3003	657	2	γ1,q+1	γ1,q+1	PUNCT
ejpam-3003	658	1	+	+	CCONJ
ejpam-3003	658	2	1	1	NUM
ejpam-3003	658	3	2	2	NUM
ejpam-3003	658	4	g(t)‖∇u(t)‖22	g(t)‖∇u(t)‖22	NOUN
ejpam-3003	658	5	−	−	NOUN
ejpam-3003	658	6	1	1	NUM
ejpam-3003	658	7	2	2	NUM
ejpam-3003	658	8	∫	∫	PROPN
ejpam-3003	658	9	ω	ω	NUM
ejpam-3003	658	10	∫	∫	PROPN
ejpam-3003	658	11	t	t	PROPN
ejpam-3003	658	12	0	0	NUM
ejpam-3003	659	1	g′(t−	g′(t−	PROPN
ejpam-3003	659	2	s)[∇u(s)−∇u(t)]2dsdx	s)[∇u(s)−∇u(t)]2dsdx	X
ejpam-3003	659	3	≥	≥	NOUN
ejpam-3003	659	4	0	0	NUM
ejpam-3003	659	5	.	.	PUNCT
ejpam-3003	660	1	(	(	PUNCT
ejpam-3003	660	2	5.7	5.7	NUM
ejpam-3003	660	3	)	)	PUNCT
ejpam-3003	660	4	hence	hence	ADV
ejpam-3003	660	5	n(t	n(t	NUM
ejpam-3003	660	6	)	)	PUNCT
ejpam-3003	660	7	≥	≥	PROPN
ejpam-3003	660	8	n(0	n(0	PROPN
ejpam-3003	660	9	)	)	PUNCT
ejpam-3003	660	10	=	=	PRON
ejpam-3003	660	11	βd̃−	βd̃−	VERB
ejpam-3003	660	12	e(0	e(0	NOUN
ejpam-3003	660	13	)	)	PUNCT
ejpam-3003	660	14	>	>	X
ejpam-3003	661	1	0	0	X
ejpam-3003	661	2	.	.	PUNCT
ejpam-3003	662	1	(	(	PUNCT
ejpam-3003	662	2	5.8	5.8	NUM
ejpam-3003	662	3	)	)	PUNCT
ejpam-3003	662	4	from	from	ADP
ejpam-3003	662	5	the	the	DET
ejpam-3003	662	6	lemma	lemma	PROPN
ejpam-3003	662	7	4	4	NUM
ejpam-3003	662	8	and	and	CCONJ
ejpam-3003	662	9	(	(	PUNCT
ejpam-3003	662	10	2.1	2.1	NUM
ejpam-3003	662	11	)	)	PUNCT
ejpam-3003	662	12	,	,	PUNCT
ejpam-3003	662	13	it	it	PRON
ejpam-3003	662	14	follows	follow	VERB
ejpam-3003	662	15	that	that	SCONJ
ejpam-3003	662	16	n(t	n(t	NOUN
ejpam-3003	662	17	)	)	PUNCT
ejpam-3003	662	18	≤	≤	NOUN
ejpam-3003	662	19	βd̃+	βd̃+	SYM
ejpam-3003	662	20	1	1	NUM
ejpam-3003	662	21	p+	p+	NOUN
ejpam-3003	662	22	1	1	NUM
ejpam-3003	662	23	‖u‖p+1	‖u‖p+1	NOUN
ejpam-3003	662	24	p+1	p+1	NOUN
ejpam-3003	662	25	≤	≤	NUM
ejpam-3003	662	26	(	(	PUNCT
ejpam-3003	662	27	β(p−	β(p−	VERB
ejpam-3003	662	28	1	1	NUM
ejpam-3003	662	29	)	)	PUNCT
ejpam-3003	662	30	2(p+	2(p+	NUM
ejpam-3003	662	31	1	1	NUM
ejpam-3003	662	32	)	)	PUNCT
ejpam-3003	662	33	+	+	CCONJ
ejpam-3003	662	34	1	1	NUM
ejpam-3003	662	35	p+	p+	NOUN
ejpam-3003	662	36	1	1	NUM
ejpam-3003	662	37	)	)	PUNCT
ejpam-3003	662	38	‖u‖p+1	‖u‖p+1	PROPN
ejpam-3003	662	39	p+1	p+1	NOUN
ejpam-3003	662	40	,	,	PUNCT
ejpam-3003	662	41	(	(	PUNCT
ejpam-3003	662	42	5.9	5.9	NUM
ejpam-3003	662	43	)	)	PUNCT
ejpam-3003	662	44	for	for	ADP
ejpam-3003	662	45	all	all	DET
ejpam-3003	662	46	t	t	NOUN
ejpam-3003	662	47	∈	∈	PROPN
ejpam-3003	663	1	[	[	X
ejpam-3003	663	2	0	0	NUM
ejpam-3003	663	3	,	,	PUNCT
ejpam-3003	663	4	t	t	X
ejpam-3003	663	5	]	]	PUNCT
ejpam-3003	663	6	.	.	PUNCT
ejpam-3003	664	1	next	next	ADV
ejpam-3003	664	2	,	,	PUNCT
ejpam-3003	664	3	we	we	PRON
ejpam-3003	664	4	define	define	VERB
ejpam-3003	664	5	g(t	g(t	PROPN
ejpam-3003	664	6	)	)	PUNCT
ejpam-3003	664	7	=	=	SYM
ejpam-3003	664	8	n1−σ(t	n1−σ(t	PROPN
ejpam-3003	664	9	)	)	PUNCT
ejpam-3003	665	1	+	+	CCONJ
ejpam-3003	665	2	ε	ε	PROPN
ejpam-3003	665	3	ρ	ρ	PROPN
ejpam-3003	665	4	∫	∫	PROPN
ejpam-3003	665	5	ω	ω	PROPN
ejpam-3003	665	6	u|ut|ρ−1utdx	u|ut|ρ−1utdx	PROPN
ejpam-3003	665	7	,	,	PUNCT
ejpam-3003	665	8	∀	∀	PUNCT
ejpam-3003	665	9	t	t	NOUN
ejpam-3003	665	10	∈	∈	PROPN
ejpam-3003	666	1	[	[	X
ejpam-3003	666	2	0	0	NUM
ejpam-3003	666	3	,	,	PUNCT
ejpam-3003	666	4	t	t	X
ejpam-3003	666	5	]	]	PUNCT
ejpam-3003	666	6	,	,	PUNCT
ejpam-3003	666	7	(	(	PUNCT
ejpam-3003	666	8	5.10	5.10	NUM
ejpam-3003	666	9	)	)	PUNCT
ejpam-3003	666	10	where	where	SCONJ
ejpam-3003	666	11	0	0	NUM
ejpam-3003	666	12	<	<	X
ejpam-3003	666	13	ε	ε	X
ejpam-3003	666	14	�	�	PROPN
ejpam-3003	666	15	1	1	NUM
ejpam-3003	666	16	to	to	PART
ejpam-3003	666	17	be	be	AUX
ejpam-3003	666	18	chosen	choose	VERB
ejpam-3003	666	19	later	later	ADV
ejpam-3003	666	20	and	and	CCONJ
ejpam-3003	666	21	0	0	NUM
ejpam-3003	666	22	<	<	X
ejpam-3003	666	23	σ	σ	X
ejpam-3003	666	24	<	<	X
ejpam-3003	666	25	min	min	PROPN
ejpam-3003	666	26	{	{	PUNCT
ejpam-3003	666	27	1	1	NUM
ejpam-3003	666	28	ρ+	ρ+	NUM
ejpam-3003	666	29	1	1	NUM
ejpam-3003	666	30	,	,	PUNCT
ejpam-3003	666	31	1	1	NUM
ejpam-3003	666	32	q	q	NOUN
ejpam-3003	666	33	}	}	PUNCT
ejpam-3003	666	34	,	,	PUNCT
ejpam-3003	666	35	(	(	PUNCT
ejpam-3003	666	36	5.11	5.11	NUM
ejpam-3003	666	37	)	)	PUNCT
ejpam-3003	666	38	which	which	PRON
ejpam-3003	666	39	will	will	AUX
ejpam-3003	666	40	be	be	AUX
ejpam-3003	666	41	used	use	VERB
ejpam-3003	666	42	later	later	ADV
ejpam-3003	666	43	.	.	PUNCT
ejpam-3003	667	1	differentiating	differentiate	VERB
ejpam-3003	667	2	the	the	DET
ejpam-3003	667	3	identity	identity	NOUN
ejpam-3003	667	4	(	(	PUNCT
ejpam-3003	667	5	5.10	5.10	NUM
ejpam-3003	667	6	)	)	PUNCT
ejpam-3003	667	7	with	with	ADP
ejpam-3003	667	8	respect	respect	NOUN
ejpam-3003	667	9	to	to	ADP
ejpam-3003	667	10	t	t	NOUN
ejpam-3003	667	11	and	and	CCONJ
ejpam-3003	667	12	using	use	VERB
ejpam-3003	667	13	equation	equation	NOUN
ejpam-3003	667	14	(	(	PUNCT
ejpam-3003	667	15	1.1	1.1	NUM
ejpam-3003	667	16	)	)	PUNCT
ejpam-3003	667	17	,	,	PUNCT
ejpam-3003	667	18	we	we	PRON
ejpam-3003	667	19	obtain	obtain	VERB
ejpam-3003	667	20	g′(t	g′(t	NOUN
ejpam-3003	667	21	)	)	PUNCT
ejpam-3003	667	22	=	=	SYM
ejpam-3003	667	23	(	(	PUNCT
ejpam-3003	667	24	1−	1−	NUM
ejpam-3003	667	25	σ)n−σ(t)n	σ)n−σ(t)n	PROPN
ejpam-3003	667	26	′(t	′(t	NOUN
ejpam-3003	667	27	)	)	PUNCT
ejpam-3003	668	1	+	+	CCONJ
ejpam-3003	668	2	ε	ε	PROPN
ejpam-3003	668	3	ρ	ρ	PROPN
ejpam-3003	668	4	‖ut‖ρ+1	‖ut‖ρ+1	PROPN
ejpam-3003	668	5	ρ+1	ρ+1	NOUN
ejpam-3003	668	6	+	+	CCONJ
ejpam-3003	668	7	ε(|ut|ρ−1utt	ε(|ut|ρ−1utt	NOUN
ejpam-3003	668	8	,	,	PUNCT
ejpam-3003	668	9	u	u	NOUN
ejpam-3003	668	10	)	)	PUNCT
ejpam-3003	668	11	=	=	SYM
ejpam-3003	668	12	(	(	PUNCT
ejpam-3003	668	13	1−	1−	NUM
ejpam-3003	668	14	σ)n−σ(t)n	σ)n−σ(t)n	PROPN
ejpam-3003	668	15	′(t	′(t	NOUN
ejpam-3003	668	16	)	)	PUNCT
ejpam-3003	669	1	+	+	CCONJ
ejpam-3003	669	2	ε	ε	PROPN
ejpam-3003	669	3	ρ	ρ	PROPN
ejpam-3003	669	4	‖ut‖ρ+1	‖ut‖ρ+1	PROPN
ejpam-3003	669	5	ρ+1	ρ+1	NOUN
ejpam-3003	669	6	−	−	PROPN
ejpam-3003	669	7	ε‖∇u‖	ε‖∇u‖	NOUN
ejpam-3003	669	8	2	2	NUM
ejpam-3003	669	9	2	2	NUM
ejpam-3003	669	10	+	+	CCONJ
ejpam-3003	669	11	ε‖u‖p+1	ε‖u‖p+1	VERB
ejpam-3003	669	12	p+1	p+1	NOUN
ejpam-3003	669	13	+	+	CCONJ
ejpam-3003	669	14	ε	ε	PROPN
ejpam-3003	669	15	∫	∫	PROPN
ejpam-3003	669	16	ω	ω	PROPN
ejpam-3003	669	17	∇u(t	∇u(t	PROPN
ejpam-3003	669	18	)	)	PUNCT
ejpam-3003	669	19	∫	∫	PROPN
ejpam-3003	669	20	t	t	PROPN
ejpam-3003	669	21	0	0	NUM
ejpam-3003	669	22	g(t−	g(t−	PROPN
ejpam-3003	669	23	s)∇u(s)dsdx−	s)∇u(s)dsdx−	PROPN
ejpam-3003	669	24	ε	ε	PROPN
ejpam-3003	669	25	∫	∫	PROPN
ejpam-3003	669	26	γ1	γ1	PROPN
ejpam-3003	669	27	|ut|q−1utudγ	|ut|q−1utudγ	PROPN
ejpam-3003	669	28	.	.	PUNCT
ejpam-3003	670	1	(	(	PUNCT
ejpam-3003	670	2	5.12	5.12	NUM
ejpam-3003	670	3	)	)	PUNCT
ejpam-3003	670	4	considering	consider	VERB
ejpam-3003	670	5	the	the	DET
ejpam-3003	670	6	relation	relation	NOUN
ejpam-3003	670	7	(	(	PUNCT
ejpam-3003	670	8	p+	p+	PROPN
ejpam-3003	670	9	1−	1−	NUM
ejpam-3003	670	10	γ)n(t	γ)n(t	NOUN
ejpam-3003	670	11	)	)	PUNCT
ejpam-3003	670	12	=	=	PRON
ejpam-3003	670	13	(	(	PUNCT
ejpam-3003	670	14	p+	p+	PROPN
ejpam-3003	670	15	1−	1−	NUM
ejpam-3003	670	16	γ)βd̃−	γ)βd̃−	PROPN
ejpam-3003	670	17	p+	p+	PROPN
ejpam-3003	670	18	1−	1−	NUM
ejpam-3003	670	19	γ	γ	PROPN
ejpam-3003	670	20	ρ+	ρ+	NUM
ejpam-3003	670	21	1	1	NUM
ejpam-3003	670	22	‖ut‖ρ+1	‖ut‖ρ+1	NUM
ejpam-3003	670	23	ρ+1	ρ+1	NUM
ejpam-3003	670	24	−	−	PROPN
ejpam-3003	670	25	p+	p+	NOUN
ejpam-3003	670	26	1−	1−	NUM
ejpam-3003	670	27	γ	γ	SYM
ejpam-3003	670	28	2	2	NUM
ejpam-3003	670	29	l(t)‖∇u‖22	l(t)‖∇u‖22	NOUN
ejpam-3003	670	30	−	−	PROPN
ejpam-3003	670	31	p+	p+	PROPN
ejpam-3003	670	32	1−	1−	NUM
ejpam-3003	670	33	γ	γ	X
ejpam-3003	670	34	2	2	NUM
ejpam-3003	670	35	(	(	PUNCT
ejpam-3003	670	36	g	g	PROPN
ejpam-3003	670	37	◦	◦	PROPN
ejpam-3003	670	38	∇u)(t	∇u)(t	PROPN
ejpam-3003	670	39	)	)	PUNCT
ejpam-3003	670	40	+	+	CCONJ
ejpam-3003	670	41	(	(	PUNCT
ejpam-3003	670	42	p+	p+	PROPN
ejpam-3003	670	43	1−	1−	NUM
ejpam-3003	670	44	γ	γ	X
ejpam-3003	670	45	)	)	PUNCT
ejpam-3003	670	46	p+	p+	VERB
ejpam-3003	670	47	1	1	NUM
ejpam-3003	670	48	‖u‖p+1	‖u‖p+1	PROPN
ejpam-3003	670	49	p+1	p+1	NOUN
ejpam-3003	670	50	(	(	PUNCT
ejpam-3003	670	51	5.13	5.13	NUM
ejpam-3003	670	52	)	)	PUNCT
ejpam-3003	670	53	h.f	h.f	PROPN
ejpam-3003	670	54	.	.	PROPN
ejpam-3003	670	55	di	di	PROPN
ejpam-3003	670	56	,	,	PUNCT
ejpam-3003	670	57	y.d	y.d	PROPN
ejpam-3003	670	58	.	.	PROPN
ejpam-3003	670	59	shang	shang	PROPN
ejpam-3003	670	60	/	/	SYM
ejpam-3003	670	61	eur	eur	PROPN
ejpam-3003	670	62	.	.	PUNCT
ejpam-3003	671	1	j.	j.	PROPN
ejpam-3003	671	2	pure	pure	PROPN
ejpam-3003	671	3	appl	appl	PROPN
ejpam-3003	671	4	.	.	PROPN
ejpam-3003	671	5	math	math	PROPN
ejpam-3003	671	6	,	,	PUNCT
ejpam-3003	671	7	10	10	NUM
ejpam-3003	671	8	(	(	PUNCT
ejpam-3003	671	9	4	4	NUM
ejpam-3003	671	10	)	)	PUNCT
ejpam-3003	671	11	(	(	PUNCT
ejpam-3003	671	12	2017	2017	NUM
ejpam-3003	671	13	)	)	PUNCT
ejpam-3003	671	14	,	,	PUNCT
ejpam-3003	671	15	668	668	NUM
ejpam-3003	671	16	-	-	SYM
ejpam-3003	671	17	701	701	NUM
ejpam-3003	671	18	695	695	NUM
ejpam-3003	671	19	and	and	CCONJ
ejpam-3003	671	20	young	young	ADJ
ejpam-3003	671	21	inequality∫	inequality∫	NUM
ejpam-3003	671	22	ω	ω	NUM
ejpam-3003	671	23	∇u(t	∇u(t	NOUN
ejpam-3003	671	24	)	)	PUNCT
ejpam-3003	672	1	∫	∫	PROPN
ejpam-3003	672	2	t	t	PROPN
ejpam-3003	672	3	0	0	NUM
ejpam-3003	672	4	g(t−	g(t−	PROPN
ejpam-3003	672	5	s)[∇u(s)−∇u(t)]dsdx	s)[∇u(s)−∇u(t)]dsdx	PROPN
ejpam-3003	672	6	≤	≤	NOUN
ejpam-3003	672	7	1	1	NUM
ejpam-3003	672	8	4ξ	4ξ	NUM
ejpam-3003	672	9	∫	∫	PROPN
ejpam-3003	672	10	t	t	PROPN
ejpam-3003	672	11	0	0	NUM
ejpam-3003	672	12	g(s)ds‖∇u(t)‖22	g(s)ds‖∇u(t)‖22	NOUN
ejpam-3003	672	13	+	+	CCONJ
ejpam-3003	672	14	ξ	ξ	PROPN
ejpam-3003	672	15	∫	∫	PROPN
ejpam-3003	672	16	t	t	PROPN
ejpam-3003	672	17	0	0	NUM
ejpam-3003	672	18	g(t−	g(t−	PROPN
ejpam-3003	672	19	s	s	PART
ejpam-3003	672	20	)	)	PUNCT
ejpam-3003	672	21	∫	∫	PROPN
ejpam-3003	672	22	ω	ω	NUM
ejpam-3003	672	23	|∇u(s)−∇u(t)|2dsdx	|∇u(s)−∇u(t)|2dsdx	PROPN
ejpam-3003	672	24	,	,	PUNCT
ejpam-3003	672	25	(	(	PUNCT
ejpam-3003	672	26	5.14	5.14	NUM
ejpam-3003	672	27	)	)	PUNCT
ejpam-3003	672	28	∫	∫	PROPN
ejpam-3003	672	29	γ1	γ1	PROPN
ejpam-3003	672	30	|ut|q−1utudγ	|ut|q−1utudγ	PROPN
ejpam-3003	672	31	≤	≤	NUM
ejpam-3003	672	32	µq+1	µq+1	NOUN
ejpam-3003	672	33	q	q	X
ejpam-3003	673	1	+	+	NUM
ejpam-3003	673	2	1	1	NUM
ejpam-3003	673	3	‖u‖q+1	‖u‖q+1	PROPN
ejpam-3003	673	4	γ1,q+1	γ1,q+1	PUNCT
ejpam-3003	674	1	+	+	NUM
ejpam-3003	674	2	q	q	ADJ
ejpam-3003	674	3	q	q	NOUN
ejpam-3003	674	4	+	+	NUM
ejpam-3003	674	5	1	1	NUM
ejpam-3003	674	6	µ	µ	PRON
ejpam-3003	674	7	−	−	PROPN
ejpam-3003	674	8	q+1	q+1	NUM
ejpam-3003	674	9	q	q	PROPN
ejpam-3003	674	10	‖ut‖q+1	‖ut‖q+1	PROPN
ejpam-3003	674	11	γ1,q+1	γ1,q+1	PROPN
ejpam-3003	674	12	,	,	PUNCT
ejpam-3003	674	13	(	(	PUNCT
ejpam-3003	674	14	5.15	5.15	NUM
ejpam-3003	674	15	)	)	PUNCT
ejpam-3003	674	16	where	where	SCONJ
ejpam-3003	674	17	γ	γ	X
ejpam-3003	674	18	,	,	PUNCT
ejpam-3003	674	19	ξ	ξ	PROPN
ejpam-3003	674	20	,	,	PUNCT
ejpam-3003	674	21	µ	µ	X
ejpam-3003	674	22	>	>	X
ejpam-3003	674	23	0	0	PUNCT
ejpam-3003	674	24	to	to	PART
ejpam-3003	674	25	be	be	AUX
ejpam-3003	674	26	determined	determine	VERB
ejpam-3003	674	27	later	later	ADV
ejpam-3003	674	28	,	,	PUNCT
ejpam-3003	674	29	we	we	PRON
ejpam-3003	674	30	get	get	VERB
ejpam-3003	674	31	from	from	ADP
ejpam-3003	674	32	(	(	PUNCT
ejpam-3003	674	33	5.12	5.12	NUM
ejpam-3003	674	34	)	)	PUNCT
ejpam-3003	674	35	that	that	SCONJ
ejpam-3003	674	36	g′(t	g′(t	VERB
ejpam-3003	674	37	)	)	PUNCT
ejpam-3003	674	38	=	=	SYM
ejpam-3003	674	39	(	(	PUNCT
ejpam-3003	674	40	1−	1−	NUM
ejpam-3003	674	41	σ)n−σ(t)n	σ)n−σ(t)n	PROPN
ejpam-3003	674	42	′(t	′(t	NOUN
ejpam-3003	674	43	)	)	PUNCT
ejpam-3003	675	1	+	+	CCONJ
ejpam-3003	676	1	ε(p+	ε(p+	PROPN
ejpam-3003	676	2	1−	1−	NUM
ejpam-3003	676	3	γ)n(t)−	γ)n(t)−	PROPN
ejpam-3003	676	4	ε(p+	ε(p+	PROPN
ejpam-3003	676	5	1−	1−	NUM
ejpam-3003	676	6	γ)βd̃+	γ)βd̃+	PROPN
ejpam-3003	676	7	ε	ε	PROPN
ejpam-3003	676	8	ρ	ρ	PROPN
ejpam-3003	676	9	‖ut‖ρ+1	‖ut‖ρ+1	PROPN
ejpam-3003	676	10	ρ+1	ρ+1	NOUN
ejpam-3003	676	11	+	+	CCONJ
ejpam-3003	676	12	ε	ε	PROPN
ejpam-3003	676	13	p+	p+	PROPN
ejpam-3003	676	14	1−	1−	NUM
ejpam-3003	676	15	γ	γ	PROPN
ejpam-3003	676	16	ρ+	ρ+	NUM
ejpam-3003	676	17	1	1	NUM
ejpam-3003	676	18	‖ut‖ρ+1	‖ut‖ρ+1	SYM
ejpam-3003	676	19	ρ+1	ρ+1	NOUN
ejpam-3003	676	20	+	+	CCONJ
ejpam-3003	676	21	ε	ε	PROPN
ejpam-3003	676	22	p+	p+	PROPN
ejpam-3003	676	23	1−	1−	NUM
ejpam-3003	676	24	γ	γ	SYM
ejpam-3003	676	25	2	2	NUM
ejpam-3003	676	26	l(t)‖∇u‖22	l(t)‖∇u‖22	NOUN
ejpam-3003	676	27	+	+	CCONJ
ejpam-3003	676	28	ε	ε	PROPN
ejpam-3003	676	29	p+	p+	PROPN
ejpam-3003	676	30	1−	1−	NUM
ejpam-3003	676	31	γ	γ	X
ejpam-3003	676	32	2	2	NUM
ejpam-3003	676	33	(	(	PUNCT
ejpam-3003	676	34	g	g	PROPN
ejpam-3003	676	35	◦	◦	PROPN
ejpam-3003	676	36	∇u)(t	∇u)(t	PROPN
ejpam-3003	676	37	)	)	PUNCT
ejpam-3003	676	38	−	−	PROPN
ejpam-3003	677	1	ε(p+	ε(p+	PROPN
ejpam-3003	677	2	1−	1−	NUM
ejpam-3003	677	3	γ	γ	X
ejpam-3003	677	4	)	)	PUNCT
ejpam-3003	677	5	p+	p+	VERB
ejpam-3003	677	6	1	1	NUM
ejpam-3003	677	7	‖u‖p+1	‖u‖p+1	NOUN
ejpam-3003	677	8	p+1	p+1	NOUN
ejpam-3003	677	9	−	−	NOUN
ejpam-3003	677	10	ε‖∇u‖	ε‖∇u‖	NOUN
ejpam-3003	677	11	2	2	NUM
ejpam-3003	677	12	2	2	NUM
ejpam-3003	677	13	+	+	CCONJ
ejpam-3003	677	14	ε	ε	PROPN
ejpam-3003	677	15	∫	∫	PROPN
ejpam-3003	677	16	ω	ω	PROPN
ejpam-3003	677	17	∇u(t	∇u(t	PROPN
ejpam-3003	677	18	)	)	PUNCT
ejpam-3003	677	19	∫	∫	PROPN
ejpam-3003	677	20	t	t	PROPN
ejpam-3003	677	21	0	0	NUM
ejpam-3003	677	22	g(t−	g(t−	NOUN
ejpam-3003	677	23	s)∇u(s)dsdx+	s)∇u(s)dsdx+	ADJ
ejpam-3003	677	24	ε‖u‖p+1	ε‖u‖p+1	VERB
ejpam-3003	678	1	p+1	p+1	NOUN
ejpam-3003	678	2	−	−	NOUN
ejpam-3003	678	3	ε	ε	PROPN
ejpam-3003	678	4	µ	µ	PROPN
ejpam-3003	678	5	q+1	q+1	X
ejpam-3003	678	6	q	q	NOUN
ejpam-3003	679	1	+	+	NUM
ejpam-3003	679	2	1	1	NUM
ejpam-3003	679	3	‖u‖q+1	‖u‖q+1	PROPN
ejpam-3003	679	4	γ1,q+1	γ1,q+1	PUNCT
ejpam-3003	679	5	−	−	PROPN
ejpam-3003	679	6	ε	ε	PROPN
ejpam-3003	679	7	q	q	PROPN
ejpam-3003	679	8	q	q	PROPN
ejpam-3003	680	1	+	+	NUM
ejpam-3003	680	2	1	1	NUM
ejpam-3003	680	3	µ	µ	PRON
ejpam-3003	680	4	−	−	PROPN
ejpam-3003	680	5	q+1	q+1	NUM
ejpam-3003	680	6	q	q	PROPN
ejpam-3003	680	7	‖ut‖q+1	‖ut‖q+1	PROPN
ejpam-3003	680	8	γ1,q+1	γ1,q+1	PROPN
ejpam-3003	680	9	≥	≥	X
ejpam-3003	680	10	[	[	PUNCT
ejpam-3003	680	11	(	(	PUNCT
ejpam-3003	680	12	1−	1−	NUM
ejpam-3003	680	13	σ)n−σ(t)−	σ)n−σ(t)−	PROPN
ejpam-3003	680	14	ε	ε	PROPN
ejpam-3003	680	15	q	q	PROPN
ejpam-3003	680	16	q	q	PROPN
ejpam-3003	681	1	+	+	NUM
ejpam-3003	681	2	1	1	NUM
ejpam-3003	681	3	µ	µ	PRON
ejpam-3003	681	4	−	−	PROPN
ejpam-3003	681	5	q+1	q+1	NUM
ejpam-3003	681	6	q	q	X
ejpam-3003	681	7	]	]	X
ejpam-3003	681	8	‖ut‖q+1	‖ut‖q+1	PUNCT
ejpam-3003	681	9	γ1,q+1	γ1,q+1	PUNCT
ejpam-3003	682	1	+	+	CCONJ
ejpam-3003	682	2	ε(p+	ε(p+	PROPN
ejpam-3003	682	3	1−	1−	NUM
ejpam-3003	682	4	γ)n(t	γ)n(t	PROPN
ejpam-3003	682	5	)	)	PUNCT
ejpam-3003	683	1	+	+	CCONJ
ejpam-3003	683	2	ε	ε	PROPN
ejpam-3003	683	3	[	[	PUNCT
ejpam-3003	683	4	(	(	PUNCT
ejpam-3003	683	5	p+	p+	X
ejpam-3003	683	6	1−	1−	NUM
ejpam-3003	683	7	γ	γ	NOUN
ejpam-3003	683	8	2	2	NUM
ejpam-3003	683	9	−	−	PROPN
ejpam-3003	683	10	1)−	1)−	PROPN
ejpam-3003	683	11	(	(	PUNCT
ejpam-3003	683	12	p+	p+	PROPN
ejpam-3003	683	13	1−	1−	NUM
ejpam-3003	683	14	γ	γ	X
ejpam-3003	683	15	2	2	NUM
ejpam-3003	683	16	+	+	SYM
ejpam-3003	683	17	1	1	NUM
ejpam-3003	683	18	4ξ	4ξ	NUM
ejpam-3003	683	19	)	)	PUNCT
ejpam-3003	683	20	∫	∫	PROPN
ejpam-3003	683	21	t	t	PROPN
ejpam-3003	683	22	0	0	NUM
ejpam-3003	683	23	g(s)ds	g(s)ds	PROPN
ejpam-3003	683	24	]	]	PUNCT
ejpam-3003	683	25	‖∇u‖22	‖∇u‖22	PROPN
ejpam-3003	683	26	+	+	CCONJ
ejpam-3003	683	27	ε	ε	PROPN
ejpam-3003	683	28	[	[	PUNCT
ejpam-3003	683	29	1	1	NUM
ejpam-3003	683	30	ρ	ρ	NUM
ejpam-3003	683	31	+	+	X
ejpam-3003	683	32	p+	p+	PROPN
ejpam-3003	683	33	1−	1−	NUM
ejpam-3003	683	34	γ	γ	NOUN
ejpam-3003	683	35	ρ+	ρ+	NUM
ejpam-3003	683	36	1	1	NUM
ejpam-3003	683	37	]	]	PUNCT
ejpam-3003	683	38	‖ut‖ρ+1	‖ut‖ρ+1	VERB
ejpam-3003	683	39	ρ+1	ρ+1	NOUN
ejpam-3003	683	40	+	+	CCONJ
ejpam-3003	683	41	ε	ε	PROPN
ejpam-3003	683	42	[	[	PUNCT
ejpam-3003	683	43	p+	p+	NOUN
ejpam-3003	683	44	1−	1−	NUM
ejpam-3003	683	45	γ	γ	NOUN
ejpam-3003	683	46	2	2	NUM
ejpam-3003	683	47	−	−	PROPN
ejpam-3003	683	48	ξ	ξ	SYM
ejpam-3003	683	49	]	]	PUNCT
ejpam-3003	683	50	(	(	PUNCT
ejpam-3003	683	51	g	g	NOUN
ejpam-3003	683	52	◦	◦	NOUN
ejpam-3003	683	53	∇u)(t)−	∇u)(t)−	PROPN
ejpam-3003	683	54	ε(p+	ε(p+	PROPN
ejpam-3003	683	55	1−	1−	NUM
ejpam-3003	683	56	γ)βd̃	γ)βd̃	PROPN
ejpam-3003	683	57	+	+	CCONJ
ejpam-3003	683	58	ε	ε	PROPN
ejpam-3003	683	59	γ	γ	PROPN
ejpam-3003	683	60	p+	p+	PROPN
ejpam-3003	683	61	1	1	NUM
ejpam-3003	683	62	‖u‖p+1	‖u‖p+1	NOUN
ejpam-3003	683	63	p+1	p+1	NOUN
ejpam-3003	683	64	−	−	X
ejpam-3003	683	65	ε	ε	PROPN
ejpam-3003	683	66	µq+1	µq+1	PROPN
ejpam-3003	683	67	q	q	PROPN
ejpam-3003	684	1	+	+	NUM
ejpam-3003	684	2	1	1	NUM
ejpam-3003	684	3	‖u‖q+1	‖u‖q+1	PROPN
ejpam-3003	684	4	γ1,q+1	γ1,q+1	PROPN
ejpam-3003	684	5	.	.	PROPN
ejpam-3003	685	1	(	(	PUNCT
ejpam-3003	685	2	5.16	5.16	NUM
ejpam-3003	685	3	)	)	PUNCT
ejpam-3003	685	4	as	as	ADP
ejpam-3003	685	5	in	in	ADP
ejpam-3003	685	6	[	[	X
ejpam-3003	685	7	9	9	NUM
ejpam-3003	685	8	]	]	PUNCT
ejpam-3003	685	9	,	,	PUNCT
ejpam-3003	685	10	we	we	PRON
ejpam-3003	685	11	take	take	VERB
ejpam-3003	685	12	µ	µ	PRON
ejpam-3003	685	13	−	−	PROPN
ejpam-3003	685	14	q+1	q+1	NUM
ejpam-3003	685	15	q	q	NOUN
ejpam-3003	685	16	=	=	SYM
ejpam-3003	685	17	dn−σ(t	dn−σ(t	NOUN
ejpam-3003	685	18	)	)	PUNCT
ejpam-3003	685	19	for	for	SCONJ
ejpam-3003	685	20	some	some	DET
ejpam-3003	685	21	large	large	ADJ
ejpam-3003	685	22	d	d	NOUN
ejpam-3003	685	23	to	to	PART
ejpam-3003	685	24	be	be	AUX
ejpam-3003	685	25	specified	specify	VERB
ejpam-3003	685	26	later	later	ADV
ejpam-3003	685	27	and	and	CCONJ
ejpam-3003	685	28	if	if	SCONJ
ejpam-3003	685	29	this	this	PRON
ejpam-3003	685	30	is	be	AUX
ejpam-3003	685	31	substituted	substitute	VERB
ejpam-3003	685	32	in	in	ADP
ejpam-3003	685	33	(	(	PUNCT
ejpam-3003	685	34	5.16	5.16	NUM
ejpam-3003	685	35	)	)	PUNCT
ejpam-3003	685	36	,	,	PUNCT
ejpam-3003	685	37	we	we	PRON
ejpam-3003	685	38	have	have	VERB
ejpam-3003	685	39	g′(t	g′(t	NOUN
ejpam-3003	685	40	)	)	PUNCT
ejpam-3003	685	41	≥	≥	NOUN
ejpam-3003	685	42	[	[	PUNCT
ejpam-3003	685	43	(	(	PUNCT
ejpam-3003	685	44	1−	1−	NUM
ejpam-3003	685	45	σ)−	σ)−	PROPN
ejpam-3003	685	46	ε	ε	PROPN
ejpam-3003	685	47	q	q	PROPN
ejpam-3003	685	48	q	q	PROPN
ejpam-3003	686	1	+	+	NUM
ejpam-3003	686	2	1	1	NUM
ejpam-3003	686	3	d	d	NOUN
ejpam-3003	686	4	]	]	X
ejpam-3003	686	5	n−σ(t)‖ut‖q+1	n−σ(t)‖ut‖q+1	PROPN
ejpam-3003	686	6	γ1,q+1	γ1,q+1	PROPN
ejpam-3003	687	1	+	+	NUM
ejpam-3003	687	2	ε	ε	PROPN
ejpam-3003	687	3	[	[	PUNCT
ejpam-3003	687	4	1	1	NUM
ejpam-3003	687	5	ρ	ρ	NUM
ejpam-3003	687	6	+	+	X
ejpam-3003	687	7	p+	p+	PROPN
ejpam-3003	687	8	1−	1−	NUM
ejpam-3003	687	9	γ	γ	NOUN
ejpam-3003	687	10	ρ+	ρ+	NUM
ejpam-3003	687	11	1	1	NUM
ejpam-3003	687	12	]	]	PUNCT
ejpam-3003	687	13	‖ut‖ρ+1	‖ut‖ρ+1	VERB
ejpam-3003	687	14	ρ+1	ρ+1	NOUN
ejpam-3003	687	15	+	+	CCONJ
ejpam-3003	687	16	ε	ε	X
ejpam-3003	687	17	[	[	PUNCT
ejpam-3003	687	18	(	(	PUNCT
ejpam-3003	687	19	p+	p+	PROPN
ejpam-3003	687	20	1−	1−	NUM
ejpam-3003	687	21	γ)n(t)−	γ)n(t)−	PROPN
ejpam-3003	687	22	d−q	d−q	PROPN
ejpam-3003	687	23	q	q	PROPN
ejpam-3003	688	1	+	+	PROPN
ejpam-3003	688	2	1	1	NUM
ejpam-3003	688	3	nσq(t)‖u‖q+1	nσq(t)‖u‖q+1	PROPN
ejpam-3003	688	4	γ1,q+1	γ1,q+1	PUNCT
ejpam-3003	688	5	]	]	PUNCT
ejpam-3003	689	1	−	−	PROPN
ejpam-3003	689	2	ε(p+	ε(p+	PROPN
ejpam-3003	689	3	1−	1−	NUM
ejpam-3003	689	4	γ)βd̃	γ)βd̃	NOUN
ejpam-3003	689	5	+	+	CCONJ
ejpam-3003	689	6	ε	ε	PROPN
ejpam-3003	689	7	[	[	PUNCT
ejpam-3003	689	8	(	(	PUNCT
ejpam-3003	689	9	p+	p+	X
ejpam-3003	689	10	1−	1−	NUM
ejpam-3003	689	11	γ	γ	NOUN
ejpam-3003	689	12	2	2	NUM
ejpam-3003	689	13	−	−	PROPN
ejpam-3003	689	14	1)−	1)−	PROPN
ejpam-3003	689	15	(	(	PUNCT
ejpam-3003	689	16	p+	p+	PROPN
ejpam-3003	689	17	1−	1−	NUM
ejpam-3003	689	18	γ	γ	X
ejpam-3003	689	19	2	2	NUM
ejpam-3003	689	20	+	+	SYM
ejpam-3003	689	21	1	1	NUM
ejpam-3003	689	22	4ξ	4ξ	NUM
ejpam-3003	689	23	)	)	PUNCT
ejpam-3003	689	24	∫	∫	PROPN
ejpam-3003	690	1	t	t	PROPN
ejpam-3003	690	2	0	0	NUM
ejpam-3003	690	3	g(s)ds	g(s)ds	PROPN
ejpam-3003	690	4	]	]	PUNCT
ejpam-3003	690	5	‖∇u‖22	‖∇u‖22	PROPN
ejpam-3003	690	6	+	+	CCONJ
ejpam-3003	690	7	ε	ε	PROPN
ejpam-3003	690	8	[	[	PUNCT
ejpam-3003	690	9	p+	p+	NOUN
ejpam-3003	690	10	1−	1−	NUM
ejpam-3003	690	11	γ	γ	NOUN
ejpam-3003	690	12	2	2	NUM
ejpam-3003	690	13	−	−	PROPN
ejpam-3003	690	14	ξ	ξ	SYM
ejpam-3003	690	15	]	]	PUNCT
ejpam-3003	690	16	(	(	PUNCT
ejpam-3003	690	17	g	g	PROPN
ejpam-3003	690	18	◦	◦	PROPN
ejpam-3003	690	19	∇u)(t	∇u)(t	PROPN
ejpam-3003	690	20	)	)	PUNCT
ejpam-3003	691	1	+	+	CCONJ
ejpam-3003	691	2	ε	ε	PROPN
ejpam-3003	691	3	γ	γ	PROPN
ejpam-3003	691	4	p+	p+	VERB
ejpam-3003	691	5	1	1	NUM
ejpam-3003	691	6	‖u‖p+1	‖u‖p+1	NOUN
ejpam-3003	691	7	p+1	p+1	NOUN
ejpam-3003	691	8	.	.	PUNCT
ejpam-3003	692	1	(	(	PUNCT
ejpam-3003	692	2	5.17	5.17	NUM
ejpam-3003	692	3	)	)	PUNCT
ejpam-3003	692	4	taking	take	VERB
ejpam-3003	692	5	into	into	ADP
ejpam-3003	692	6	account	account	NOUN
ejpam-3003	692	7	the	the	DET
ejpam-3003	692	8	lemma	lemma	PROPN
ejpam-3003	692	9	4	4	NUM
ejpam-3003	692	10	,	,	PUNCT
ejpam-3003	692	11	we	we	PRON
ejpam-3003	692	12	deduce	deduce	VERB
ejpam-3003	692	13	−ε(p+	−ε(p+	PROPN
ejpam-3003	692	14	1−	1−	NUM
ejpam-3003	692	15	γ)βd̃	γ)βd̃	PROPN
ejpam-3003	692	16	≥	≥	X
ejpam-3003	692	17	−ε(p+	−ε(p+	VERB
ejpam-3003	692	18	1)β	1)β	NUM
ejpam-3003	692	19	(	(	PUNCT
ejpam-3003	692	20	1	1	NUM
ejpam-3003	692	21	2	2	NUM
ejpam-3003	692	22	−	−	NUM
ejpam-3003	692	23	1	1	NUM
ejpam-3003	692	24	p+	p+	NOUN
ejpam-3003	692	25	1	1	NUM
ejpam-3003	692	26	)	)	PUNCT
ejpam-3003	693	1	[	[	X
ejpam-3003	693	2	l(t)‖∇u‖22	l(t)‖∇u‖22	X
ejpam-3003	693	3	+	+	CCONJ
ejpam-3003	693	4	(	(	PUNCT
ejpam-3003	693	5	g	g	PROPN
ejpam-3003	693	6	◦	◦	PROPN
ejpam-3003	693	7	∇u)(t	∇u)(t	PROPN
ejpam-3003	693	8	)	)	PUNCT
ejpam-3003	693	9	]	]	PUNCT
ejpam-3003	694	1	h.f	h.f	PROPN
ejpam-3003	694	2	.	.	PROPN
ejpam-3003	694	3	di	di	PROPN
ejpam-3003	694	4	,	,	PUNCT
ejpam-3003	694	5	y.d	y.d	PROPN
ejpam-3003	694	6	.	.	PROPN
ejpam-3003	694	7	shang	shang	PROPN
ejpam-3003	694	8	/	/	SYM
ejpam-3003	694	9	eur	eur	PROPN
ejpam-3003	694	10	.	.	PUNCT
ejpam-3003	695	1	j.	j.	PROPN
ejpam-3003	695	2	pure	pure	PROPN
ejpam-3003	695	3	appl	appl	PROPN
ejpam-3003	695	4	.	.	PROPN
ejpam-3003	695	5	math	math	PROPN
ejpam-3003	695	6	,	,	PUNCT
ejpam-3003	695	7	10	10	NUM
ejpam-3003	695	8	(	(	PUNCT
ejpam-3003	695	9	4	4	NUM
ejpam-3003	695	10	)	)	PUNCT
ejpam-3003	695	11	(	(	PUNCT
ejpam-3003	695	12	2017	2017	NUM
ejpam-3003	695	13	)	)	PUNCT
ejpam-3003	695	14	,	,	PUNCT
ejpam-3003	695	15	668	668	NUM
ejpam-3003	695	16	-	-	SYM
ejpam-3003	695	17	701	701	NUM
ejpam-3003	695	18	696	696	NUM
ejpam-3003	695	19	=	=	SYM
ejpam-3003	695	20	−εβ(p−	−εβ(p−	NUM
ejpam-3003	695	21	1	1	NUM
ejpam-3003	695	22	)	)	PUNCT
ejpam-3003	695	23	2	2	NUM
ejpam-3003	695	24	[	[	NOUN
ejpam-3003	695	25	l(t)‖∇u‖22	l(t)‖∇u‖22	X
ejpam-3003	695	26	+	+	CCONJ
ejpam-3003	695	27	(	(	PUNCT
ejpam-3003	695	28	g	g	PROPN
ejpam-3003	695	29	◦	◦	PROPN
ejpam-3003	695	30	∇u)(t	∇u)(t	PROPN
ejpam-3003	695	31	)	)	PUNCT
ejpam-3003	695	32	]	]	PUNCT
ejpam-3003	695	33	.	.	PUNCT
ejpam-3003	696	1	(	(	PUNCT
ejpam-3003	696	2	5.18	5.18	NUM
ejpam-3003	696	3	)	)	PUNCT
ejpam-3003	696	4	from	from	ADP
ejpam-3003	696	5	(	(	PUNCT
ejpam-3003	696	6	5.5),(5.9	5.5),(5.9	NUM
ejpam-3003	696	7	)	)	PUNCT
ejpam-3003	696	8	and	and	CCONJ
ejpam-3003	696	9	trace	trace	NOUN
ejpam-3003	696	10	theorem	theorem	VERB
ejpam-3003	696	11	,	,	PUNCT
ejpam-3003	696	12	we	we	PRON
ejpam-3003	696	13	get	get	VERB
ejpam-3003	696	14	nσq(t)‖u‖q+1	nσq(t)‖u‖q+1	PROPN
ejpam-3003	696	15	γ1,q+1	γ1,q+1	PROPN
ejpam-3003	696	16	≤	≤	PROPN
ejpam-3003	696	17	(	(	PUNCT
ejpam-3003	696	18	β(p−	β(p−	VERB
ejpam-3003	696	19	1	1	NUM
ejpam-3003	696	20	)	)	PUNCT
ejpam-3003	696	21	+	+	CCONJ
ejpam-3003	696	22	2	2	NUM
ejpam-3003	696	23	2(p+	2(p+	NUM
ejpam-3003	696	24	1	1	NUM
ejpam-3003	696	25	)	)	PUNCT
ejpam-3003	696	26	)	)	PUNCT
ejpam-3003	697	1	σq	σq	PROPN
ejpam-3003	698	1	‖u‖(p+1)σq	‖u‖(p+1)σq	PROPN
ejpam-3003	698	2	p+1	p+1	PROPN
ejpam-3003	698	3	‖u‖q+1	‖u‖q+1	PROPN
ejpam-3003	698	4	γ1,q+1	γ1,q+1	PROPN
ejpam-3003	698	5	≤	≤	PROPN
ejpam-3003	698	6	(	(	PUNCT
ejpam-3003	698	7	β(p−	β(p−	VERB
ejpam-3003	698	8	1	1	NUM
ejpam-3003	698	9	)	)	PUNCT
ejpam-3003	698	10	+	+	CCONJ
ejpam-3003	698	11	2	2	NUM
ejpam-3003	698	12	2(p+	2(p+	NUM
ejpam-3003	698	13	1	1	NUM
ejpam-3003	698	14	)	)	PUNCT
ejpam-3003	698	15	)	)	PUNCT
ejpam-3003	699	1	σq	σq	PROPN
ejpam-3003	699	2	‖u‖(p+1)σq	‖u‖(p+1)σq	PROPN
ejpam-3003	699	3	p+1	p+1	PROPN
ejpam-3003	699	4	bq+1	bq+1	PROPN
ejpam-3003	699	5	q+1‖∇u‖	q+1‖∇u‖	NUM
ejpam-3003	699	6	q+1	q+1	NUM
ejpam-3003	699	7	2	2	NUM
ejpam-3003	699	8	≤	≤	NOUN
ejpam-3003	699	9	(	(	PUNCT
ejpam-3003	699	10	β(p−	β(p−	VERB
ejpam-3003	699	11	1	1	NUM
ejpam-3003	699	12	)	)	PUNCT
ejpam-3003	699	13	+	+	CCONJ
ejpam-3003	699	14	2	2	NUM
ejpam-3003	699	15	2(p+	2(p+	NUM
ejpam-3003	699	16	1	1	NUM
ejpam-3003	699	17	)	)	PUNCT
ejpam-3003	699	18	)	)	PUNCT
ejpam-3003	700	1	σq	σq	PROPN
ejpam-3003	700	2	‖u‖(p+1)σq	‖u‖(p+1)σq	PROPN
ejpam-3003	700	3	p+1	p+1	PROPN
ejpam-3003	700	4	bq+1	bq+1	PUNCT
ejpam-3003	701	1	q+1δ	q+1δ	PROPN
ejpam-3003	701	2	q+1	q+1	NUM
ejpam-3003	701	3	2	2	NUM
ejpam-3003	701	4	2	2	NUM
ejpam-3003	701	5	.	.	PUNCT
ejpam-3003	702	1	(	(	PUNCT
ejpam-3003	702	2	5.19	5.19	NUM
ejpam-3003	702	3	)	)	PUNCT
ejpam-3003	702	4	using	use	VERB
ejpam-3003	702	5	the	the	DET
ejpam-3003	702	6	following	follow	VERB
ejpam-3003	702	7	inequality	inequality	NOUN
ejpam-3003	702	8	zθ	zθ	NOUN
ejpam-3003	702	9	≤	≤	NOUN
ejpam-3003	702	10	z	z	NOUN
ejpam-3003	703	1	+	+	CCONJ
ejpam-3003	703	2	1	1	NUM
ejpam-3003	703	3	≤	≤	NOUN
ejpam-3003	703	4	(	(	PUNCT
ejpam-3003	703	5	1	1	NUM
ejpam-3003	703	6	+	+	SYM
ejpam-3003	703	7	1	1	NUM
ejpam-3003	703	8	ς	ς	NOUN
ejpam-3003	703	9	)	)	PUNCT
ejpam-3003	703	10	(	(	PUNCT
ejpam-3003	703	11	z	z	X
ejpam-3003	703	12	+	+	CCONJ
ejpam-3003	703	13	ς	ς	PROPN
ejpam-3003	703	14	)	)	PUNCT
ejpam-3003	703	15	,	,	PUNCT
ejpam-3003	703	16	0	0	NUM
ejpam-3003	703	17	<	<	X
ejpam-3003	703	18	θ	θ	X
ejpam-3003	703	19	≤	≤	NUM
ejpam-3003	703	20	1	1	NUM
ejpam-3003	703	21	,	,	PUNCT
ejpam-3003	703	22	∀	∀	X
ejpam-3003	703	23	z	z	NOUN
ejpam-3003	703	24	>	>	X
ejpam-3003	703	25	0	0	NUM
ejpam-3003	703	26	,	,	PUNCT
ejpam-3003	703	27	ς	ς	PROPN
ejpam-3003	703	28	>	>	X
ejpam-3003	703	29	0	0	NUM
ejpam-3003	703	30	,	,	PUNCT
ejpam-3003	703	31	and	and	CCONJ
ejpam-3003	703	32	taking	take	VERB
ejpam-3003	703	33	ς	ς	PROPN
ejpam-3003	703	34	=	=	SYM
ejpam-3003	703	35	n(0	n(0	PROPN
ejpam-3003	703	36	)	)	PUNCT
ejpam-3003	703	37	,	,	PUNCT
ejpam-3003	703	38	then	then	ADV
ejpam-3003	703	39	we	we	PRON
ejpam-3003	703	40	have	have	VERB
ejpam-3003	703	41	nσq(t)‖u‖q+1	nσq(t)‖u‖q+1	PROPN
ejpam-3003	703	42	γ1,q+1	γ1,q+1	PROPN
ejpam-3003	703	43	≤	≤	PROPN
ejpam-3003	703	44	(	(	PUNCT
ejpam-3003	703	45	β(p−	β(p−	VERB
ejpam-3003	703	46	1	1	NUM
ejpam-3003	703	47	)	)	PUNCT
ejpam-3003	703	48	+	+	CCONJ
ejpam-3003	703	49	2	2	NUM
ejpam-3003	703	50	2(p+	2(p+	NUM
ejpam-3003	703	51	1	1	NUM
ejpam-3003	703	52	)	)	PUNCT
ejpam-3003	703	53	)	)	PUNCT
ejpam-3003	704	1	σq	σq	NOUN
ejpam-3003	704	2	bq+1	bq+1	NOUN
ejpam-3003	705	1	q+1δ	q+1δ	PROPN
ejpam-3003	705	2	q+1	q+1	NUM
ejpam-3003	705	3	2	2	NUM
ejpam-3003	705	4	2	2	NUM
ejpam-3003	705	5	k	k	NOUN
ejpam-3003	705	6	(	(	PUNCT
ejpam-3003	705	7	‖u‖(p+1	‖u‖(p+1	PROPN
ejpam-3003	705	8	)	)	PUNCT
ejpam-3003	705	9	p+1	p+1	NOUN
ejpam-3003	705	10	+	+	PROPN
ejpam-3003	705	11	n(t	n(t	X
ejpam-3003	705	12	)	)	PUNCT
ejpam-3003	705	13	)	)	PUNCT
ejpam-3003	705	14	,	,	PUNCT
ejpam-3003	705	15	(	(	PUNCT
ejpam-3003	705	16	5.20	5.20	NUM
ejpam-3003	705	17	)	)	PUNCT
ejpam-3003	706	1	where	where	SCONJ
ejpam-3003	706	2	k	k	NOUN
ejpam-3003	706	3	=	=	SYM
ejpam-3003	706	4	1	1	NUM
ejpam-3003	706	5	+	+	SYM
ejpam-3003	706	6	1	1	NUM
ejpam-3003	706	7	n(0	n(0	PROPN
ejpam-3003	706	8	)	)	PUNCT
ejpam-3003	706	9	.	.	PUNCT
ejpam-3003	707	1	inserting	insert	VERB
ejpam-3003	707	2	(	(	PUNCT
ejpam-3003	707	3	5.18	5.18	NUM
ejpam-3003	707	4	)	)	PUNCT
ejpam-3003	707	5	and	and	CCONJ
ejpam-3003	707	6	(	(	PUNCT
ejpam-3003	707	7	5.20	5.20	NUM
ejpam-3003	707	8	)	)	PUNCT
ejpam-3003	707	9	into	into	ADP
ejpam-3003	707	10	(	(	PUNCT
ejpam-3003	707	11	5.17	5.17	NUM
ejpam-3003	707	12	)	)	PUNCT
ejpam-3003	707	13	,	,	PUNCT
ejpam-3003	707	14	we	we	PRON
ejpam-3003	707	15	obtain	obtain	VERB
ejpam-3003	707	16	g′(t	g′(t	NOUN
ejpam-3003	707	17	)	)	PUNCT
ejpam-3003	707	18	≥	≥	NOUN
ejpam-3003	707	19	[	[	PUNCT
ejpam-3003	707	20	(	(	PUNCT
ejpam-3003	707	21	1−	1−	NUM
ejpam-3003	707	22	σ)−	σ)−	PROPN
ejpam-3003	707	23	ε	ε	PROPN
ejpam-3003	707	24	q	q	PROPN
ejpam-3003	707	25	q	q	PROPN
ejpam-3003	708	1	+	+	NUM
ejpam-3003	708	2	1	1	NUM
ejpam-3003	708	3	d	d	NOUN
ejpam-3003	708	4	]	]	X
ejpam-3003	708	5	n−σ(t)‖ut‖q+1	n−σ(t)‖ut‖q+1	PROPN
ejpam-3003	708	6	γ1,q+1	γ1,q+1	PROPN
ejpam-3003	709	1	+	+	NUM
ejpam-3003	709	2	ε	ε	PROPN
ejpam-3003	709	3	[	[	PUNCT
ejpam-3003	709	4	1	1	NUM
ejpam-3003	709	5	ρ	ρ	NUM
ejpam-3003	709	6	+	+	X
ejpam-3003	709	7	p+	p+	PROPN
ejpam-3003	709	8	1−	1−	NUM
ejpam-3003	709	9	γ	γ	NOUN
ejpam-3003	709	10	ρ+	ρ+	NUM
ejpam-3003	709	11	1	1	NUM
ejpam-3003	709	12	]	]	PUNCT
ejpam-3003	709	13	‖ut‖ρ+1	‖ut‖ρ+1	VERB
ejpam-3003	709	14	ρ+1	ρ+1	NOUN
ejpam-3003	709	15	+	+	CCONJ
ejpam-3003	709	16	ε	ε	X
ejpam-3003	709	17	[	[	PUNCT
ejpam-3003	709	18	(	(	PUNCT
ejpam-3003	709	19	p+	p+	NOUN
ejpam-3003	709	20	1−	1−	NUM
ejpam-3003	709	21	γ)−	γ)−	PROPN
ejpam-3003	709	22	d−q	d−q	X
ejpam-3003	709	23	q	q	PROPN
ejpam-3003	710	1	+	+	NUM
ejpam-3003	710	2	1	1	NUM
ejpam-3003	710	3	(	(	PUNCT
ejpam-3003	710	4	β(p−	β(p−	PROPN
ejpam-3003	710	5	1	1	NUM
ejpam-3003	710	6	)	)	PUNCT
ejpam-3003	710	7	+	+	CCONJ
ejpam-3003	710	8	2	2	NUM
ejpam-3003	710	9	2(p+	2(p+	NUM
ejpam-3003	710	10	1	1	NUM
ejpam-3003	710	11	)	)	PUNCT
ejpam-3003	710	12	)	)	PUNCT
ejpam-3003	711	1	σq	σq	NOUN
ejpam-3003	711	2	bq+1	bq+1	NOUN
ejpam-3003	712	1	q+1δ	q+1δ	PROPN
ejpam-3003	712	2	q+1	q+1	NUM
ejpam-3003	712	3	2	2	NUM
ejpam-3003	712	4	2	2	NUM
ejpam-3003	712	5	k	k	NOUN
ejpam-3003	712	6	]	]	X
ejpam-3003	712	7	n(t	n(t	PROPN
ejpam-3003	712	8	)	)	PUNCT
ejpam-3003	713	1	+	+	CCONJ
ejpam-3003	713	2	ε	ε	PROPN
ejpam-3003	713	3	[	[	PUNCT
ejpam-3003	713	4	p−	p−	NOUN
ejpam-3003	713	5	1−	1−	NUM
ejpam-3003	713	6	γ	γ	X
ejpam-3003	713	7	2	2	NUM
ejpam-3003	713	8	−	−	NOUN
ejpam-3003	713	9	β(p−	β(p−	ADJ
ejpam-3003	713	10	1	1	NUM
ejpam-3003	713	11	)	)	PUNCT
ejpam-3003	713	12	2	2	NUM
ejpam-3003	713	13	−	−	PROPN
ejpam-3003	713	14	(	(	PUNCT
ejpam-3003	713	15	p+	p+	PROPN
ejpam-3003	713	16	1−	1−	NUM
ejpam-3003	713	17	γ	γ	SYM
ejpam-3003	713	18	2	2	NUM
ejpam-3003	713	19	−	−	NOUN
ejpam-3003	713	20	β(p−	β(p−	ADJ
ejpam-3003	713	21	1	1	NUM
ejpam-3003	713	22	)	)	PUNCT
ejpam-3003	713	23	2	2	NUM
ejpam-3003	713	24	+	+	SYM
ejpam-3003	713	25	1	1	NUM
ejpam-3003	713	26	4ξ	4ξ	NUM
ejpam-3003	713	27	)	)	PUNCT
ejpam-3003	713	28	∫	∫	PROPN
ejpam-3003	714	1	t	t	PROPN
ejpam-3003	714	2	0	0	NUM
ejpam-3003	714	3	g(s)ds	g(s)ds	PROPN
ejpam-3003	714	4	]	]	PUNCT
ejpam-3003	714	5	‖∇u‖22	‖∇u‖22	PROPN
ejpam-3003	714	6	+	+	CCONJ
ejpam-3003	714	7	ε	ε	PROPN
ejpam-3003	714	8	[	[	PUNCT
ejpam-3003	714	9	p+	p+	NOUN
ejpam-3003	714	10	1−	1−	NUM
ejpam-3003	714	11	γ	γ	SYM
ejpam-3003	714	12	2	2	NUM
ejpam-3003	714	13	−	−	NOUN
ejpam-3003	714	14	β(p−	β(p−	ADJ
ejpam-3003	714	15	1	1	NUM
ejpam-3003	714	16	)	)	PUNCT
ejpam-3003	714	17	2	2	NUM
ejpam-3003	714	18	−	−	PROPN
ejpam-3003	714	19	ξ	ξ	SYM
ejpam-3003	714	20	]	]	PUNCT
ejpam-3003	714	21	(	(	PUNCT
ejpam-3003	714	22	g	g	PROPN
ejpam-3003	714	23	◦	◦	PROPN
ejpam-3003	714	24	∇u)(t	∇u)(t	PROPN
ejpam-3003	714	25	)	)	PUNCT
ejpam-3003	714	26	+	+	NUM
ejpam-3003	714	27	ε	ε	PROPN
ejpam-3003	714	28	[	[	PUNCT
ejpam-3003	714	29	γ	γ	X
ejpam-3003	714	30	p+	p+	VERB
ejpam-3003	714	31	1	1	NUM
ejpam-3003	714	32	−	−	NOUN
ejpam-3003	714	33	d−q	d−q	X
ejpam-3003	714	34	q	q	PROPN
ejpam-3003	715	1	+	+	NUM
ejpam-3003	715	2	1	1	NUM
ejpam-3003	715	3	(	(	PUNCT
ejpam-3003	715	4	β(p−	β(p−	PROPN
ejpam-3003	715	5	1	1	NUM
ejpam-3003	715	6	)	)	PUNCT
ejpam-3003	715	7	+	+	CCONJ
ejpam-3003	715	8	2	2	NUM
ejpam-3003	715	9	2(p+	2(p+	NUM
ejpam-3003	715	10	1	1	NUM
ejpam-3003	715	11	)	)	PUNCT
ejpam-3003	715	12	)	)	PUNCT
ejpam-3003	716	1	σq	σq	NOUN
ejpam-3003	716	2	bq+1	bq+1	NOUN
ejpam-3003	717	1	q+1δ	q+1δ	PROPN
ejpam-3003	717	2	q+1	q+1	NUM
ejpam-3003	717	3	2	2	NUM
ejpam-3003	717	4	2	2	NUM
ejpam-3003	717	5	k	k	NOUN
ejpam-3003	717	6	]	]	PUNCT
ejpam-3003	717	7	‖u‖p+1	‖u‖p+1	PUNCT
ejpam-3003	717	8	p+1	p+1	NOUN
ejpam-3003	717	9	=	=	PUNCT
ejpam-3003	718	1	k1n	k1n	PROPN
ejpam-3003	718	2	−σ(t)‖ut‖q+1	−σ(t)‖ut‖q+1	PROPN
ejpam-3003	718	3	γ1,q+1	γ1,q+1	PROPN
ejpam-3003	719	1	+	+	NUM
ejpam-3003	719	2	ε	ε	PROPN
ejpam-3003	719	3	[	[	PUNCT
ejpam-3003	719	4	1	1	NUM
ejpam-3003	719	5	ρ	ρ	NUM
ejpam-3003	719	6	+	+	X
ejpam-3003	719	7	p+	p+	PROPN
ejpam-3003	719	8	1−	1−	NUM
ejpam-3003	719	9	γ	γ	NOUN
ejpam-3003	719	10	ρ+	ρ+	NUM
ejpam-3003	719	11	1	1	NUM
ejpam-3003	719	12	]	]	PUNCT
ejpam-3003	719	13	‖ut‖ρ+1	‖ut‖ρ+1	VERB
ejpam-3003	719	14	ρ+1	ρ+1	ADJ
ejpam-3003	720	1	+	+	ADJ
ejpam-3003	720	2	k2n(t	k2n(t	X
ejpam-3003	720	3	)	)	PUNCT
ejpam-3003	720	4	+	+	NOUN
ejpam-3003	720	5	k3‖u‖p+1	k3‖u‖p+1	NOUN
ejpam-3003	720	6	p+1	p+1	NOUN
ejpam-3003	721	1	+	+	NOUN
ejpam-3003	721	2	k4‖∇u‖22	k4‖∇u‖22	X
ejpam-3003	721	3	+	+	ADJ
ejpam-3003	721	4	k5(g	k5(g	PROPN
ejpam-3003	721	5	◦	◦	NOUN
ejpam-3003	721	6	∇u)(t	∇u)(t	PROPN
ejpam-3003	721	7	)	)	PUNCT
ejpam-3003	721	8	.	.	PUNCT
ejpam-3003	722	1	(	(	PUNCT
ejpam-3003	722	2	5.21	5.21	NUM
ejpam-3003	722	3	)	)	PUNCT
ejpam-3003	722	4	utilizing	utilizing	NOUN
ejpam-3003	722	5	(	(	PUNCT
ejpam-3003	722	6	5.2	5.2	NUM
ejpam-3003	722	7	)	)	PUNCT
ejpam-3003	722	8	and	and	CCONJ
ejpam-3003	722	9	taking	take	VERB
ejpam-3003	722	10	0	0	NUM
ejpam-3003	722	11	<	<	X
ejpam-3003	722	12	ξ	ξ	X
ejpam-3003	722	13	≤	≤	NOUN
ejpam-3003	722	14	(	(	PUNCT
ejpam-3003	722	15	1−β)(p−1	1−β)(p−1	NUM
ejpam-3003	722	16	)	)	PUNCT
ejpam-3003	722	17	2	2	NUM
ejpam-3003	722	18	+	+	SYM
ejpam-3003	722	19	2−γ	2−γ	NUM
ejpam-3003	722	20	2	2	NUM
ejpam-3003	722	21	,	,	PUNCT
ejpam-3003	722	22	we	we	PRON
ejpam-3003	722	23	have	have	VERB
ejpam-3003	722	24	k4	k4	NOUN
ejpam-3003	722	25	=	=	SYM
ejpam-3003	722	26	(	(	PUNCT
ejpam-3003	722	27	p−	p−	NOUN
ejpam-3003	722	28	1)(1−	1)(1−	NUM
ejpam-3003	722	29	β)−	β)−	PUNCT
ejpam-3003	722	30	γ	γ	X
ejpam-3003	722	31	2	2	NUM
ejpam-3003	722	32	−	−	PROPN
ejpam-3003	722	33	(	(	PUNCT
ejpam-3003	722	34	(	(	PUNCT
ejpam-3003	722	35	1−	1−	NUM
ejpam-3003	722	36	β)(p−	β)(p−	NOUN
ejpam-3003	722	37	1	1	NUM
ejpam-3003	722	38	)	)	PUNCT
ejpam-3003	722	39	2	2	NUM
ejpam-3003	722	40	+	+	CCONJ
ejpam-3003	722	41	2−	2−	NUM
ejpam-3003	722	42	γ	γ	NOUN
ejpam-3003	722	43	2	2	NUM
ejpam-3003	722	44	+	+	SYM
ejpam-3003	722	45	1	1	NUM
ejpam-3003	722	46	4ξ	4ξ	NUM
ejpam-3003	722	47	)	)	PUNCT
ejpam-3003	723	1	∫	∫	PROPN
ejpam-3003	723	2	t	t	PROPN
ejpam-3003	723	3	0	0	NUM
ejpam-3003	724	1	g(s)ds	g(s)ds	X
ejpam-3003	724	2	>	>	X
ejpam-3003	724	3	0	0	NUM
ejpam-3003	724	4	,	,	PUNCT
ejpam-3003	724	5	(	(	PUNCT
ejpam-3003	724	6	5.22	5.22	NUM
ejpam-3003	724	7	)	)	PUNCT
ejpam-3003	724	8	k5	k5	PROPN
ejpam-3003	724	9	=	=	SYM
ejpam-3003	724	10	(	(	PUNCT
ejpam-3003	724	11	1−	1−	NUM
ejpam-3003	724	12	β)(p−	β)(p−	NOUN
ejpam-3003	724	13	1	1	NUM
ejpam-3003	724	14	)	)	PUNCT
ejpam-3003	724	15	2	2	NUM
ejpam-3003	724	16	+	+	NUM
ejpam-3003	724	17	2−	2−	NUM
ejpam-3003	724	18	γ	γ	NOUN
ejpam-3003	724	19	2	2	NUM
ejpam-3003	724	20	−	−	PROPN
ejpam-3003	724	21	ξ	ξ	X
ejpam-3003	724	22	≥	≥	NOUN
ejpam-3003	724	23	0	0	NUM
ejpam-3003	724	24	,	,	PUNCT
ejpam-3003	724	25	(	(	PUNCT
ejpam-3003	724	26	5.23	5.23	NUM
ejpam-3003	724	27	)	)	PUNCT
ejpam-3003	724	28	h.f	h.f	PROPN
ejpam-3003	724	29	.	.	PROPN
ejpam-3003	724	30	di	di	PROPN
ejpam-3003	724	31	,	,	PUNCT
ejpam-3003	724	32	y.d	y.d	PROPN
ejpam-3003	724	33	.	.	PROPN
ejpam-3003	724	34	shang	shang	PROPN
ejpam-3003	724	35	/	/	SYM
ejpam-3003	724	36	eur	eur	PROPN
ejpam-3003	724	37	.	.	PUNCT
ejpam-3003	725	1	j.	j.	PROPN
ejpam-3003	725	2	pure	pure	PROPN
ejpam-3003	725	3	appl	appl	PROPN
ejpam-3003	725	4	.	.	PROPN
ejpam-3003	725	5	math	math	PROPN
ejpam-3003	725	6	,	,	PUNCT
ejpam-3003	725	7	10	10	NUM
ejpam-3003	725	8	(	(	PUNCT
ejpam-3003	725	9	4	4	NUM
ejpam-3003	725	10	)	)	PUNCT
ejpam-3003	725	11	(	(	PUNCT
ejpam-3003	725	12	2017	2017	NUM
ejpam-3003	725	13	)	)	PUNCT
ejpam-3003	725	14	,	,	PUNCT
ejpam-3003	725	15	668	668	NUM
ejpam-3003	725	16	-	-	SYM
ejpam-3003	725	17	701	701	NUM
ejpam-3003	725	18	697	697	NUM
ejpam-3003	725	19	where	where	SCONJ
ejpam-3003	725	20	the	the	DET
ejpam-3003	725	21	positive	positive	ADJ
ejpam-3003	725	22	constant	constant	ADJ
ejpam-3003	725	23	γ	γ	NOUN
ejpam-3003	725	24	satisfies	satisfie	NOUN
ejpam-3003	725	25	0	0	PUNCT
ejpam-3003	725	26	<	<	X
ejpam-3003	725	27	γ	γ	X
ejpam-3003	725	28	<	<	X
ejpam-3003	725	29	(	(	PUNCT
ejpam-3003	725	30	p−	p−	NOUN
ejpam-3003	725	31	1)(1−	1)(1−	NUM
ejpam-3003	725	32	β	β	NOUN
ejpam-3003	725	33	)	)	PUNCT
ejpam-3003	725	34	.	.	PUNCT
ejpam-3003	726	1	at	at	ADP
ejpam-3003	726	2	this	this	DET
ejpam-3003	726	3	point	point	NOUN
ejpam-3003	726	4	,	,	PUNCT
ejpam-3003	726	5	we	we	PRON
ejpam-3003	726	6	choose	choose	VERB
ejpam-3003	726	7	d	d	NOUN
ejpam-3003	726	8	large	large	ADJ
ejpam-3003	726	9	enough	enough	ADV
ejpam-3003	726	10	such	such	ADJ
ejpam-3003	726	11	that	that	DET
ejpam-3003	726	12	k2	k2	NOUN
ejpam-3003	726	13	=	=	SYM
ejpam-3003	726	14	(	(	PUNCT
ejpam-3003	726	15	p+	p+	NOUN
ejpam-3003	726	16	1−	1−	NUM
ejpam-3003	726	17	γ)−	γ)−	PROPN
ejpam-3003	726	18	d−q	d−q	X
ejpam-3003	726	19	q	q	PROPN
ejpam-3003	727	1	+	+	NUM
ejpam-3003	727	2	1	1	NUM
ejpam-3003	727	3	(	(	PUNCT
ejpam-3003	727	4	β(p−	β(p−	PROPN
ejpam-3003	727	5	1	1	NUM
ejpam-3003	727	6	)	)	PUNCT
ejpam-3003	727	7	+	+	CCONJ
ejpam-3003	727	8	2	2	NUM
ejpam-3003	727	9	2(p+	2(p+	NUM
ejpam-3003	727	10	1	1	NUM
ejpam-3003	727	11	)	)	PUNCT
ejpam-3003	727	12	)	)	PUNCT
ejpam-3003	728	1	σq	σq	NOUN
ejpam-3003	728	2	bq+1	bq+1	NOUN
ejpam-3003	729	1	q+1δ	q+1δ	PROPN
ejpam-3003	729	2	q+1	q+1	NUM
ejpam-3003	729	3	2	2	NUM
ejpam-3003	729	4	2	2	NUM
ejpam-3003	729	5	k	k	X
ejpam-3003	729	6	>	>	X
ejpam-3003	729	7	0	0	NUM
ejpam-3003	729	8	,	,	PUNCT
ejpam-3003	729	9	(	(	PUNCT
ejpam-3003	729	10	5.24	5.24	NUM
ejpam-3003	729	11	)	)	PUNCT
ejpam-3003	729	12	k3	k3	NOUN
ejpam-3003	729	13	=	=	PUNCT
ejpam-3003	729	14	γ	γ	X
ejpam-3003	729	15	p+	p+	VERB
ejpam-3003	729	16	1	1	NUM
ejpam-3003	729	17	−	−	NOUN
ejpam-3003	729	18	d−q	d−q	X
ejpam-3003	729	19	q	q	PROPN
ejpam-3003	730	1	+	+	NUM
ejpam-3003	730	2	1	1	NUM
ejpam-3003	730	3	(	(	PUNCT
ejpam-3003	730	4	β(p−	β(p−	PROPN
ejpam-3003	730	5	1	1	NUM
ejpam-3003	730	6	)	)	PUNCT
ejpam-3003	730	7	+	+	CCONJ
ejpam-3003	730	8	2	2	NUM
ejpam-3003	730	9	2(p+	2(p+	NUM
ejpam-3003	730	10	1	1	NUM
ejpam-3003	730	11	)	)	PUNCT
ejpam-3003	730	12	)	)	PUNCT
ejpam-3003	731	1	σq	σq	NOUN
ejpam-3003	731	2	bq+1	bq+1	NOUN
ejpam-3003	732	1	q+1δ	q+1δ	PROPN
ejpam-3003	732	2	q+1	q+1	NUM
ejpam-3003	732	3	2	2	NUM
ejpam-3003	732	4	2	2	NUM
ejpam-3003	732	5	k	k	X
ejpam-3003	732	6	>	>	X
ejpam-3003	732	7	0	0	X
ejpam-3003	732	8	.	.	PUNCT
ejpam-3003	733	1	(	(	PUNCT
ejpam-3003	733	2	5.25	5.25	NUM
ejpam-3003	733	3	)	)	PUNCT
ejpam-3003	733	4	once	once	ADV
ejpam-3003	733	5	d	d	PROPN
ejpam-3003	733	6	is	be	AUX
ejpam-3003	733	7	fixed	fix	VERB
ejpam-3003	733	8	,	,	PUNCT
ejpam-3003	733	9	we	we	PRON
ejpam-3003	733	10	pick	pick	VERB
ejpam-3003	733	11	ε	ε	PROPN
ejpam-3003	733	12	small	small	ADJ
ejpam-3003	733	13	enough	enough	ADV
ejpam-3003	733	14	so	so	SCONJ
ejpam-3003	733	15	that	that	SCONJ
ejpam-3003	733	16	k1	k1	NOUN
ejpam-3003	733	17	=	=	SYM
ejpam-3003	733	18	(	(	PUNCT
ejpam-3003	733	19	1−	1−	NUM
ejpam-3003	733	20	σ)−	σ)−	PROPN
ejpam-3003	733	21	ε	ε	PROPN
ejpam-3003	733	22	q	q	PROPN
ejpam-3003	733	23	q	q	PROPN
ejpam-3003	734	1	+	+	NUM
ejpam-3003	734	2	1	1	NUM
ejpam-3003	734	3	d	d	X
ejpam-3003	734	4	>	>	X
ejpam-3003	734	5	0	0	NUM
ejpam-3003	734	6	,	,	PUNCT
ejpam-3003	734	7	(	(	PUNCT
ejpam-3003	734	8	5.26	5.26	NUM
ejpam-3003	734	9	)	)	PUNCT
ejpam-3003	734	10	and	and	CCONJ
ejpam-3003	734	11	g(0	g(0	PROPN
ejpam-3003	734	12	)	)	PUNCT
ejpam-3003	734	13	=	=	SYM
ejpam-3003	734	14	n1−σ(0	n1−σ(0	NOUN
ejpam-3003	734	15	)	)	PUNCT
ejpam-3003	734	16	+	+	CCONJ
ejpam-3003	735	1	ε	ε	PROPN
ejpam-3003	735	2	ρ	ρ	PROPN
ejpam-3003	735	3	∫	∫	PROPN
ejpam-3003	735	4	ω	ω	PROPN
ejpam-3003	735	5	u0|u1|ρ−1u1dx	u0|u1|ρ−1u1dx	PROPN
ejpam-3003	735	6	>	>	X
ejpam-3003	735	7	0	0	NUM
ejpam-3003	735	8	.	.	PUNCT
ejpam-3003	735	9	(	(	PUNCT
ejpam-3003	735	10	5.27	5.27	NUM
ejpam-3003	735	11	)	)	PUNCT
ejpam-3003	735	12	thus	thus	ADV
ejpam-3003	735	13	,	,	PUNCT
ejpam-3003	735	14	we	we	PRON
ejpam-3003	735	15	have	have	VERB
ejpam-3003	735	16	g′(t	g′(t	NOUN
ejpam-3003	735	17	)	)	PUNCT
ejpam-3003	735	18	≥	≥	NOUN
ejpam-3003	735	19	εη	εη	PROPN
ejpam-3003	735	20	[	[	PUNCT
ejpam-3003	735	21	n(t	n(t	PROPN
ejpam-3003	735	22	)	)	PUNCT
ejpam-3003	735	23	+	+	PUNCT
ejpam-3003	736	1	‖ut‖ρ+1	‖ut‖ρ+1	PROPN
ejpam-3003	736	2	ρ+1	ρ+1	NOUN
ejpam-3003	736	3	+	+	CCONJ
ejpam-3003	736	4	‖∇u‖22	‖∇u‖22	NOUN
ejpam-3003	736	5	+	+	CCONJ
ejpam-3003	736	6	(	(	PUNCT
ejpam-3003	736	7	g	g	PROPN
ejpam-3003	736	8	◦	◦	PROPN
ejpam-3003	736	9	∇u)(t	∇u)(t	PROPN
ejpam-3003	736	10	)	)	PUNCT
ejpam-3003	737	1	+	+	NUM
ejpam-3003	737	2	‖u‖p+1	‖u‖p+1	NOUN
ejpam-3003	737	3	p+1	p+1	NOUN
ejpam-3003	737	4	]	]	X
ejpam-3003	737	5	≥	≥	NOUN
ejpam-3003	737	6	0	0	NUM
ejpam-3003	737	7	,	,	PUNCT
ejpam-3003	737	8	(	(	PUNCT
ejpam-3003	737	9	5.28	5.28	NUM
ejpam-3003	737	10	)	)	PUNCT
ejpam-3003	737	11	for	for	ADP
ejpam-3003	737	12	some	some	DET
ejpam-3003	737	13	small	small	ADJ
ejpam-3003	737	14	number	number	NOUN
ejpam-3003	737	15	η	η	PROPN
ejpam-3003	737	16	>	>	X
ejpam-3003	737	17	0	0	NUM
ejpam-3003	737	18	.	.	PUNCT
ejpam-3003	738	1	consequently	consequently	ADV
ejpam-3003	738	2	,	,	PUNCT
ejpam-3003	738	3	from	from	ADP
ejpam-3003	738	4	(	(	PUNCT
ejpam-3003	738	5	5.27	5.27	NUM
ejpam-3003	738	6	)	)	PUNCT
ejpam-3003	738	7	and	and	CCONJ
ejpam-3003	738	8	(	(	PUNCT
ejpam-3003	738	9	5.28	5.28	NUM
ejpam-3003	738	10	)	)	PUNCT
ejpam-3003	738	11	we	we	PRON
ejpam-3003	738	12	obtain	obtain	VERB
ejpam-3003	738	13	g(t	g(t	PROPN
ejpam-3003	738	14	)	)	PUNCT
ejpam-3003	738	15	≥	≥	NOUN
ejpam-3003	739	1	g(0	g(0	NOUN
ejpam-3003	739	2	)	)	PUNCT
ejpam-3003	739	3	>	>	X
ejpam-3003	739	4	0	0	PROPN
ejpam-3003	739	5	,	,	PUNCT
ejpam-3003	739	6	t	t	PROPN
ejpam-3003	739	7	≥	≥	NUM
ejpam-3003	739	8	0	0	NUM
ejpam-3003	739	9	.	.	PUNCT
ejpam-3003	740	1	(	(	PUNCT
ejpam-3003	740	2	5.29	5.29	NUM
ejpam-3003	740	3	)	)	PUNCT
ejpam-3003	740	4	now	now	ADV
ejpam-3003	740	5	,	,	PUNCT
ejpam-3003	740	6	by	by	ADP
ejpam-3003	740	7	the	the	DET
ejpam-3003	740	8	hölder	hölder	NOUN
ejpam-3003	740	9	inequality	inequality	NOUN
ejpam-3003	740	10	and	and	CCONJ
ejpam-3003	740	11	sobolev	sobolev	NOUN
ejpam-3003	740	12	inequality	inequality	NOUN
ejpam-3003	740	13	,	,	PUNCT
ejpam-3003	740	14	we	we	PRON
ejpam-3003	740	15	estimate∣∣	estimate∣∣	ADJ
ejpam-3003	740	16	∫	∫	PROPN
ejpam-3003	740	17	ω	ω	PROPN
ejpam-3003	740	18	u|ut|ρ−1ut	u|ut|ρ−1ut	PROPN
ejpam-3003	740	19	∣∣	∣∣	NUM
ejpam-3003	740	20	1	1	NUM
ejpam-3003	740	21	1−σ	1−σ	NUM
ejpam-3003	740	22	≤	≤	ADJ
ejpam-3003	740	23	‖ut‖	‖ut‖	PROPN
ejpam-3003	740	24	ρ	ρ	X
ejpam-3003	740	25	1−σ	1−σ	NUM
ejpam-3003	741	1	ρ+1	ρ+1	NUM
ejpam-3003	741	2	‖u‖	‖u‖	PROPN
ejpam-3003	741	3	1	1	NUM
ejpam-3003	741	4	1−σ	1−σ	NUM
ejpam-3003	741	5	ρ+1	ρ+1	NOUN
ejpam-3003	741	6	≤	≤	NUM
ejpam-3003	741	7	c‖ut‖	c‖ut‖	NOUN
ejpam-3003	741	8	ρ	ρ	X
ejpam-3003	741	9	1−σ	1−σ	NUM
ejpam-3003	742	1	ρ+1	ρ+1	NUM
ejpam-3003	742	2	‖u‖	‖u‖	PROPN
ejpam-3003	742	3	1	1	NUM
ejpam-3003	742	4	1−σ	1−σ	NUM
ejpam-3003	742	5	p+1	p+1	NOUN
ejpam-3003	742	6	≤	≤	PUNCT
ejpam-3003	742	7	c(‖ut‖	c(‖ut‖	ADJ
ejpam-3003	742	8	ρ%	ρ%	NUM
ejpam-3003	742	9	1−σ	1−σ	NUM
ejpam-3003	742	10	ρ+1	ρ+1	NOUN
ejpam-3003	743	1	+	+	CCONJ
ejpam-3003	743	2	‖u‖	‖u‖	NOUN
ejpam-3003	744	1	%	%	INTJ
ejpam-3003	744	2	′	′	NOUN
ejpam-3003	745	1	1−σ	1−σ	NUM
ejpam-3003	745	2	p+1	p+1	NOUN
ejpam-3003	745	3	)	)	PUNCT
ejpam-3003	745	4	,	,	PUNCT
ejpam-3003	745	5	(	(	PUNCT
ejpam-3003	745	6	5.30	5.30	NUM
ejpam-3003	745	7	)	)	PUNCT
ejpam-3003	746	1	where	where	SCONJ
ejpam-3003	746	2	1	1	NUM
ejpam-3003	746	3	%	%	NOUN
ejpam-3003	746	4	+	+	CCONJ
ejpam-3003	746	5	1	1	NUM
ejpam-3003	746	6	%	%	NOUN
ejpam-3003	746	7	′	′	NUM
ejpam-3003	747	1	=	=	NOUN
ejpam-3003	747	2	1	1	X
ejpam-3003	747	3	.	.	X
ejpam-3003	748	1	we	we	PRON
ejpam-3003	748	2	choose	choose	VERB
ejpam-3003	748	3	%	%	NOUN
ejpam-3003	748	4	=	=	SYM
ejpam-3003	748	5	(	(	PUNCT
ejpam-3003	748	6	ρ+1)(1−σ	ρ+1)(1−σ	PROPN
ejpam-3003	748	7	)	)	PUNCT
ejpam-3003	748	8	ρ	ρ	NOUN
ejpam-3003	748	9	(	(	PUNCT
ejpam-3003	748	10	>	>	X
ejpam-3003	748	11	1	1	NUM
ejpam-3003	748	12	)	)	PUNCT
ejpam-3003	748	13	,	,	PUNCT
ejpam-3003	748	14	then	then	ADV
ejpam-3003	748	15	%	%	INTJ
ejpam-3003	748	16	′	′	NUM
ejpam-3003	749	1	1−	1−	NUM
ejpam-3003	749	2	σ	σ	NUM
ejpam-3003	749	3	=	=	SYM
ejpam-3003	749	4	ρ+	ρ+	NUM
ejpam-3003	749	5	1	1	NUM
ejpam-3003	749	6	(	(	PUNCT
ejpam-3003	749	7	ρ+	ρ+	NUM
ejpam-3003	749	8	1)(1−	1)(1−	NUM
ejpam-3003	749	9	σ)−	σ)−	PROPN
ejpam-3003	749	10	ρ	ρ	PROPN
ejpam-3003	749	11	.	.	PUNCT
ejpam-3003	750	1	(	(	PUNCT
ejpam-3003	750	2	5.31	5.31	NUM
ejpam-3003	750	3	)	)	PUNCT
ejpam-3003	750	4	by	by	ADP
ejpam-3003	750	5	using	use	VERB
ejpam-3003	750	6	lemma	lemma	PROPN
ejpam-3003	750	7	9	9	NUM
ejpam-3003	750	8	and	and	CCONJ
ejpam-3003	750	9	(	(	PUNCT
ejpam-3003	750	10	5.31	5.31	NUM
ejpam-3003	750	11	)	)	PUNCT
ejpam-3003	750	12	,	,	PUNCT
ejpam-3003	750	13	then	then	ADV
ejpam-3003	750	14	(	(	PUNCT
ejpam-3003	750	15	5.30	5.30	NUM
ejpam-3003	750	16	)	)	PUNCT
ejpam-3003	750	17	becomes∣∣	becomes∣∣	PROPN
ejpam-3003	751	1	∫	∫	PROPN
ejpam-3003	751	2	ω	ω	PROPN
ejpam-3003	751	3	u|ut|ρ−1ut	u|ut|ρ−1ut	PROPN
ejpam-3003	751	4	∣∣	∣∣	NUM
ejpam-3003	751	5	1	1	NUM
ejpam-3003	751	6	1−σ	1−σ	NUM
ejpam-3003	751	7	≤	≤	NUM
ejpam-3003	751	8	c	c	NOUN
ejpam-3003	751	9	(	(	PUNCT
ejpam-3003	751	10	‖ut‖ρ+1	‖ut‖ρ+1	PROPN
ejpam-3003	751	11	ρ+1	ρ+1	NOUN
ejpam-3003	751	12	+	+	CCONJ
ejpam-3003	751	13	‖∇u‖22	‖∇u‖22	NOUN
ejpam-3003	751	14	+	+	CCONJ
ejpam-3003	751	15	‖u‖p+1	‖u‖p+1	NOUN
ejpam-3003	751	16	p+1	p+1	NOUN
ejpam-3003	751	17	)	)	PUNCT
ejpam-3003	751	18	.	.	PUNCT
ejpam-3003	752	1	(	(	PUNCT
ejpam-3003	752	2	5.32	5.32	NUM
ejpam-3003	752	3	)	)	PUNCT
ejpam-3003	752	4	hence	hence	ADV
ejpam-3003	752	5	,	,	PUNCT
ejpam-3003	752	6	combining	combine	VERB
ejpam-3003	752	7	(	(	PUNCT
ejpam-3003	752	8	5.10	5.10	NUM
ejpam-3003	752	9	)	)	PUNCT
ejpam-3003	752	10	and	and	CCONJ
ejpam-3003	752	11	(	(	PUNCT
ejpam-3003	752	12	5.32	5.32	NUM
ejpam-3003	752	13	)	)	PUNCT
ejpam-3003	752	14	,	,	PUNCT
ejpam-3003	752	15	we	we	PRON
ejpam-3003	752	16	deduce	deduce	VERB
ejpam-3003	752	17	that	that	SCONJ
ejpam-3003	752	18	g	g	PROPN
ejpam-3003	752	19	1	1	NUM
ejpam-3003	752	20	1−σ	1−σ	NUM
ejpam-3003	752	21	(	(	PUNCT
ejpam-3003	752	22	t	t	NOUN
ejpam-3003	752	23	)	)	PUNCT
ejpam-3003	752	24	=	=	PRON
ejpam-3003	752	25	(	(	PUNCT
ejpam-3003	752	26	n1−σ(t	n1−σ(t	PROPN
ejpam-3003	752	27	)	)	PUNCT
ejpam-3003	753	1	+	+	CCONJ
ejpam-3003	753	2	ε	ε	PROPN
ejpam-3003	753	3	ρ	ρ	PROPN
ejpam-3003	753	4	∫	∫	PROPN
ejpam-3003	753	5	ω	ω	PROPN
ejpam-3003	753	6	|ut|ρ−1utudx	|ut|ρ−1utudx	PROPN
ejpam-3003	753	7	)	)	PUNCT
ejpam-3003	753	8	1	1	NUM
ejpam-3003	753	9	1−σ	1−σ	NUM
ejpam-3003	753	10	h.f	h.f	PROPN
ejpam-3003	753	11	.	.	PROPN
ejpam-3003	753	12	di	di	PROPN
ejpam-3003	753	13	,	,	PUNCT
ejpam-3003	753	14	y.d	y.d	PROPN
ejpam-3003	753	15	.	.	PROPN
ejpam-3003	753	16	shang	shang	PROPN
ejpam-3003	753	17	/	/	SYM
ejpam-3003	753	18	eur	eur	PROPN
ejpam-3003	753	19	.	.	PUNCT
ejpam-3003	754	1	j.	j.	PROPN
ejpam-3003	754	2	pure	pure	PROPN
ejpam-3003	754	3	appl	appl	PROPN
ejpam-3003	754	4	.	.	PROPN
ejpam-3003	754	5	math	math	PROPN
ejpam-3003	754	6	,	,	PUNCT
ejpam-3003	754	7	10	10	NUM
ejpam-3003	754	8	(	(	PUNCT
ejpam-3003	754	9	4	4	NUM
ejpam-3003	754	10	)	)	PUNCT
ejpam-3003	754	11	(	(	PUNCT
ejpam-3003	754	12	2017	2017	NUM
ejpam-3003	754	13	)	)	PUNCT
ejpam-3003	754	14	,	,	PUNCT
ejpam-3003	754	15	668	668	NUM
ejpam-3003	754	16	-	-	SYM
ejpam-3003	754	17	701	701	NUM
ejpam-3003	754	18	698	698	NUM
ejpam-3003	754	19	≤	≤	NUM
ejpam-3003	754	20	c	c	NOUN
ejpam-3003	754	21	(	(	PUNCT
ejpam-3003	754	22	n(t	n(t	PROPN
ejpam-3003	754	23	)	)	PUNCT
ejpam-3003	754	24	+	+	PUNCT
ejpam-3003	754	25	‖ut‖ρ+1	‖ut‖ρ+1	PROPN
ejpam-3003	754	26	ρ+1	ρ+1	NOUN
ejpam-3003	754	27	+	+	CCONJ
ejpam-3003	754	28	‖∇u‖22	‖∇u‖22	NOUN
ejpam-3003	754	29	+	+	CCONJ
ejpam-3003	754	30	‖u‖p+1	‖u‖p+1	NOUN
ejpam-3003	754	31	p+1	p+1	NOUN
ejpam-3003	754	32	)	)	PUNCT
ejpam-3003	754	33	.	.	PUNCT
ejpam-3003	755	1	(	(	PUNCT
ejpam-3003	755	2	5.33	5.33	NUM
ejpam-3003	755	3	)	)	PUNCT
ejpam-3003	755	4	by	by	ADP
ejpam-3003	755	5	the	the	DET
ejpam-3003	755	6	combination	combination	NOUN
ejpam-3003	755	7	of	of	ADP
ejpam-3003	755	8	(	(	PUNCT
ejpam-3003	755	9	5.28	5.28	NUM
ejpam-3003	755	10	)	)	PUNCT
ejpam-3003	755	11	and	and	CCONJ
ejpam-3003	755	12	(	(	PUNCT
ejpam-3003	755	13	5.33	5.33	NUM
ejpam-3003	755	14	)	)	PUNCT
ejpam-3003	755	15	,	,	PUNCT
ejpam-3003	755	16	we	we	PRON
ejpam-3003	755	17	obtain	obtain	VERB
ejpam-3003	755	18	g′(t	g′(t	PROPN
ejpam-3003	755	19	)	)	PUNCT
ejpam-3003	755	20	≥	≥	NOUN
ejpam-3003	755	21	qg	qg	PROPN
ejpam-3003	755	22	1	1	NUM
ejpam-3003	755	23	1−σ	1−σ	NUM
ejpam-3003	755	24	(	(	PUNCT
ejpam-3003	755	25	t	t	PROPN
ejpam-3003	755	26	)	)	PUNCT
ejpam-3003	755	27	,	,	PUNCT
ejpam-3003	756	1	∀	∀	X
ejpam-3003	756	2	t	t	X
ejpam-3003	756	3	∈	∈	PROPN
ejpam-3003	757	1	[	[	X
ejpam-3003	757	2	0	0	NUM
ejpam-3003	757	3	,	,	PUNCT
ejpam-3003	757	4	t	t	X
ejpam-3003	757	5	]	]	PUNCT
ejpam-3003	757	6	,	,	PUNCT
ejpam-3003	757	7	(	(	PUNCT
ejpam-3003	757	8	5.34	5.34	NUM
ejpam-3003	757	9	)	)	PUNCT
ejpam-3003	757	10	where	where	SCONJ
ejpam-3003	757	11	q	q	NOUN
ejpam-3003	757	12	is	be	AUX
ejpam-3003	757	13	a	a	DET
ejpam-3003	757	14	positive	positive	ADJ
ejpam-3003	757	15	constant	constant	ADJ
ejpam-3003	757	16	depending	depend	VERB
ejpam-3003	757	17	only	only	ADV
ejpam-3003	757	18	on	on	ADP
ejpam-3003	757	19	c	c	PROPN
ejpam-3003	757	20	and	and	CCONJ
ejpam-3003	757	21	εη	εη	NOUN
ejpam-3003	757	22	.	.	PUNCT
ejpam-3003	757	23	a	a	DET
ejpam-3003	757	24	simple	simple	ADJ
ejpam-3003	757	25	integration	integration	NOUN
ejpam-3003	757	26	of	of	ADP
ejpam-3003	757	27	(	(	PUNCT
ejpam-3003	757	28	5.34	5.34	NUM
ejpam-3003	757	29	)	)	PUNCT
ejpam-3003	757	30	over	over	ADP
ejpam-3003	757	31	(	(	PUNCT
ejpam-3003	757	32	0,t	0,t	PROPN
ejpam-3003	757	33	)	)	PUNCT
ejpam-3003	757	34	,	,	PUNCT
ejpam-3003	757	35	it	it	PRON
ejpam-3003	757	36	follows	follow	VERB
ejpam-3003	757	37	that	that	SCONJ
ejpam-3003	757	38	g	g	PROPN
ejpam-3003	757	39	σ	σ	PROPN
ejpam-3003	757	40	1−σ	1−σ	NUM
ejpam-3003	757	41	(	(	PUNCT
ejpam-3003	757	42	t	t	PROPN
ejpam-3003	757	43	)	)	PUNCT
ejpam-3003	757	44	≥	≥	NOUN
ejpam-3003	757	45	1	1	NUM
ejpam-3003	757	46	g−σ/(1−σ)(0)−qσt/(1−	g−σ/(1−σ)(0)−qσt/(1−	PROPN
ejpam-3003	757	47	σ	σ	PROPN
ejpam-3003	757	48	)	)	PUNCT
ejpam-3003	757	49	,	,	PUNCT
ejpam-3003	757	50	∀	∀	X
ejpam-3003	757	51	t	t	NOUN
ejpam-3003	757	52	∈	∈	PROPN
ejpam-3003	758	1	[	[	X
ejpam-3003	758	2	0	0	NUM
ejpam-3003	758	3	,	,	PUNCT
ejpam-3003	758	4	t	t	X
ejpam-3003	758	5	]	]	PUNCT
ejpam-3003	758	6	.	.	PUNCT
ejpam-3003	759	1	(	(	PUNCT
ejpam-3003	759	2	5.35	5.35	NUM
ejpam-3003	759	3	)	)	PUNCT
ejpam-3003	759	4	this	this	PRON
ejpam-3003	759	5	shows	show	VERB
ejpam-3003	759	6	that	that	SCONJ
ejpam-3003	759	7	g(t	g(t	PROPN
ejpam-3003	759	8	)	)	PUNCT
ejpam-3003	759	9	blows	blow	VERB
ejpam-3003	759	10	up	up	ADP
ejpam-3003	759	11	in	in	ADP
ejpam-3003	759	12	finite	finite	ADJ
ejpam-3003	759	13	time	time	NOUN
ejpam-3003	759	14	t	t	PROPN
ejpam-3003	759	15	∗	∗	VERB
ejpam-3003	759	16	≤	≤	NUM
ejpam-3003	759	17	1−	1−	NUM
ejpam-3003	759	18	σ	σ	NOUN
ejpam-3003	759	19	gσ/1−σ(0)qσ	gσ/1−σ(0)qσ	PROPN
ejpam-3003	759	20	.	.	PUNCT
ejpam-3003	760	1	(	(	PUNCT
ejpam-3003	760	2	5.36	5.36	NUM
ejpam-3003	760	3	)	)	PUNCT
ejpam-3003	760	4	furthermore	furthermore	ADV
ejpam-3003	760	5	,	,	PUNCT
ejpam-3003	760	6	we	we	PRON
ejpam-3003	760	7	have	have	VERB
ejpam-3003	760	8	from	from	ADP
ejpam-3003	760	9	(	(	PUNCT
ejpam-3003	760	10	5.33	5.33	NUM
ejpam-3003	760	11	)	)	PUNCT
ejpam-3003	760	12	that	that	SCONJ
ejpam-3003	760	13	there	there	PRON
ejpam-3003	760	14	exists	exist	VERB
ejpam-3003	760	15	a	a	DET
ejpam-3003	760	16	finite	finite	ADJ
ejpam-3003	760	17	time	time	NOUN
ejpam-3003	760	18	t	t	PROPN
ejpam-3003	760	19	∗	∗	X
ejpam-3003	760	20	∈	∈	PROPN
ejpam-3003	760	21	(	(	PUNCT
ejpam-3003	760	22	0	0	NUM
ejpam-3003	760	23	,	,	PUNCT
ejpam-3003	760	24	t	t	NOUN
ejpam-3003	760	25	)	)	PUNCT
ejpam-3003	760	26	such	such	ADJ
ejpam-3003	760	27	that	that	SCONJ
ejpam-3003	760	28	lim	lim	PROPN
ejpam-3003	760	29	t→t	t→t	NUM
ejpam-3003	760	30	∗−	∗−	ADJ
ejpam-3003	760	31	(	(	PUNCT
ejpam-3003	760	32	‖ut‖ρ+1	‖ut‖ρ+1	PROPN
ejpam-3003	760	33	ρ+1	ρ+1	NOUN
ejpam-3003	760	34	+	+	CCONJ
ejpam-3003	760	35	‖∇u‖22	‖∇u‖22	NOUN
ejpam-3003	761	1	+	+	CCONJ
ejpam-3003	761	2	‖u‖p+1	‖u‖p+1	NOUN
ejpam-3003	761	3	p+1	p+1	NOUN
ejpam-3003	761	4	)	)	PUNCT
ejpam-3003	762	1	=	=	PUNCT
ejpam-3003	763	1	+	+	NUM
ejpam-3003	763	2	∞	∞	PROPN
ejpam-3003	763	3	,	,	PUNCT
ejpam-3003	763	4	which	which	PRON
ejpam-3003	763	5	contradicts	contradict	VERB
ejpam-3003	763	6	tmax	tmax	ADP
ejpam-3003	763	7	=	=	NOUN
ejpam-3003	763	8	∞.	∞.	PROPN
ejpam-3003	763	9	hence	hence	ADV
ejpam-3003	763	10	,	,	PUNCT
ejpam-3003	763	11	the	the	DET
ejpam-3003	763	12	solutions	solution	NOUN
ejpam-3003	763	13	of	of	ADP
ejpam-3003	763	14	the	the	DET
ejpam-3003	763	15	problem	problem	NOUN
ejpam-3003	763	16	(	(	PUNCT
ejpam-3003	763	17	1.1	1.1	NUM
ejpam-3003	763	18	)	)	PUNCT
ejpam-3003	763	19	blows	blow	VERB
ejpam-3003	763	20	up	up	ADP
ejpam-3003	763	21	in	in	ADP
ejpam-3003	763	22	finite	finite	ADJ
ejpam-3003	763	23	time	time	NOUN
ejpam-3003	763	24	.	.	PUNCT
ejpam-3003	764	1	remark	remark	PROPN
ejpam-3003	764	2	3	3	NUM
ejpam-3003	764	3	.	.	PUNCT
ejpam-3003	765	1	noting	note	VERB
ejpam-3003	765	2	that	that	SCONJ
ejpam-3003	765	3	from	from	ADP
ejpam-3003	765	4	1	1	NUM
ejpam-3003	765	5	ρ+	ρ+	NUM
ejpam-3003	765	6	1	1	NUM
ejpam-3003	765	7	‖u1‖ρ+1	‖u1‖ρ+1	SYM
ejpam-3003	765	8	ρ+1	ρ+1	NOUN
ejpam-3003	765	9	+	+	CCONJ
ejpam-3003	765	10	p−	p−	NOUN
ejpam-3003	765	11	1	1	NUM
ejpam-3003	765	12	2(p+	2(p+	NUM
ejpam-3003	765	13	1	1	NUM
ejpam-3003	765	14	)	)	PUNCT
ejpam-3003	765	15	‖∇u0‖22	‖∇u0‖22	NOUN
ejpam-3003	765	16	+	+	CCONJ
ejpam-3003	765	17	1	1	NUM
ejpam-3003	765	18	p+	p+	NOUN
ejpam-3003	765	19	1	1	NUM
ejpam-3003	765	20	i(u0	i(u0	NOUN
ejpam-3003	765	21	)	)	PUNCT
ejpam-3003	765	22	≤	≤	NUM
ejpam-3003	765	23	1	1	NUM
ejpam-3003	765	24	ρ+	ρ+	NUM
ejpam-3003	765	25	1	1	NUM
ejpam-3003	765	26	‖u1‖ρ+1	‖u1‖ρ+1	SYM
ejpam-3003	765	27	ρ+1	ρ+1	NOUN
ejpam-3003	765	28	+	+	NOUN
ejpam-3003	765	29	j(u0	j(u0	NOUN
ejpam-3003	765	30	)	)	PUNCT
ejpam-3003	765	31	=	=	SYM
ejpam-3003	766	1	e(0	e(0	NOUN
ejpam-3003	766	2	)	)	PUNCT
ejpam-3003	766	3	,	,	PUNCT
ejpam-3003	766	4	(	(	PUNCT
ejpam-3003	766	5	5.37	5.37	NUM
ejpam-3003	766	6	)	)	PUNCT
ejpam-3003	766	7	we	we	PRON
ejpam-3003	766	8	see	see	VERB
ejpam-3003	766	9	that	that	SCONJ
ejpam-3003	766	10	if	if	SCONJ
ejpam-3003	766	11	e(0	e(0	NOUN
ejpam-3003	766	12	)	)	PUNCT
ejpam-3003	766	13	<	<	X
ejpam-3003	766	14	0	0	NUM
ejpam-3003	766	15	,	,	PUNCT
ejpam-3003	766	16	then	then	ADV
ejpam-3003	766	17	i(u0	i(u0	PROPN
ejpam-3003	766	18	)	)	PUNCT
ejpam-3003	766	19	≥	≥	PROPN
ejpam-3003	766	20	0	0	NUM
ejpam-3003	766	21	is	be	AUX
ejpam-3003	766	22	impossible	impossible	ADJ
ejpam-3003	766	23	.	.	PUNCT
ejpam-3003	767	1	if	if	SCONJ
ejpam-3003	767	2	e(0	e(0	NOUN
ejpam-3003	767	3	)	)	PUNCT
ejpam-3003	767	4	=	=	SYM
ejpam-3003	767	5	0	0	NUM
ejpam-3003	767	6	,	,	PUNCT
ejpam-3003	767	7	then	then	ADV
ejpam-3003	767	8	either	either	CCONJ
ejpam-3003	767	9	i(u0	i(u0	PROPN
ejpam-3003	767	10	)	)	PUNCT
ejpam-3003	767	11	>	>	X
ejpam-3003	767	12	0	0	PUNCT
ejpam-3003	767	13	or	or	CCONJ
ejpam-3003	767	14	i(u0	i(u0	NOUN
ejpam-3003	767	15	)	)	PUNCT
ejpam-3003	768	1	=	=	SYM
ejpam-3003	768	2	0	0	NUM
ejpam-3003	768	3	with	with	ADP
ejpam-3003	768	4	‖∇u0‖22	‖∇u0‖22	PROPN
ejpam-3003	768	5	6=	6=	SYM
ejpam-3003	768	6	0	0	NUM
ejpam-3003	768	7	is	be	AUX
ejpam-3003	768	8	impossible	impossible	ADJ
ejpam-3003	768	9	.	.	PUNCT
ejpam-3003	769	1	if	if	SCONJ
ejpam-3003	769	2	0	0	NUM
ejpam-3003	769	3	<	<	X
ejpam-3003	769	4	e(0	e(0	NOUN
ejpam-3003	769	5	)	)	PUNCT
ejpam-3003	769	6	<	<	X
ejpam-3003	769	7	βd̃	βd̃	PRON
ejpam-3003	769	8	(	(	PUNCT
ejpam-3003	769	9	βd̃	βd̃	X
ejpam-3003	769	10	<	<	X
ejpam-3003	769	11	d̃	d̃	PROPN
ejpam-3003	769	12	)	)	PUNCT
ejpam-3003	769	13	,	,	PUNCT
ejpam-3003	769	14	it	it	PRON
ejpam-3003	769	15	follows	follow	VERB
ejpam-3003	769	16	from	from	ADP
ejpam-3003	769	17	the	the	DET
ejpam-3003	769	18	definition	definition	NOUN
ejpam-3003	769	19	of	of	ADP
ejpam-3003	769	20	d	d	PROPN
ejpam-3003	769	21	that	that	DET
ejpam-3003	769	22	i(u0	i(u0	NOUN
ejpam-3003	769	23	)	)	PUNCT
ejpam-3003	770	1	=	=	SYM
ejpam-3003	770	2	0	0	NUM
ejpam-3003	770	3	with	with	ADP
ejpam-3003	770	4	‖∇u0‖22	‖∇u0‖22	PROPN
ejpam-3003	770	5	6=	6=	SYM
ejpam-3003	770	6	0	0	NUM
ejpam-3003	770	7	is	be	AUX
ejpam-3003	770	8	impossible	impossible	ADJ
ejpam-3003	770	9	.	.	PUNCT
ejpam-3003	771	1	otherwise	otherwise	ADV
ejpam-3003	771	2	,	,	PUNCT
ejpam-3003	771	3	we	we	PRON
ejpam-3003	771	4	have	have	VERB
ejpam-3003	771	5	j(u0	j(u0	NOUN
ejpam-3003	771	6	)	)	PUNCT
ejpam-3003	771	7	≥	≥	PROPN
ejpam-3003	772	1	d	d	NOUN
ejpam-3003	772	2	which	which	PRON
ejpam-3003	772	3	contradicts	contradict	VERB
ejpam-3003	772	4	(	(	PUNCT
ejpam-3003	772	5	5.37	5.37	NUM
ejpam-3003	772	6	)	)	PUNCT
ejpam-3003	772	7	.	.	PUNCT
ejpam-3003	773	1	thus	thus	ADV
ejpam-3003	773	2	,	,	PUNCT
ejpam-3003	773	3	all	all	DET
ejpam-3003	773	4	possible	possible	ADJ
ejpam-3003	773	5	cases	case	NOUN
ejpam-3003	773	6	already	already	ADV
ejpam-3003	773	7	have	have	AUX
ejpam-3003	773	8	been	be	AUX
ejpam-3003	773	9	considered	consider	VERB
ejpam-3003	773	10	in	in	ADP
ejpam-3003	773	11	theorems	theorem	NOUN
ejpam-3003	773	12	1	1	NUM
ejpam-3003	773	13	,	,	PUNCT
ejpam-3003	773	14	3	3	NUM
ejpam-3003	773	15	.	.	NOUN
ejpam-3003	773	16	from	from	ADP
ejpam-3003	773	17	the	the	DET
ejpam-3003	773	18	discussion	discussion	NOUN
ejpam-3003	773	19	above	above	ADP
ejpam-3003	773	20	in	in	ADP
ejpam-3003	773	21	sections	section	NOUN
ejpam-3003	773	22	3	3	NUM
ejpam-3003	773	23	,	,	PUNCT
ejpam-3003	773	24	5	5	NUM
ejpam-3003	773	25	,	,	PUNCT
ejpam-3003	773	26	a	a	DET
ejpam-3003	773	27	threshold	threshold	NOUN
ejpam-3003	773	28	result	result	NOUN
ejpam-3003	773	29	of	of	ADP
ejpam-3003	773	30	global	global	ADJ
ejpam-3003	773	31	existence	existence	NOUN
ejpam-3003	773	32	and	and	CCONJ
ejpam-3003	773	33	nonexistence	nonexistence	NOUN
ejpam-3003	773	34	of	of	ADP
ejpam-3003	773	35	solutions	solution	NOUN
ejpam-3003	773	36	for	for	ADP
ejpam-3003	773	37	problem	problem	NOUN
ejpam-3003	773	38	(	(	PUNCT
ejpam-3003	773	39	1.1	1.1	NUM
ejpam-3003	773	40	)	)	PUNCT
ejpam-3003	773	41	has	have	AUX
ejpam-3003	773	42	been	be	AUX
ejpam-3003	773	43	obtained	obtain	VERB
ejpam-3003	773	44	as	as	ADP
ejpam-3003	773	45	follows	follow	VERB
ejpam-3003	773	46	.	.	PUNCT
ejpam-3003	774	1	corollary	corollary	ADJ
ejpam-3003	774	2	1	1	NUM
ejpam-3003	774	3	.	.	PUNCT
ejpam-3003	775	1	let	let	VERB
ejpam-3003	775	2	the	the	DET
ejpam-3003	775	3	assumptions	assumption	NOUN
ejpam-3003	775	4	ρ	ρ	X
ejpam-3003	775	5	<	<	X
ejpam-3003	775	6	p	p	X
ejpam-3003	775	7	,	,	PUNCT
ejpam-3003	775	8	(	(	PUNCT
ejpam-3003	775	9	a1	a1	NOUN
ejpam-3003	775	10	)	)	PUNCT
ejpam-3003	775	11	,	,	PUNCT
ejpam-3003	775	12	(	(	PUNCT
ejpam-3003	775	13	a3	a3	NOUN
ejpam-3003	775	14	)	)	PUNCT
ejpam-3003	775	15	and	and	CCONJ
ejpam-3003	775	16	(	(	PUNCT
ejpam-3003	775	17	5.2	5.2	NUM
ejpam-3003	775	18	)	)	PUNCT
ejpam-3003	775	19	hold	hold	VERB
ejpam-3003	775	20	.	.	PUNCT
ejpam-3003	776	1	further	far	ADV
ejpam-3003	776	2	assume	assume	VERB
ejpam-3003	776	3	that	that	SCONJ
ejpam-3003	776	4	u0(x	u0(x	NOUN
ejpam-3003	776	5	)	)	PUNCT
ejpam-3003	776	6	∈	∈	PROPN
ejpam-3003	776	7	h1	h1	NOUN
ejpam-3003	776	8	0	0	NUM
ejpam-3003	776	9	(	(	PUNCT
ejpam-3003	776	10	ω	ω	NOUN
ejpam-3003	776	11	)	)	PUNCT
ejpam-3003	776	12	,	,	PUNCT
ejpam-3003	776	13	u1(x	u1(x	NOUN
ejpam-3003	776	14	)	)	PUNCT
ejpam-3003	776	15	∈	∈	PROPN
ejpam-3003	776	16	lρ+1(ω)∩lq+1(γ1	lρ+1(ω)∩lq+1(γ1	X
ejpam-3003	776	17	)	)	PUNCT
ejpam-3003	776	18	and	and	CCONJ
ejpam-3003	776	19	e(0	e(0	NOUN
ejpam-3003	776	20	)	)	PUNCT
ejpam-3003	776	21	<	<	X
ejpam-3003	776	22	βd̃	βd̃	PRON
ejpam-3003	776	23	(	(	PUNCT
ejpam-3003	776	24	βd̃	βd̃	X
ejpam-3003	776	25	<	<	X
ejpam-3003	776	26	d̃	d̃	PROPN
ejpam-3003	776	27	)	)	PUNCT
ejpam-3003	776	28	.	.	PUNCT
ejpam-3003	777	1	then	then	ADV
ejpam-3003	777	2	problem	problem	NOUN
ejpam-3003	777	3	(	(	PUNCT
ejpam-3003	777	4	1.1	1.1	NUM
ejpam-3003	777	5	)	)	PUNCT
ejpam-3003	777	6	admits	admit	VERB
ejpam-3003	777	7	a	a	DET
ejpam-3003	777	8	global	global	ADJ
ejpam-3003	777	9	weak	weak	ADJ
ejpam-3003	777	10	solution	solution	NOUN
ejpam-3003	777	11	provided	provide	VERB
ejpam-3003	777	12	i(u0	i(u0	NOUN
ejpam-3003	777	13	)	)	PUNCT
ejpam-3003	777	14	≥	≥	NOUN
ejpam-3003	777	15	0	0	NUM
ejpam-3003	777	16	(	(	PUNCT
ejpam-3003	777	17	includes	include	VERB
ejpam-3003	777	18	‖∇u0‖22	‖∇u0‖22	NOUN
ejpam-3003	777	19	=	=	SYM
ejpam-3003	777	20	0	0	NUM
ejpam-3003	777	21	)	)	PUNCT
ejpam-3003	777	22	;	;	PUNCT
ejpam-3003	777	23	problem	problem	NOUN
ejpam-3003	777	24	(	(	PUNCT
ejpam-3003	777	25	1.1	1.1	NUM
ejpam-3003	777	26	)	)	PUNCT
ejpam-3003	777	27	dose	dose	NOUN
ejpam-3003	777	28	not	not	PART
ejpam-3003	777	29	admit	admit	VERB
ejpam-3003	777	30	any	any	DET
ejpam-3003	777	31	global	global	ADJ
ejpam-3003	777	32	solutions	solution	NOUN
ejpam-3003	777	33	provided	provide	VERB
ejpam-3003	777	34	i(u0	i(u0	NOUN
ejpam-3003	777	35	)	)	PUNCT
ejpam-3003	777	36	<	<	X
ejpam-3003	777	37	0	0	X
ejpam-3003	777	38	.	.	PUNCT
ejpam-3003	777	39	remark	remark	PROPN
ejpam-3003	777	40	4	4	NUM
ejpam-3003	777	41	.	.	PUNCT
ejpam-3003	778	1	in	in	ADP
ejpam-3003	778	2	the	the	DET
ejpam-3003	778	3	above	above	ADJ
ejpam-3003	778	4	threshold	threshold	NOUN
ejpam-3003	778	5	result	result	NOUN
ejpam-3003	778	6	stated	state	VERB
ejpam-3003	778	7	in	in	ADP
ejpam-3003	778	8	corollary	corollary	ADJ
ejpam-3003	778	9	1	1	NUM
ejpam-3003	778	10	,	,	PUNCT
ejpam-3003	778	11	we	we	PRON
ejpam-3003	778	12	see	see	VERB
ejpam-3003	778	13	that	that	SCONJ
ejpam-3003	778	14	the	the	DET
ejpam-3003	778	15	manifold	manifold	ADJ
ejpam-3003	778	16	n	n	NOUN
ejpam-3003	778	17	=	=	PUNCT
ejpam-3003	778	18	{	{	PUNCT
ejpam-3003	778	19	u	u	NOUN
ejpam-3003	778	20	∈	∈	PROPN
ejpam-3003	778	21	h1	h1	PROPN
ejpam-3003	778	22	γ0	γ0	PROPN
ejpam-3003	778	23	(	(	PUNCT
ejpam-3003	778	24	ω	ω	NOUN
ejpam-3003	778	25	)	)	PUNCT
ejpam-3003	778	26	∣∣	∣∣	PROPN
ejpam-3003	778	27	i(u	i(u	PROPN
ejpam-3003	778	28	)	)	PUNCT
ejpam-3003	778	29	=	=	SYM
ejpam-3003	779	1	0	0	X
ejpam-3003	779	2	}	}	PUNCT
ejpam-3003	779	3	plays	play	VERB
ejpam-3003	779	4	a	a	DET
ejpam-3003	779	5	key	key	ADJ
ejpam-3003	779	6	role	role	NOUN
ejpam-3003	779	7	as	as	ADP
ejpam-3003	779	8	a	a	DET
ejpam-3003	779	9	borderline	borderline	NOUN
ejpam-3003	779	10	separating	separate	VERB
ejpam-3003	779	11	region	region	NOUN
ejpam-3003	779	12	of	of	ADP
ejpam-3003	779	13	weak	weak	ADJ
ejpam-3003	779	14	solutions	solution	NOUN
ejpam-3003	779	15	with	with	ADP
ejpam-3003	779	16	the	the	DET
ejpam-3003	779	17	initial	initial	ADJ
ejpam-3003	779	18	energy	energy	NOUN
ejpam-3003	779	19	e(0	e(0	NOUN
ejpam-3003	779	20	)	)	PUNCT
ejpam-3003	779	21	<	<	X
ejpam-3003	779	22	βd̃	βd̃	PRON
ejpam-3003	779	23	(	(	PUNCT
ejpam-3003	779	24	βd̃	βd̃	X
ejpam-3003	779	25	<	<	X
ejpam-3003	779	26	d̃	d̃	PROPN
ejpam-3003	779	27	)	)	PUNCT
ejpam-3003	779	28	into	into	ADP
ejpam-3003	779	29	two	two	NUM
ejpam-3003	779	30	parts	part	NOUN
ejpam-3003	779	31	:	:	PUNCT
ejpam-3003	779	32	the	the	DET
ejpam-3003	779	33	global	global	ADJ
ejpam-3003	779	34	existence	existence	NOUN
ejpam-3003	779	35	and	and	CCONJ
ejpam-3003	779	36	finite	finite	ADJ
ejpam-3003	779	37	time	time	NOUN
ejpam-3003	779	38	blow	blow	VERB
ejpam-3003	779	39	up	up	ADP
ejpam-3003	779	40	of	of	ADP
ejpam-3003	779	41	weak	weak	ADJ
ejpam-3003	779	42	solutions	solution	NOUN
ejpam-3003	779	43	for	for	ADP
ejpam-3003	779	44	the	the	DET
ejpam-3003	779	45	problem	problem	NOUN
ejpam-3003	779	46	(	(	PUNCT
ejpam-3003	779	47	1.1	1.1	NUM
ejpam-3003	779	48	)	)	PUNCT
ejpam-3003	779	49	.	.	PUNCT
ejpam-3003	780	1	references	reference	NOUN
ejpam-3003	780	2	699	699	NUM
ejpam-3003	780	3	acknowledgements	acknowledgement	NOUN
ejpam-3003	780	4	this	this	DET
ejpam-3003	780	5	work	work	NOUN
ejpam-3003	780	6	is	be	AUX
ejpam-3003	780	7	supported	support	VERB
ejpam-3003	780	8	by	by	ADP
ejpam-3003	780	9	the	the	DET
ejpam-3003	780	10	nsf	nsf	PROPN
ejpam-3003	780	11	of	of	ADP
ejpam-3003	780	12	china	china	PROPN
ejpam-3003	780	13	(	(	PUNCT
ejpam-3003	780	14	11626070	11626070	NUM
ejpam-3003	780	15	)	)	PUNCT
ejpam-3003	780	16	,	,	PUNCT
ejpam-3003	780	17	the	the	DET
ejpam-3003	780	18	scientific	scientific	ADJ
ejpam-3003	780	19	program	program	NOUN
ejpam-3003	780	20	(	(	PUNCT
ejpam-3003	780	21	2016a030310262	2016a030310262	NUM
ejpam-3003	780	22	)	)	PUNCT
ejpam-3003	780	23	of	of	ADP
ejpam-3003	780	24	guangdong	guangdong	PROPN
ejpam-3003	780	25	province	province	PROPN
ejpam-3003	780	26	.	.	PUNCT
ejpam-3003	781	1	references	reference	NOUN
ejpam-3003	781	2	[	[	X
ejpam-3003	781	3	1	1	NUM
ejpam-3003	781	4	]	]	X
ejpam-3003	781	5	a.b	a.b	PROPN
ejpam-3003	781	6	.	.	PROPN
ejpam-3003	781	7	al’shin	al’shin	PROPN
ejpam-3003	781	8	,	,	PUNCT
ejpam-3003	781	9	m.o	m.o	PROPN
ejpam-3003	781	10	.	.	PROPN
ejpam-3003	781	11	korpusov	korpusov	PROPN
ejpam-3003	781	12	,	,	PUNCT
ejpam-3003	781	13	a.g	a.g	PROPN
ejpam-3003	781	14	.	.	PROPN
ejpam-3003	781	15	siveshnikov	siveshnikov	PROPN
ejpam-3003	781	16	,	,	PUNCT
ejpam-3003	781	17	blow	blow	VERB
ejpam-3003	781	18	up	up	ADP
ejpam-3003	781	19	in	in	ADP
ejpam-3003	781	20	nonlinear	nonlinear	ADJ
ejpam-3003	781	21	sobolev	sobolev	ADJ
ejpam-3003	781	22	type	type	NOUN
ejpam-3003	781	23	equations	equation	NOUN
ejpam-3003	781	24	,	,	PUNCT
ejpam-3003	781	25	de	de	X
ejpam-3003	781	26	gruyter	gruyter	NOUN
ejpam-3003	781	27	series	series	PROPN
ejpam-3003	781	28	in	in	ADP
ejpam-3003	781	29	nonlinear	nonlinear	ADJ
ejpam-3003	781	30	aanlysis	aanlysis	NOUN
ejpam-3003	781	31	and	and	CCONJ
ejpam-3003	781	32	applicationss	applications	NOUN
ejpam-3003	781	33	15	15	NUM
ejpam-3003	781	34	,	,	PUNCT
ejpam-3003	781	35	berlin	berlin	PROPN
ejpam-3003	781	36	,	,	PUNCT
ejpam-3003	781	37	2011	2011	NUM
ejpam-3003	781	38	.	.	PUNCT
ejpam-3003	782	1	[	[	X
ejpam-3003	782	2	2	2	NUM
ejpam-3003	782	3	]	]	X
ejpam-3003	782	4	a.y	a.y	PROPN
ejpam-3003	782	5	.	.	PROPN
ejpam-3003	782	6	kolesov	kolesov	PROPN
ejpam-3003	782	7	,	,	PUNCT
ejpam-3003	782	8	e.f	e.f	PROPN
ejpam-3003	782	9	.	.	PROPN
ejpam-3003	782	10	mishchenko	mishchenko	PROPN
ejpam-3003	782	11	,	,	PUNCT
ejpam-3003	782	12	n.k	n.k	PROPN
ejpam-3003	782	13	.	.	PROPN
ejpam-3003	782	14	rozov	rozov	PROPN
ejpam-3003	782	15	,	,	PUNCT
ejpam-3003	782	16	asymptotic	asymptotic	ADJ
ejpam-3003	782	17	methods	method	NOUN
ejpam-3003	782	18	of	of	ADP
ejpam-3003	782	19	investigation	investigation	NOUN
ejpam-3003	782	20	of	of	ADP
ejpam-3003	782	21	periodic	periodic	ADJ
ejpam-3003	782	22	solutions	solution	NOUN
ejpam-3003	782	23	of	of	ADP
ejpam-3003	782	24	nonlinear	nonlinear	ADJ
ejpam-3003	782	25	hyperbolic	hyperbolic	ADJ
ejpam-3003	782	26	equations	equation	NOUN
ejpam-3003	782	27	,	,	PUNCT
ejpam-3003	782	28	trudy	trudy	PROPN
ejpam-3003	782	29	mat	mat	PROPN
ejpam-3003	782	30	.	.	PROPN
ejpam-3003	782	31	inst	inst	PROPN
ejpam-3003	782	32	.	.	PUNCT
ejpam-3003	782	33	steklova	steklova	PROPN
ejpam-3003	782	34	222	222	NUM
ejpam-3003	782	35	(	(	PUNCT
ejpam-3003	782	36	1998	1998	NUM
ejpam-3003	782	37	)	)	PUNCT
ejpam-3003	782	38	3	3	NUM
ejpam-3003	782	39	-	-	SYM
ejpam-3003	782	40	191	191	NUM
ejpam-3003	782	41	.	.	PUNCT
ejpam-3003	783	1	[	[	X
ejpam-3003	783	2	3	3	X
ejpam-3003	783	3	]	]	X
ejpam-3003	783	4	b.k	b.k	PROPN
ejpam-3003	783	5	.	.	PROPN
ejpam-3003	783	6	shivamoggi	shivamoggi	PROPN
ejpam-3003	783	7	,	,	PUNCT
ejpam-3003	783	8	a	a	DET
ejpam-3003	783	9	symmetric	symmetric	ADJ
ejpam-3003	783	10	regularized	regularize	VERB
ejpam-3003	783	11	long	long	ADJ
ejpam-3003	783	12	wave	wave	NOUN
ejpam-3003	783	13	equation	equation	NOUN
ejpam-3003	783	14	for	for	ADP
ejpam-3003	783	15	shallow	shallow	ADJ
ejpam-3003	783	16	water	water	NOUN
ejpam-3003	783	17	waves	wave	NOUN
ejpam-3003	783	18	,	,	PUNCT
ejpam-3003	783	19	physics	physics	NOUN
ejpam-3003	783	20	of	of	ADP
ejpam-3003	783	21	fluids	fluid	NOUN
ejpam-3003	783	22	29	29	NUM
ejpam-3003	783	23	(	(	PUNCT
ejpam-3003	783	24	1986	1986	NUM
ejpam-3003	783	25	)	)	PUNCT
ejpam-3003	783	26	890	890	NUM
ejpam-3003	783	27	-	-	SYM
ejpam-3003	783	28	891	891	NUM
ejpam-3003	783	29	.	.	PUNCT
ejpam-3003	784	1	[	[	X
ejpam-3003	784	2	4	4	X
ejpam-3003	784	3	]	]	PUNCT
ejpam-3003	784	4	p.	p.	NOUN
ejpam-3003	784	5	rosenau	rosenau	PROPN
ejpam-3003	784	6	,	,	PUNCT
ejpam-3003	784	7	evolution	evolution	NOUN
ejpam-3003	784	8	and	and	CCONJ
ejpam-3003	784	9	breaking	breaking	NOUN
ejpam-3003	784	10	of	of	ADP
ejpam-3003	784	11	the	the	DET
ejpam-3003	784	12	ion	ion	NOUN
ejpam-3003	784	13	-	-	PUNCT
ejpam-3003	784	14	acoustic	acoustic	ADJ
ejpam-3003	784	15	waves	wave	NOUN
ejpam-3003	784	16	,	,	PUNCT
ejpam-3003	784	17	physics	physics	NOUN
ejpam-3003	784	18	of	of	ADP
ejpam-3003	784	19	fluids	fluid	NOUN
ejpam-3003	784	20	31	31	NUM
ejpam-3003	784	21	(	(	PUNCT
ejpam-3003	784	22	1988	1988	NUM
ejpam-3003	784	23	)	)	PUNCT
ejpam-3003	784	24	1317	1317	NUM
ejpam-3003	784	25	-	-	SYM
ejpam-3003	784	26	1319	1319	NUM
ejpam-3003	784	27	.	.	PUNCT
ejpam-3003	785	1	[	[	X
ejpam-3003	785	2	5	5	X
ejpam-3003	785	3	]	]	PUNCT
ejpam-3003	785	4	s.	s.	PROPN
ejpam-3003	785	5	berrimi	berrimi	PROPN
ejpam-3003	785	6	,	,	PUNCT
ejpam-3003	785	7	s.a	s.a	PROPN
ejpam-3003	785	8	.	.	PROPN
ejpam-3003	785	9	messaoudi	messaoudi	PROPN
ejpam-3003	785	10	,	,	PUNCT
ejpam-3003	785	11	existence	existence	NOUN
ejpam-3003	785	12	and	and	CCONJ
ejpam-3003	785	13	decay	decay	NOUN
ejpam-3003	785	14	of	of	ADP
ejpam-3003	785	15	solutions	solution	NOUN
ejpam-3003	785	16	of	of	ADP
ejpam-3003	785	17	a	a	DET
ejpam-3003	785	18	viscoelastic	viscoelastic	ADJ
ejpam-3003	785	19	equation	equation	NOUN
ejpam-3003	785	20	with	with	ADP
ejpam-3003	785	21	a	a	DET
ejpam-3003	785	22	nonlinear	nonlinear	ADJ
ejpam-3003	785	23	source	source	NOUN
ejpam-3003	785	24	,	,	PUNCT
ejpam-3003	785	25	nonlinear	nonlinear	ADJ
ejpam-3003	785	26	anal	anal	NOUN
ejpam-3003	785	27	.	.	PUNCT
ejpam-3003	786	1	64	64	NUM
ejpam-3003	786	2	(	(	PUNCT
ejpam-3003	786	3	2006	2006	NUM
ejpam-3003	786	4	)	)	PUNCT
ejpam-3003	786	5	2314	2314	NUM
ejpam-3003	786	6	-	-	SYM
ejpam-3003	786	7	2331	2331	NUM
ejpam-3003	786	8	.	.	PUNCT
ejpam-3003	787	1	[	[	X
ejpam-3003	787	2	6	6	NUM
ejpam-3003	787	3	]	]	X
ejpam-3003	787	4	j.a	j.a	PROPN
ejpam-3003	787	5	.	.	PROPN
ejpam-3003	787	6	kim	kim	PROPN
ejpam-3003	787	7	,	,	PUNCT
ejpam-3003	787	8	y.h	y.h	PROPN
ejpam-3003	787	9	.	.	PROPN
ejpam-3003	787	10	han	han	PROPN
ejpam-3003	787	11	,	,	PUNCT
ejpam-3003	787	12	blow	blow	VERB
ejpam-3003	787	13	up	up	ADP
ejpam-3003	787	14	of	of	ADP
ejpam-3003	787	15	solutions	solution	NOUN
ejpam-3003	787	16	of	of	ADP
ejpam-3003	787	17	a	a	DET
ejpam-3003	787	18	nonlinear	nonlinear	ADJ
ejpam-3003	787	19	viscoelastic	viscoelastic	ADJ
ejpam-3003	787	20	wave	wave	NOUN
ejpam-3003	787	21	equation	equation	NOUN
ejpam-3003	787	22	,	,	PUNCT
ejpam-3003	787	23	acta	acta	PROPN
ejpam-3003	787	24	.	.	PUNCT
ejpam-3003	788	1	appl	appl	PROPN
ejpam-3003	788	2	.	.	PROPN
ejpam-3003	788	3	math	math	PROPN
ejpam-3003	788	4	.	.	PUNCT
ejpam-3003	789	1	111	111	NUM
ejpam-3003	789	2	(	(	PUNCT
ejpam-3003	789	3	2010	2010	NUM
ejpam-3003	789	4	)	)	PUNCT
ejpam-3003	789	5	1	1	NUM
ejpam-3003	789	6	-	-	SYM
ejpam-3003	789	7	6	6	NUM
ejpam-3003	789	8	.	.	PUNCT
ejpam-3003	790	1	[	[	X
ejpam-3003	790	2	7	7	X
ejpam-3003	790	3	]	]	X
ejpam-3003	790	4	y.j	y.j	PROPN
ejpam-3003	790	5	.	.	PROPN
ejpam-3003	790	6	wang	wang	PROPN
ejpam-3003	790	7	,	,	PUNCT
ejpam-3003	790	8	y.f	y.f	PROPN
ejpam-3003	790	9	.	.	PUNCT
ejpam-3003	790	10	wang	wang	PROPN
ejpam-3003	790	11	,	,	PUNCT
ejpam-3003	790	12	exponential	exponential	ADJ
ejpam-3003	790	13	energy	energy	NOUN
ejpam-3003	790	14	decay	decay	NOUN
ejpam-3003	790	15	of	of	ADP
ejpam-3003	790	16	solutions	solution	NOUN
ejpam-3003	790	17	of	of	ADP
ejpam-3003	790	18	viscoelastic	viscoelastic	ADJ
ejpam-3003	790	19	wave	wave	NOUN
ejpam-3003	790	20	equations	equation	NOUN
ejpam-3003	790	21	,	,	PUNCT
ejpam-3003	790	22	j.	j.	PROPN
ejpam-3003	790	23	math	math	PROPN
ejpam-3003	790	24	.	.	PUNCT
ejpam-3003	791	1	anal	anal	PROPN
ejpam-3003	791	2	.	.	PUNCT
ejpam-3003	792	1	appl	appl	PROPN
ejpam-3003	792	2	.	.	PUNCT
ejpam-3003	793	1	347	347	NUM
ejpam-3003	793	2	(	(	PUNCT
ejpam-3003	793	3	2008	2008	NUM
ejpam-3003	793	4	)	)	PUNCT
ejpam-3003	793	5	18	18	NUM
ejpam-3003	793	6	-	-	SYM
ejpam-3003	793	7	25	25	NUM
ejpam-3003	793	8	.	.	PUNCT
ejpam-3003	794	1	[	[	X
ejpam-3003	794	2	8	8	NUM
ejpam-3003	794	3	]	]	X
ejpam-3003	794	4	y.j	y.j	PROPN
ejpam-3003	794	5	.	.	PROPN
ejpam-3003	794	6	wang	wang	PROPN
ejpam-3003	794	7	,	,	PUNCT
ejpam-3003	794	8	a	a	DET
ejpam-3003	794	9	global	global	ADJ
ejpam-3003	794	10	nonexistence	nonexistence	NOUN
ejpam-3003	794	11	theorem	theorem	NOUN
ejpam-3003	794	12	for	for	ADP
ejpam-3003	794	13	viscoelastic	viscoelastic	ADJ
ejpam-3003	794	14	equations	equation	NOUN
ejpam-3003	794	15	with	with	ADP
ejpam-3003	794	16	arbitrary	arbitrary	ADJ
ejpam-3003	794	17	positive	positive	ADJ
ejpam-3003	794	18	initial	initial	ADJ
ejpam-3003	794	19	energy	energy	NOUN
ejpam-3003	794	20	,	,	PUNCT
ejpam-3003	794	21	appl	appl	PROPN
ejpam-3003	794	22	.	.	PROPN
ejpam-3003	794	23	math	math	PROPN
ejpam-3003	794	24	.	.	PUNCT
ejpam-3003	795	1	lett	lett	PROPN
ejpam-3003	795	2	.	.	PUNCT
ejpam-3003	796	1	22	22	NUM
ejpam-3003	796	2	(	(	PUNCT
ejpam-3003	796	3	2009	2009	NUM
ejpam-3003	796	4	)	)	PUNCT
ejpam-3003	796	5	1394	1394	NUM
ejpam-3003	796	6	-	-	SYM
ejpam-3003	796	7	1400	1400	NUM
ejpam-3003	796	8	.	.	PUNCT
ejpam-3003	797	1	[	[	X
ejpam-3003	797	2	9	9	NUM
ejpam-3003	797	3	]	]	X
ejpam-3003	797	4	s.a	s.a	PROPN
ejpam-3003	797	5	.	.	PROPN
ejpam-3003	797	6	messaoudi	messaoudi	PROPN
ejpam-3003	797	7	,	,	PUNCT
ejpam-3003	797	8	blow	blow	VERB
ejpam-3003	797	9	up	up	ADP
ejpam-3003	797	10	and	and	CCONJ
ejpam-3003	797	11	global	global	ADJ
ejpam-3003	797	12	existence	existence	NOUN
ejpam-3003	797	13	in	in	ADP
ejpam-3003	797	14	a	a	DET
ejpam-3003	797	15	nonlinear	nonlinear	ADJ
ejpam-3003	797	16	viscoelastic	viscoelastic	ADJ
ejpam-3003	797	17	wave	wave	NOUN
ejpam-3003	797	18	equation	equation	NOUN
ejpam-3003	797	19	,	,	PUNCT
ejpam-3003	797	20	math	math	NOUN
ejpam-3003	797	21	.	.	PUNCT
ejpam-3003	798	1	nachrichten	nachrichten	PROPN
ejpam-3003	798	2	260	260	NUM
ejpam-3003	798	3	(	(	PUNCT
ejpam-3003	798	4	2003	2003	NUM
ejpam-3003	798	5	)	)	PUNCT
ejpam-3003	798	6	58	58	NUM
ejpam-3003	798	7	-	-	SYM
ejpam-3003	798	8	66	66	NUM
ejpam-3003	798	9	.	.	PUNCT
ejpam-3003	799	1	[	[	X
ejpam-3003	799	2	10	10	NUM
ejpam-3003	799	3	]	]	X
ejpam-3003	799	4	s.a	s.a	PROPN
ejpam-3003	799	5	.	.	PROPN
ejpam-3003	799	6	messaoudi	messaoudi	PROPN
ejpam-3003	799	7	,	,	PUNCT
ejpam-3003	799	8	blow	blow	VERB
ejpam-3003	799	9	up	up	ADP
ejpam-3003	799	10	of	of	ADP
ejpam-3003	799	11	solutions	solution	NOUN
ejpam-3003	799	12	with	with	ADP
ejpam-3003	799	13	positive	positive	ADJ
ejpam-3003	799	14	initial	initial	ADJ
ejpam-3003	799	15	energy	energy	NOUN
ejpam-3003	799	16	in	in	ADP
ejpam-3003	799	17	a	a	DET
ejpam-3003	799	18	nonlinear	nonlinear	ADJ
ejpam-3003	799	19	viscoelastic	viscoelastic	ADJ
ejpam-3003	799	20	equation	equation	NOUN
ejpam-3003	799	21	,	,	PUNCT
ejpam-3003	799	22	j.	j.	PROPN
ejpam-3003	799	23	math	math	PROPN
ejpam-3003	799	24	.	.	PUNCT
ejpam-3003	800	1	anal	anal	PROPN
ejpam-3003	800	2	.	.	PUNCT
ejpam-3003	801	1	appl	appl	PROPN
ejpam-3003	801	2	.	.	PROPN
ejpam-3003	802	1	320	320	NUM
ejpam-3003	802	2	(	(	PUNCT
ejpam-3003	802	3	2006)902	2006)902	PROPN
ejpam-3003	802	4	-	-	PUNCT
ejpam-3003	802	5	915	915	NUM
ejpam-3003	802	6	.	.	PUNCT
ejpam-3003	803	1	[	[	X
ejpam-3003	803	2	11	11	NUM
ejpam-3003	803	3	]	]	X
ejpam-3003	803	4	h.t	h.t	PROPN
ejpam-3003	803	5	.	.	PROPN
ejpam-3003	803	6	song	song	PROPN
ejpam-3003	803	7	,	,	PUNCT
ejpam-3003	803	8	c.k	c.k	PROPN
ejpam-3003	803	9	.	.	PUNCT
ejpam-3003	803	10	zhong	zhong	PROPN
ejpam-3003	803	11	,	,	PUNCT
ejpam-3003	803	12	blow	blow	NOUN
ejpam-3003	803	13	-	-	PUNCT
ejpam-3003	803	14	up	up	NOUN
ejpam-3003	803	15	of	of	ADP
ejpam-3003	803	16	solutions	solution	NOUN
ejpam-3003	803	17	of	of	ADP
ejpam-3003	803	18	a	a	DET
ejpam-3003	803	19	nonlinear	nonlinear	ADJ
ejpam-3003	803	20	viscoelastic	viscoelastic	ADJ
ejpam-3003	803	21	wave	wave	NOUN
ejpam-3003	803	22	equation	equation	NOUN
ejpam-3003	803	23	,	,	PUNCT
ejpam-3003	803	24	nonlinear	nonlinear	ADJ
ejpam-3003	803	25	anal	anal	NOUN
ejpam-3003	803	26	.	.	PUNCT
ejpam-3003	804	1	rwa	rwa	PROPN
ejpam-3003	804	2	.	.	PROPN
ejpam-3003	804	3	11	11	NUM
ejpam-3003	804	4	(	(	PUNCT
ejpam-3003	804	5	2010	2010	NUM
ejpam-3003	804	6	)	)	PUNCT
ejpam-3003	804	7	3877	3877	NUM
ejpam-3003	804	8	-	-	SYM
ejpam-3003	804	9	3883	3883	NUM
ejpam-3003	804	10	.	.	PUNCT
ejpam-3003	805	1	[	[	X
ejpam-3003	805	2	12	12	NUM
ejpam-3003	805	3	]	]	X
ejpam-3003	805	4	x.s	x.s	PROPN
ejpam-3003	805	5	.	.	PROPN
ejpam-3003	805	6	han	han	PROPN
ejpam-3003	805	7	,	,	PUNCT
ejpam-3003	805	8	m.x	m.x	PROPN
ejpam-3003	805	9	.	.	PROPN
ejpam-3003	805	10	wang	wang	PROPN
ejpam-3003	805	11	,	,	PUNCT
ejpam-3003	805	12	general	general	ADJ
ejpam-3003	805	13	decay	decay	NOUN
ejpam-3003	805	14	of	of	ADP
ejpam-3003	805	15	energy	energy	NOUN
ejpam-3003	805	16	for	for	ADP
ejpam-3003	805	17	a	a	DET
ejpam-3003	805	18	viscoelastic	viscoelastic	ADJ
ejpam-3003	805	19	equation	equation	NOUN
ejpam-3003	805	20	with	with	ADP
ejpam-3003	805	21	nonlinear	nonlinear	ADJ
ejpam-3003	805	22	damping	damping	NOUN
ejpam-3003	805	23	,	,	PUNCT
ejpam-3003	805	24	j.	j.	PROPN
ejpam-3003	805	25	franklin	franklin	PROPN
ejpam-3003	805	26	inst	inst	PROPN
ejpam-3003	805	27	.	.	PUNCT
ejpam-3003	806	1	347	347	NUM
ejpam-3003	806	2	(	(	PUNCT
ejpam-3003	806	3	2010	2010	NUM
ejpam-3003	806	4	)	)	PUNCT
ejpam-3003	806	5	806	806	NUM
ejpam-3003	806	6	-	-	SYM
ejpam-3003	806	7	817	817	NUM
ejpam-3003	806	8	.	.	PUNCT
ejpam-3003	807	1	[	[	X
ejpam-3003	807	2	13	13	NUM
ejpam-3003	807	3	]	]	X
ejpam-3003	807	4	r.z	r.z	PROPN
ejpam-3003	807	5	.	.	PROPN
ejpam-3003	808	1	xu	xu	PROPN
ejpam-3003	808	2	,	,	PUNCT
ejpam-3003	808	3	y.b	y.b	PROPN
ejpam-3003	808	4	.	.	PROPN
ejpam-3003	808	5	yang	yang	PROPN
ejpam-3003	808	6	,	,	PUNCT
ejpam-3003	808	7	y.c	y.c	PROPN
ejpam-3003	808	8	.	.	PROPN
ejpam-3003	808	9	liu	liu	PROPN
ejpam-3003	808	10	,	,	PUNCT
ejpam-3003	808	11	global	global	ADJ
ejpam-3003	808	12	well	well	NOUN
ejpam-3003	808	13	-	-	PUNCT
ejpam-3003	808	14	posedness	posedness	NOUN
ejpam-3003	808	15	for	for	ADP
ejpam-3003	808	16	strongly	strongly	ADV
ejpam-3003	808	17	damped	damp	VERB
ejpam-3003	808	18	viscoelastic	viscoelastic	ADJ
ejpam-3003	808	19	wave	wave	NOUN
ejpam-3003	808	20	equation	equation	NOUN
ejpam-3003	808	21	,	,	PUNCT
ejpam-3003	808	22	appl	appl	PROPN
ejpam-3003	808	23	.	.	PROPN
ejpam-3003	809	1	anal	anal	PROPN
ejpam-3003	809	2	.	.	PUNCT
ejpam-3003	810	1	92	92	NUM
ejpam-3003	810	2	(	(	PUNCT
ejpam-3003	810	3	2013	2013	NUM
ejpam-3003	810	4	)	)	PUNCT
ejpam-3003	810	5	138	138	NUM
ejpam-3003	810	6	-	-	SYM
ejpam-3003	810	7	157	157	NUM
ejpam-3003	810	8	.	.	PUNCT
ejpam-3003	810	9	references	reference	NOUN
ejpam-3003	810	10	700	700	NUM
ejpam-3003	810	11	[	[	SYM
ejpam-3003	810	12	14	14	NUM
ejpam-3003	810	13	]	]	X
ejpam-3003	810	14	s.a	s.a	PROPN
ejpam-3003	810	15	.	.	PROPN
ejpam-3003	810	16	messaoudi	messaoudi	PROPN
ejpam-3003	810	17	,	,	PUNCT
ejpam-3003	810	18	n.e	n.e	PROPN
ejpam-3003	810	19	.	.	PROPN
ejpam-3003	810	20	tatar	tatar	PROPN
ejpam-3003	810	21	,	,	PUNCT
ejpam-3003	810	22	global	global	ADJ
ejpam-3003	810	23	existence	existence	NOUN
ejpam-3003	810	24	and	and	CCONJ
ejpam-3003	810	25	uniform	uniform	ADJ
ejpam-3003	810	26	stability	stability	NOUN
ejpam-3003	810	27	of	of	ADP
ejpam-3003	810	28	solutions	solution	NOUN
ejpam-3003	810	29	for	for	ADP
ejpam-3003	810	30	a	a	DET
ejpam-3003	810	31	quasilinear	quasilinear	ADJ
ejpam-3003	810	32	viscoelastic	viscoelastic	ADJ
ejpam-3003	810	33	problem	problem	NOUN
ejpam-3003	810	34	,	,	PUNCT
ejpam-3003	810	35	math	math	NOUN
ejpam-3003	810	36	.	.	PUNCT
ejpam-3003	811	1	methods	method	NOUN
ejpam-3003	811	2	appl	appl	PROPN
ejpam-3003	811	3	.	.	PUNCT
ejpam-3003	812	1	sci	sci	PROPN
ejpam-3003	812	2	.	.	PROPN
ejpam-3003	812	3	30	30	NUM
ejpam-3003	812	4	(	(	PUNCT
ejpam-3003	812	5	2007	2007	NUM
ejpam-3003	812	6	)	)	PUNCT
ejpam-3003	812	7	665	665	NUM
ejpam-3003	812	8	-	-	SYM
ejpam-3003	812	9	680	680	NUM
ejpam-3003	812	10	.	.	PUNCT
ejpam-3003	813	1	[	[	X
ejpam-3003	813	2	15	15	NUM
ejpam-3003	813	3	]	]	X
ejpam-3003	813	4	w.j	w.j	PROPN
ejpam-3003	813	5	.	.	PROPN
ejpam-3003	813	6	liu	liu	PROPN
ejpam-3003	813	7	,	,	PUNCT
ejpam-3003	813	8	general	general	ADJ
ejpam-3003	813	9	decay	decay	NOUN
ejpam-3003	813	10	and	and	CCONJ
ejpam-3003	813	11	blow	blow	NOUN
ejpam-3003	813	12	-	-	PUNCT
ejpam-3003	813	13	up	up	NOUN
ejpam-3003	813	14	of	of	ADP
ejpam-3003	813	15	solution	solution	NOUN
ejpam-3003	813	16	for	for	ADP
ejpam-3003	813	17	a	a	DET
ejpam-3003	813	18	quasilinear	quasilinear	ADJ
ejpam-3003	813	19	viscoelastic	viscoelastic	ADJ
ejpam-3003	813	20	problem	problem	NOUN
ejpam-3003	813	21	with	with	ADP
ejpam-3003	813	22	nonlinear	nonlinear	ADJ
ejpam-3003	813	23	source	source	NOUN
ejpam-3003	813	24	,	,	PUNCT
ejpam-3003	813	25	nonlinear	nonlinear	ADJ
ejpam-3003	813	26	anal	anal	NOUN
ejpam-3003	813	27	.	.	PUNCT
ejpam-3003	814	1	tma	tma	PROPN
ejpam-3003	814	2	.	.	PROPN
ejpam-3003	815	1	73	73	NUM
ejpam-3003	815	2	(	(	PUNCT
ejpam-3003	815	3	2010	2010	NUM
ejpam-3003	815	4	)	)	PUNCT
ejpam-3003	815	5	1890	1890	NUM
ejpam-3003	815	6	-	-	SYM
ejpam-3003	815	7	1904	1904	NUM
ejpam-3003	815	8	.	.	PUNCT
ejpam-3003	816	1	[	[	X
ejpam-3003	816	2	16	16	NUM
ejpam-3003	816	3	]	]	X
ejpam-3003	816	4	m.m	m.m	PROPN
ejpam-3003	816	5	.	.	PROPN
ejpam-3003	816	6	cavalcanti	cavalcanti	PROPN
ejpam-3003	816	7	,	,	PUNCT
ejpam-3003	816	8	v.n.d	v.n.d	NOUN
ejpam-3003	816	9	.	.	PUNCT
ejpam-3003	817	1	cavalcanti	cavalcanti	PROPN
ejpam-3003	817	2	,	,	PUNCT
ejpam-3003	817	3	j.	j.	PROPN
ejpam-3003	817	4	ferreira	ferreira	PROPN
ejpam-3003	817	5	,	,	PUNCT
ejpam-3003	817	6	existence	existence	NOUN
ejpam-3003	817	7	and	and	CCONJ
ejpam-3003	817	8	uniform	uniform	ADJ
ejpam-3003	817	9	decay	decay	NOUN
ejpam-3003	817	10	for	for	ADP
ejpam-3003	817	11	nonlinear	nonlinear	ADJ
ejpam-3003	817	12	viscoelastic	viscoelastic	ADJ
ejpam-3003	817	13	equation	equation	NOUN
ejpam-3003	817	14	with	with	ADP
ejpam-3003	817	15	strong	strong	ADJ
ejpam-3003	817	16	damping	damping	NOUN
ejpam-3003	817	17	,	,	PUNCT
ejpam-3003	817	18	math	math	NOUN
ejpam-3003	817	19	.	.	PUNCT
ejpam-3003	818	1	methods	method	NOUN
ejpam-3003	818	2	appl	appl	PROPN
ejpam-3003	818	3	.	.	PUNCT
ejpam-3003	819	1	sci	sci	PROPN
ejpam-3003	819	2	.	.	PROPN
ejpam-3003	820	1	24	24	NUM
ejpam-3003	820	2	(	(	PUNCT
ejpam-3003	820	3	2001	2001	NUM
ejpam-3003	820	4	)	)	PUNCT
ejpam-3003	820	5	1043	1043	NUM
ejpam-3003	820	6	-	-	SYM
ejpam-3003	820	7	1053	1053	NUM
ejpam-3003	820	8	.	.	PUNCT
ejpam-3003	821	1	[	[	X
ejpam-3003	821	2	17	17	NUM
ejpam-3003	821	3	]	]	X
ejpam-3003	821	4	s.t	s.t	PROPN
ejpam-3003	821	5	.	.	PROPN
ejpam-3003	821	6	wu	wu	PROPN
ejpam-3003	821	7	,	,	PUNCT
ejpam-3003	821	8	general	general	ADJ
ejpam-3003	821	9	decay	decay	NOUN
ejpam-3003	821	10	of	of	ADP
ejpam-3003	821	11	solutions	solution	NOUN
ejpam-3003	821	12	for	for	ADP
ejpam-3003	821	13	a	a	DET
ejpam-3003	821	14	viscoelastic	viscoelastic	ADJ
ejpam-3003	821	15	equation	equation	NOUN
ejpam-3003	821	16	with	with	ADP
ejpam-3003	821	17	nonlinear	nonlinear	ADJ
ejpam-3003	821	18	damping	damp	VERB
ejpam-3003	821	19	and	and	CCONJ
ejpam-3003	821	20	source	source	NOUN
ejpam-3003	821	21	terms	term	NOUN
ejpam-3003	821	22	,	,	PUNCT
ejpam-3003	821	23	acta	acta	PROPN
ejpam-3003	821	24	math	math	PROPN
ejpam-3003	821	25	.	.	PUNCT
ejpam-3003	822	1	sci	sci	PROPN
ejpam-3003	822	2	.	.	PROPN
ejpam-3003	822	3	31b	31b	PROPN
ejpam-3003	822	4	(	(	PUNCT
ejpam-3003	822	5	2011	2011	NUM
ejpam-3003	822	6	)	)	PUNCT
ejpam-3003	822	7	1436	1436	NUM
ejpam-3003	822	8	-	-	SYM
ejpam-3003	822	9	1448	1448	NUM
ejpam-3003	822	10	.	.	PUNCT
ejpam-3003	823	1	[	[	X
ejpam-3003	823	2	18	18	NUM
ejpam-3003	823	3	]	]	X
ejpam-3003	823	4	m.m	m.m	PROPN
ejpam-3003	823	5	.	.	PROPN
ejpam-3003	823	6	cavalcanti	cavalcanti	PROPN
ejpam-3003	823	7	,	,	PUNCT
ejpam-3003	823	8	v.n.d	v.n.d	NOUN
ejpam-3003	823	9	.	.	PUNCT
ejpam-3003	824	1	cavalcanti	cavalcanti	PROPN
ejpam-3003	824	2	,	,	PUNCT
ejpam-3003	824	3	j.s.p	j.s.p	PROPN
ejpam-3003	824	4	.	.	PUNCT
ejpam-3003	824	5	filho	filho	PROPN
ejpam-3003	824	6	,	,	PUNCT
ejpam-3003	824	7	j.a	j.a	PROPN
ejpam-3003	824	8	.	.	PROPN
ejpam-3003	824	9	soriano	soriano	PROPN
ejpam-3003	824	10	,	,	PUNCT
ejpam-3003	824	11	existence	existence	NOUN
ejpam-3003	824	12	and	and	CCONJ
ejpam-3003	824	13	uniform	uniform	ADJ
ejpam-3003	824	14	decay	decay	NOUN
ejpam-3003	824	15	rates	rate	NOUN
ejpam-3003	824	16	for	for	ADP
ejpam-3003	824	17	viscoelastic	viscoelastic	ADJ
ejpam-3003	824	18	problems	problem	NOUN
ejpam-3003	824	19	with	with	ADP
ejpam-3003	824	20	nonlinear	nonlinear	ADJ
ejpam-3003	824	21	boundary	boundary	ADJ
ejpam-3003	824	22	damping	damp	VERB
ejpam-3003	824	23	,	,	PUNCT
ejpam-3003	824	24	differential	differential	ADJ
ejpam-3003	824	25	integral	integral	ADJ
ejpam-3003	824	26	equations	equation	NOUN
ejpam-3003	824	27	14	14	NUM
ejpam-3003	824	28	(	(	PUNCT
ejpam-3003	824	29	2001	2001	NUM
ejpam-3003	824	30	)	)	PUNCT
ejpam-3003	824	31	85	85	NUM
ejpam-3003	824	32	-	-	SYM
ejpam-3003	824	33	116	116	NUM
ejpam-3003	824	34	.	.	PUNCT
ejpam-3003	825	1	[	[	X
ejpam-3003	825	2	19	19	NUM
ejpam-3003	825	3	]	]	X
ejpam-3003	825	4	m.m	m.m	PROPN
ejpam-3003	825	5	.	.	PROPN
ejpam-3003	825	6	cavalcanti	cavalcanti	PROPN
ejpam-3003	825	7	,	,	PUNCT
ejpam-3003	825	8	v.n.d	v.n.d	NOUN
ejpam-3003	825	9	.	.	PUNCT
ejpam-3003	826	1	cavalcanti	cavalcanti	PROPN
ejpam-3003	826	2	,	,	PUNCT
ejpam-3003	826	3	p.	p.	PROPN
ejpam-3003	826	4	martinez	martinez	PROPN
ejpam-3003	826	5	,	,	PUNCT
ejpam-3003	826	6	general	general	ADJ
ejpam-3003	826	7	decay	decay	NOUN
ejpam-3003	826	8	rate	rate	NOUN
ejpam-3003	826	9	estimates	estimate	NOUN
ejpam-3003	826	10	for	for	ADP
ejpam-3003	826	11	viscoelastic	viscoelastic	ADJ
ejpam-3003	826	12	dissipative	dissipative	NOUN
ejpam-3003	826	13	systems	system	NOUN
ejpam-3003	826	14	,	,	PUNCT
ejpam-3003	826	15	nonlinear	nonlinear	ADJ
ejpam-3003	826	16	anal	anal	NOUN
ejpam-3003	826	17	.	.	PUNCT
ejpam-3003	827	1	68	68	NUM
ejpam-3003	827	2	(	(	PUNCT
ejpam-3003	827	3	2008	2008	NUM
ejpam-3003	827	4	)	)	PUNCT
ejpam-3003	827	5	177	177	NUM
ejpam-3003	827	6	-	-	SYM
ejpam-3003	827	7	193	193	NUM
ejpam-3003	827	8	.	.	PUNCT
ejpam-3003	828	1	[	[	X
ejpam-3003	828	2	20	20	NUM
ejpam-3003	828	3	]	]	X
ejpam-3003	828	4	s.a	s.a	PROPN
ejpam-3003	828	5	.	.	PROPN
ejpam-3003	828	6	messaoudi	messaoudi	PROPN
ejpam-3003	828	7	,	,	PUNCT
ejpam-3003	828	8	m.i	m.i	PROPN
ejpam-3003	828	9	.	.	PROPN
ejpam-3003	828	10	mustafa	mustafa	PROPN
ejpam-3003	828	11	,	,	PUNCT
ejpam-3003	828	12	on	on	ADP
ejpam-3003	828	13	the	the	DET
ejpam-3003	828	14	control	control	NOUN
ejpam-3003	828	15	of	of	ADP
ejpam-3003	828	16	solutions	solution	NOUN
ejpam-3003	828	17	of	of	ADP
ejpam-3003	828	18	viscoelastic	viscoelastic	ADJ
ejpam-3003	828	19	equations	equation	NOUN
ejpam-3003	828	20	with	with	ADP
ejpam-3003	828	21	boundary	boundary	ADJ
ejpam-3003	828	22	feedback	feedback	NOUN
ejpam-3003	828	23	,	,	PUNCT
ejpam-3003	828	24	nonlinear	nonlinear	ADJ
ejpam-3003	828	25	anal	anal	NOUN
ejpam-3003	828	26	.	.	PUNCT
ejpam-3003	829	1	rwa	rwa	PROPN
ejpam-3003	829	2	.	.	PROPN
ejpam-3003	829	3	10	10	NUM
ejpam-3003	829	4	(	(	PUNCT
ejpam-3003	829	5	2009	2009	NUM
ejpam-3003	829	6	)	)	PUNCT
ejpam-3003	829	7	3132	3132	NUM
ejpam-3003	829	8	-	-	SYM
ejpam-3003	829	9	3140	3140	NUM
ejpam-3003	829	10	.	.	PUNCT
ejpam-3003	830	1	[	[	X
ejpam-3003	830	2	21	21	NUM
ejpam-3003	830	3	]	]	X
ejpam-3003	830	4	l.q	l.q	PROPN
ejpam-3003	830	5	.	.	PROPN
ejpam-3003	830	6	lu	lu	PROPN
ejpam-3003	830	7	,	,	PUNCT
ejpam-3003	830	8	s.j	s.j	PROPN
ejpam-3003	830	9	.	.	PROPN
ejpam-3003	830	10	li	li	PROPN
ejpam-3003	830	11	,	,	PUNCT
ejpam-3003	830	12	s.g	s.g	PROPN
ejpam-3003	830	13	.	.	PROPN
ejpam-3003	830	14	chai	chai	NOUN
ejpam-3003	830	15	,	,	PUNCT
ejpam-3003	830	16	on	on	ADP
ejpam-3003	830	17	a	a	DET
ejpam-3003	830	18	viscoelastic	viscoelastic	ADJ
ejpam-3003	830	19	equation	equation	NOUN
ejpam-3003	830	20	with	with	ADP
ejpam-3003	830	21	nonlinear	nonlinear	ADJ
ejpam-3003	830	22	boundary	boundary	ADJ
ejpam-3003	830	23	damping	damp	VERB
ejpam-3003	830	24	and	and	CCONJ
ejpam-3003	830	25	source	source	NOUN
ejpam-3003	830	26	terms	term	NOUN
ejpam-3003	830	27	:	:	PUNCT
ejpam-3003	830	28	global	global	ADJ
ejpam-3003	830	29	existence	existence	NOUN
ejpam-3003	830	30	and	and	CCONJ
ejpam-3003	830	31	decay	decay	NOUN
ejpam-3003	830	32	of	of	ADP
ejpam-3003	830	33	the	the	DET
ejpam-3003	830	34	solution	solution	NOUN
ejpam-3003	830	35	,	,	PUNCT
ejpam-3003	830	36	nonlinear	nonlinear	ADJ
ejpam-3003	830	37	anal	anal	NOUN
ejpam-3003	830	38	.	.	PUNCT
ejpam-3003	831	1	rwa	rwa	PROPN
ejpam-3003	831	2	.	.	PROPN
ejpam-3003	831	3	12	12	NUM
ejpam-3003	831	4	(	(	PUNCT
ejpam-3003	831	5	2012	2012	NUM
ejpam-3003	831	6	)	)	PUNCT
ejpam-3003	831	7	295	295	NUM
ejpam-3003	831	8	-	-	SYM
ejpam-3003	831	9	302	302	NUM
ejpam-3003	831	10	.	.	PUNCT
ejpam-3003	832	1	[	[	X
ejpam-3003	832	2	22	22	NUM
ejpam-3003	832	3	]	]	X
ejpam-3003	832	4	w.j	w.j	PROPN
ejpam-3003	832	5	.	.	PROPN
ejpam-3003	832	6	liu	liu	PROPN
ejpam-3003	832	7	,	,	PUNCT
ejpam-3003	832	8	j.	j.	PROPN
ejpam-3003	832	9	yu	yu	PROPN
ejpam-3003	832	10	,	,	PUNCT
ejpam-3003	832	11	on	on	ADP
ejpam-3003	832	12	decay	decay	NOUN
ejpam-3003	832	13	and	and	CCONJ
ejpam-3003	832	14	blow	blow	NOUN
ejpam-3003	832	15	-	-	PUNCT
ejpam-3003	832	16	up	up	NOUN
ejpam-3003	832	17	of	of	ADP
ejpam-3003	832	18	the	the	DET
ejpam-3003	832	19	solution	solution	NOUN
ejpam-3003	832	20	for	for	ADP
ejpam-3003	832	21	a	a	DET
ejpam-3003	832	22	viscoelastic	viscoelastic	ADJ
ejpam-3003	832	23	wave	wave	NOUN
ejpam-3003	832	24	equation	equation	NOUN
ejpam-3003	832	25	with	with	ADP
ejpam-3003	832	26	boundary	boundary	ADJ
ejpam-3003	832	27	damping	damp	VERB
ejpam-3003	832	28	and	and	CCONJ
ejpam-3003	832	29	source	source	NOUN
ejpam-3003	832	30	terms	term	NOUN
ejpam-3003	832	31	,	,	PUNCT
ejpam-3003	832	32	nonlinear	nonlinear	ADJ
ejpam-3003	832	33	anal	anal	NOUN
ejpam-3003	832	34	.	.	PUNCT
ejpam-3003	833	1	74	74	NUM
ejpam-3003	833	2	(	(	PUNCT
ejpam-3003	833	3	2011	2011	NUM
ejpam-3003	833	4	)	)	PUNCT
ejpam-3003	833	5	2175	2175	NUM
ejpam-3003	833	6	-	-	SYM
ejpam-3003	833	7	2190	2190	NUM
ejpam-3003	833	8	.	.	PUNCT
ejpam-3003	834	1	[	[	X
ejpam-3003	834	2	23	23	NUM
ejpam-3003	834	3	]	]	X
ejpam-3003	834	4	m.m	m.m	PROPN
ejpam-3003	834	5	.	.	PROPN
ejpam-3003	834	6	cavalcanti	cavalcanti	PROPN
ejpam-3003	834	7	,	,	PUNCT
ejpam-3003	834	8	v.n.d	v.n.d	NOUN
ejpam-3003	834	9	.	.	PUNCT
ejpam-3003	835	1	cavalcanti	cavalcanti	PROPN
ejpam-3003	835	2	,	,	PUNCT
ejpam-3003	835	3	j.a	j.a	PROPN
ejpam-3003	835	4	.	.	PROPN
ejpam-3003	835	5	soriano	soriano	PROPN
ejpam-3003	835	6	,	,	PUNCT
ejpam-3003	835	7	exponential	exponential	ADJ
ejpam-3003	835	8	decay	decay	NOUN
ejpam-3003	835	9	for	for	ADP
ejpam-3003	835	10	the	the	DET
ejpam-3003	835	11	solution	solution	NOUN
ejpam-3003	835	12	of	of	ADP
ejpam-3003	835	13	semilinear	semilinear	ADJ
ejpam-3003	835	14	viscoelastic	viscoelastic	PROPN
ejpam-3003	835	15	wave	wave	NOUN
ejpam-3003	835	16	equations	equation	NOUN
ejpam-3003	835	17	with	with	ADP
ejpam-3003	835	18	localized	localized	ADJ
ejpam-3003	835	19	damping	damping	NOUN
ejpam-3003	835	20	,	,	PUNCT
ejpam-3003	835	21	electron	electron	NOUN
ejpam-3003	835	22	.	.	PUNCT
ejpam-3003	836	1	j.	j.	PROPN
ejpam-3003	836	2	differ	differ	VERB
ejpam-3003	836	3	.	.	PUNCT
ejpam-3003	837	1	equ	equ	PROPN
ejpam-3003	837	2	.	.	PROPN
ejpam-3003	837	3	2002	2002	NUM
ejpam-3003	837	4	(	(	PUNCT
ejpam-3003	837	5	2002	2002	NUM
ejpam-3003	837	6	)	)	PUNCT
ejpam-3003	837	7	(	(	PUNCT
ejpam-3003	837	8	44	44	NUM
ejpam-3003	837	9	)	)	SYM
ejpam-3003	837	10	1	1	NUM
ejpam-3003	837	11	-	-	SYM
ejpam-3003	837	12	14	14	NUM
ejpam-3003	837	13	.	.	PUNCT
ejpam-3003	838	1	[	[	X
ejpam-3003	838	2	24	24	NUM
ejpam-3003	838	3	]	]	X
ejpam-3003	838	4	s.a	s.a	PROPN
ejpam-3003	838	5	.	.	PROPN
ejpam-3003	838	6	messaoudi	messaoudi	PROPN
ejpam-3003	838	7	,	,	PUNCT
ejpam-3003	838	8	general	general	ADJ
ejpam-3003	838	9	decay	decay	NOUN
ejpam-3003	838	10	of	of	ADP
ejpam-3003	838	11	the	the	DET
ejpam-3003	838	12	solution	solution	NOUN
ejpam-3003	838	13	energy	energy	NOUN
ejpam-3003	838	14	in	in	ADP
ejpam-3003	838	15	a	a	DET
ejpam-3003	838	16	viscoelastic	viscoelastic	ADJ
ejpam-3003	838	17	equation	equation	NOUN
ejpam-3003	838	18	with	with	ADP
ejpam-3003	838	19	a	a	DET
ejpam-3003	838	20	nonlinear	nonlinear	ADJ
ejpam-3003	838	21	source	source	NOUN
ejpam-3003	838	22	,	,	PUNCT
ejpam-3003	838	23	nonlinear	nonlinear	ADJ
ejpam-3003	838	24	anal	anal	NOUN
ejpam-3003	838	25	.	.	PUNCT
ejpam-3003	839	1	69	69	NUM
ejpam-3003	839	2	(	(	PUNCT
ejpam-3003	839	3	2008	2008	NUM
ejpam-3003	839	4	)	)	PUNCT
ejpam-3003	839	5	(	(	PUNCT
ejpam-3003	839	6	8)	8)	NUM
ejpam-3003	839	7	2589	2589	NUM
ejpam-3003	839	8	-	-	SYM
ejpam-3003	839	9	2598	2598	NUM
ejpam-3003	839	10	.	.	PUNCT
ejpam-3003	840	1	[	[	X
ejpam-3003	840	2	25	25	NUM
ejpam-3003	840	3	]	]	X
ejpam-3003	840	4	h.a	h.a	PROPN
ejpam-3003	840	5	.	.	PROPN
ejpam-3003	840	6	levine	levine	PROPN
ejpam-3003	840	7	,	,	PUNCT
ejpam-3003	840	8	r.a	r.a	PROPN
ejpam-3003	840	9	.	.	PROPN
ejpam-3003	840	10	smith	smith	PROPN
ejpam-3003	840	11	,	,	PUNCT
ejpam-3003	840	12	a	a	DET
ejpam-3003	840	13	potential	potential	ADJ
ejpam-3003	840	14	well	well	ADJ
ejpam-3003	840	15	theory	theory	NOUN
ejpam-3003	840	16	for	for	ADP
ejpam-3003	840	17	the	the	DET
ejpam-3003	840	18	wave	wave	NOUN
ejpam-3003	840	19	equation	equation	NOUN
ejpam-3003	840	20	with	with	ADP
ejpam-3003	840	21	a	a	DET
ejpam-3003	840	22	nonlinear	nonlinear	ADJ
ejpam-3003	840	23	boundary	boundary	ADJ
ejpam-3003	840	24	condition	condition	NOUN
ejpam-3003	840	25	,	,	PUNCT
ejpam-3003	840	26	j.	j.	PROPN
ejpam-3003	840	27	reine	reine	PROPN
ejpam-3003	840	28	angew	angew	PROPN
ejpam-3003	840	29	.	.	PUNCT
ejpam-3003	841	1	math	math	NOUN
ejpam-3003	841	2	.	.	PUNCT
ejpam-3003	842	1	374	374	NUM
ejpam-3003	842	2	(	(	PUNCT
ejpam-3003	842	3	1987	1987	NUM
ejpam-3003	842	4	)	)	PUNCT
ejpam-3003	842	5	1	1	NUM
ejpam-3003	842	6	-	-	SYM
ejpam-3003	842	7	23	23	NUM
ejpam-3003	842	8	.	.	PUNCT
ejpam-3003	843	1	[	[	X
ejpam-3003	843	2	26	26	NUM
ejpam-3003	843	3	]	]	X
ejpam-3003	843	4	d.h	d.h	PROPN
ejpam-3003	843	5	.	.	PROPN
ejpam-3003	843	6	sattinger	sattinger	PROPN
ejpam-3003	843	7	,	,	PUNCT
ejpam-3003	843	8	on	on	ADP
ejpam-3003	843	9	global	global	ADJ
ejpam-3003	843	10	solution	solution	NOUN
ejpam-3003	843	11	of	of	ADP
ejpam-3003	843	12	nonlinear	nonlinear	ADJ
ejpam-3003	843	13	hyperbolic	hyperbolic	ADJ
ejpam-3003	843	14	equations	equation	NOUN
ejpam-3003	843	15	,	,	PUNCT
ejpam-3003	843	16	arch	arch	NOUN
ejpam-3003	843	17	.	.	PUNCT
ejpam-3003	844	1	rat	rat	NOUN
ejpam-3003	844	2	.	.	PROPN
ejpam-3003	844	3	mech	mech	PROPN
ejpam-3003	844	4	.	.	PUNCT
ejpam-3003	845	1	anal	anal	PROPN
ejpam-3003	845	2	.	.	PUNCT
ejpam-3003	846	1	30	30	NUM
ejpam-3003	846	2	(	(	PUNCT
ejpam-3003	846	3	1968	1968	NUM
ejpam-3003	846	4	)	)	PUNCT
ejpam-3003	846	5	148	148	NUM
ejpam-3003	846	6	-	-	SYM
ejpam-3003	846	7	172	172	NUM
ejpam-3003	846	8	.	.	PUNCT
ejpam-3003	847	1	[	[	X
ejpam-3003	847	2	27	27	NUM
ejpam-3003	847	3	]	]	X
ejpam-3003	847	4	l.e	l.e	PROPN
ejpam-3003	847	5	.	.	PROPN
ejpam-3003	847	6	payne	payne	PROPN
ejpam-3003	847	7	,	,	PUNCT
ejpam-3003	847	8	d.h	d.h	PROPN
ejpam-3003	847	9	.	.	PROPN
ejpam-3003	847	10	sattinger	sattinger	PROPN
ejpam-3003	847	11	,	,	PUNCT
ejpam-3003	847	12	saddle	saddle	NOUN
ejpam-3003	847	13	points	point	NOUN
ejpam-3003	847	14	and	and	CCONJ
ejpam-3003	847	15	instability	instability	NOUN
ejpam-3003	847	16	on	on	ADP
ejpam-3003	847	17	nonlinear	nonlinear	ADJ
ejpam-3003	847	18	hyperbolic	hyperbolic	ADJ
ejpam-3003	847	19	equations	equation	NOUN
ejpam-3003	847	20	,	,	PUNCT
ejpam-3003	847	21	israel	israel	PROPN
ejpam-3003	847	22	.	.	PUNCT
ejpam-3003	847	23	math	math	PROPN
ejpam-3003	847	24	.	.	PUNCT
ejpam-3003	848	1	j.	j.	PROPN
ejpam-3003	848	2	22	22	NUM
ejpam-3003	848	3	(	(	PUNCT
ejpam-3003	848	4	1975	1975	NUM
ejpam-3003	848	5	)	)	PUNCT
ejpam-3003	848	6	273	273	NUM
ejpam-3003	848	7	-	-	SYM
ejpam-3003	848	8	303	303	NUM
ejpam-3003	848	9	.	.	PUNCT
ejpam-3003	849	1	[	[	X
ejpam-3003	849	2	28	28	NUM
ejpam-3003	849	3	]	]	X
ejpam-3003	849	4	y.c	y.c	PROPN
ejpam-3003	849	5	.	.	PROPN
ejpam-3003	849	6	liu	liu	PROPN
ejpam-3003	849	7	,	,	PUNCT
ejpam-3003	849	8	r.z	r.z	PROPN
ejpam-3003	849	9	.	.	PROPN
ejpam-3003	849	10	xu	xu	PROPN
ejpam-3003	849	11	,	,	PUNCT
ejpam-3003	849	12	fourth	fourth	ADJ
ejpam-3003	849	13	order	order	NOUN
ejpam-3003	849	14	wave	wave	NOUN
ejpam-3003	849	15	equations	equation	NOUN
ejpam-3003	849	16	with	with	ADP
ejpam-3003	849	17	nonlinear	nonlinear	ADJ
ejpam-3003	849	18	strain	strain	NOUN
ejpam-3003	849	19	and	and	CCONJ
ejpam-3003	849	20	source	source	NOUN
ejpam-3003	849	21	terms	term	NOUN
ejpam-3003	849	22	,	,	PUNCT
ejpam-3003	849	23	j.	j.	PROPN
ejpam-3003	849	24	math	math	PROPN
ejpam-3003	849	25	.	.	PUNCT
ejpam-3003	850	1	anal	anal	PROPN
ejpam-3003	850	2	.	.	PUNCT
ejpam-3003	850	3	appl	appl	PROPN
ejpam-3003	850	4	.	.	PUNCT
ejpam-3003	851	1	331	331	NUM
ejpam-3003	851	2	(	(	PUNCT
ejpam-3003	851	3	2007	2007	NUM
ejpam-3003	851	4	)	)	PUNCT
ejpam-3003	851	5	585	585	NUM
ejpam-3003	851	6	-	-	SYM
ejpam-3003	851	7	607	607	NUM
ejpam-3003	851	8	.	.	PUNCT
ejpam-3003	852	1	references	reference	NOUN
ejpam-3003	852	2	701	701	NUM
ejpam-3003	853	1	[	[	X
ejpam-3003	853	2	29	29	NUM
ejpam-3003	853	3	]	]	X
ejpam-3003	853	4	r.z	r.z	PROPN
ejpam-3003	853	5	.	.	PROPN
ejpam-3003	853	6	xu	xu	PROPN
ejpam-3003	853	7	,	,	PUNCT
ejpam-3003	853	8	j.	j.	PROPN
ejpam-3003	853	9	su	su	PROPN
ejpam-3003	853	10	,	,	PUNCT
ejpam-3003	853	11	global	global	ADJ
ejpam-3003	853	12	existence	existence	NOUN
ejpam-3003	853	13	and	and	CCONJ
ejpam-3003	853	14	finite	finite	ADJ
ejpam-3003	853	15	time	time	NOUN
ejpam-3003	853	16	blow	blow	VERB
ejpam-3003	853	17	up	up	ADP
ejpam-3003	853	18	for	for	ADP
ejpam-3003	853	19	a	a	DET
ejpam-3003	853	20	class	class	NOUN
ejpam-3003	853	21	of	of	ADP
ejpam-3003	853	22	semilinear	semilinear	PROPN
ejpam-3003	853	23	pseudoparabolic	pseudoparabolic	PROPN
ejpam-3003	853	24	equations	equation	NOUN
ejpam-3003	853	25	,	,	PUNCT
ejpam-3003	853	26	j.	j.	PROPN
ejpam-3003	853	27	func	func	PROPN
ejpam-3003	853	28	.	.	PUNCT
ejpam-3003	854	1	anal	anal	ADJ
ejpam-3003	854	2	.	.	PUNCT
ejpam-3003	855	1	264	264	NUM
ejpam-3003	855	2	(	(	PUNCT
ejpam-3003	855	3	2013	2013	NUM
ejpam-3003	855	4	)	)	PUNCT
ejpam-3003	855	5	2732	2732	NUM
ejpam-3003	855	6	-	-	SYM
ejpam-3003	855	7	2763	2763	NUM
ejpam-3003	855	8	.	.	PUNCT
ejpam-3003	856	1	[	[	X
ejpam-3003	856	2	30	30	NUM
ejpam-3003	856	3	]	]	X
ejpam-3003	856	4	j.l	j.l	PROPN
ejpam-3003	856	5	.	.	PROPN
ejpam-3003	856	6	lions	lion	NOUN
ejpam-3003	856	7	,	,	PUNCT
ejpam-3003	856	8	quelques	quelque	NOUN
ejpam-3003	856	9	méthodes	méthodes	PROPN
ejpam-3003	856	10	de	de	PROPN
ejpam-3003	856	11	résolutions	résolutions	PROPN
ejpam-3003	856	12	des	des	X
ejpam-3003	856	13	probléms	probléms	PROPN
ejpam-3003	856	14	aux	aux	PROPN
ejpam-3003	856	15	limites	limites	X
ejpam-3003	856	16	non	non	X
ejpam-3003	856	17	linéaires	linéaires	PROPN
ejpam-3003	856	18	,	,	PUNCT
ejpam-3003	856	19	dunod	dunod	PROPN
ejpam-3003	856	20	,	,	PUNCT
ejpam-3003	856	21	paris	paris	PROPN
ejpam-3003	856	22	,	,	PUNCT
ejpam-3003	856	23	1969	1969	NUM
ejpam-3003	856	24	.	.	PUNCT