id	sid	tid	token	lemma	pos
ejde-629	1	1	electronic	electronic	ADJ
ejde-629	1	2	journal	journal	NOUN
ejde-629	1	3	of	of	ADP
ejde-629	1	4	differential	differential	ADJ
ejde-629	1	5	equations	equation	NOUN
ejde-629	1	6	,	,	PUNCT
ejde-629	1	7	vol	vol	NOUN
ejde-629	1	8	.	.	NOUN
ejde-629	1	9	2024	2024	NUM
ejde-629	1	10	(	(	PUNCT
ejde-629	1	11	2024	2024	NUM
ejde-629	1	12	)	)	PUNCT
ejde-629	1	13	,	,	PUNCT
ejde-629	1	14	no	no	INTJ
ejde-629	1	15	.	.	NOUN
ejde-629	1	16	58	58	NUM
ejde-629	1	17	,	,	PUNCT
ejde-629	1	18	pp	pp	PROPN
ejde-629	1	19	.	.	PUNCT
ejde-629	2	1	1–14	1–14	PROPN
ejde-629	2	2	.	.	PUNCT
ejde-629	3	1	issn	issn	PROPN
ejde-629	3	2	:	:	PUNCT
ejde-629	3	3	1072	1072	NUM
ejde-629	3	4	-	-	SYM
ejde-629	3	5	6691	6691	NUM
ejde-629	3	6	.	.	PUNCT
ejde-629	4	1	url	url	PROPN
ejde-629	4	2	:	:	PUNCT
ejde-629	4	3	https://ejde.math.txstate.edu	https://ejde.math.txstate.edu	PROPN
ejde-629	4	4	,	,	PUNCT
ejde-629	4	5	https://ejde.math.unt.edu	https://ejde.math.unt.edu	PROPN
ejde-629	4	6	doi	doi	PROPN
ejde-629	4	7	:	:	PUNCT
ejde-629	4	8	10.58997	10.58997	NUM
ejde-629	4	9	/	/	SYM
ejde-629	4	10	ejde.2024.58	ejde.2024.58	NOUN
ejde-629	4	11	mild	mild	ADJ
ejde-629	4	12	solutions	solution	NOUN
ejde-629	4	13	to	to	ADP
ejde-629	4	14	fourth	fourth	ADJ
ejde-629	4	15	-	-	PUNCT
ejde-629	4	16	order	order	NOUN
ejde-629	4	17	parabolic	parabolic	ADJ
ejde-629	4	18	equations	equation	NOUN
ejde-629	4	19	modeling	model	VERB
ejde-629	4	20	thin	thin	ADJ
ejde-629	4	21	film	film	NOUN
ejde-629	4	22	growth	growth	NOUN
ejde-629	4	23	with	with	ADP
ejde-629	4	24	time	time	NOUN
ejde-629	4	25	fractional	fractional	PROPN
ejde-629	4	26	derivative	derivative	PROPN
ejde-629	4	27	qiang	qiang	PROPN
ejde-629	4	28	liu	liu	PROPN
ejde-629	4	29	,	,	PUNCT
ejde-629	4	30	wanyu	wanyu	VERB
ejde-629	4	31	zhu	zhu	PROPN
ejde-629	4	32	,	,	PUNCT
ejde-629	4	33	hailong	hailong	ADJ
ejde-629	4	34	ye	ye	NUM
ejde-629	4	35	abstract	abstract	ADJ
ejde-629	4	36	.	.	PUNCT
ejde-629	5	1	in	in	ADP
ejde-629	5	2	this	this	DET
ejde-629	5	3	article	article	NOUN
ejde-629	5	4	,	,	PUNCT
ejde-629	5	5	we	we	PRON
ejde-629	5	6	study	study	VERB
ejde-629	5	7	initial	initial	ADJ
ejde-629	5	8	-	-	PUNCT
ejde-629	5	9	boundary	boundary	NOUN
ejde-629	5	10	problems	problem	NOUN
ejde-629	5	11	for	for	ADP
ejde-629	5	12	fourth	fourth	ADJ
ejde-629	5	13	-	-	PUNCT
ejde-629	5	14	order	order	NOUN
ejde-629	5	15	nonlinear	nonlinear	ADJ
ejde-629	5	16	parabolic	parabolic	ADJ
ejde-629	5	17	equations	equation	NOUN
ejde-629	5	18	modeling	model	VERB
ejde-629	5	19	thin	thin	ADJ
ejde-629	5	20	film	film	NOUN
ejde-629	5	21	growth	growth	NOUN
ejde-629	5	22	with	with	ADP
ejde-629	5	23	caputo	caputo	NOUN
ejde-629	5	24	-	-	PUNCT
ejde-629	5	25	type	type	NOUN
ejde-629	5	26	time	time	NOUN
ejde-629	5	27	fractional	fractional	ADJ
ejde-629	5	28	derivative	derivative	NOUN
ejde-629	5	29	.	.	PUNCT
ejde-629	6	1	by	by	ADP
ejde-629	6	2	means	mean	NOUN
ejde-629	6	3	of	of	ADP
ejde-629	6	4	the	the	DET
ejde-629	6	5	theory	theory	NOUN
ejde-629	6	6	of	of	ADP
ejde-629	6	7	abstract	abstract	ADJ
ejde-629	6	8	fractional	fractional	ADJ
ejde-629	6	9	calculus	calculus	NOUN
ejde-629	6	10	and	and	CCONJ
ejde-629	6	11	lp	lp	ADJ
ejde-629	6	12	−	−	PROPN
ejde-629	6	13	lq	lq	NOUN
ejde-629	6	14	estimates	estimate	NOUN
ejde-629	6	15	,	,	PUNCT
ejde-629	6	16	we	we	PRON
ejde-629	6	17	establish	establish	VERB
ejde-629	6	18	the	the	DET
ejde-629	6	19	existence	existence	NOUN
ejde-629	6	20	and	and	CCONJ
ejde-629	6	21	uniqueness	uniqueness	NOUN
ejde-629	6	22	of	of	ADP
ejde-629	6	23	local	local	ADJ
ejde-629	6	24	mild	mild	ADJ
ejde-629	6	25	solutions	solution	NOUN
ejde-629	6	26	in	in	ADP
ejde-629	6	27	the	the	DET
ejde-629	6	28	spaces	space	NOUN
ejde-629	6	29	c([0	c([0	NOUN
ejde-629	6	30	,	,	PUNCT
ejde-629	6	31	t	t	X
ejde-629	6	32	]	]	PUNCT
ejde-629	6	33	;	;	PUNCT
ejde-629	6	34	l	l	X
ejde-629	6	35	βn	βn	X
ejde-629	6	36	2−β	2−β	NUM
ejde-629	6	37	(	(	PUNCT
ejde-629	6	38	ω	ω	NOUN
ejde-629	6	39	)	)	PUNCT
ejde-629	6	40	)	)	PUNCT
ejde-629	6	41	with	with	ADP
ejde-629	6	42	1	1	NUM
ejde-629	6	43	<	<	X
ejde-629	6	44	β	β	X
ejde-629	6	45	<	<	X
ejde-629	6	46	2	2	NUM
ejde-629	6	47	.	.	PUNCT
ejde-629	7	1	moreover	moreover	ADV
ejde-629	7	2	,	,	PUNCT
ejde-629	7	3	the	the	DET
ejde-629	7	4	local	local	ADJ
ejde-629	7	5	solutions	solution	NOUN
ejde-629	7	6	can	can	AUX
ejde-629	7	7	be	be	AUX
ejde-629	7	8	extended	extend	VERB
ejde-629	7	9	globally	globally	ADV
ejde-629	7	10	if	if	SCONJ
ejde-629	7	11	the	the	DET
ejde-629	7	12	initial	initial	ADJ
ejde-629	7	13	data	data	NOUN
ejde-629	7	14	is	be	AUX
ejde-629	7	15	sufficiently	sufficiently	ADV
ejde-629	7	16	small	small	ADJ
ejde-629	7	17	.	.	PUNCT
ejde-629	8	1	1	1	X
ejde-629	8	2	.	.	X
ejde-629	8	3	introduction	introduction	NOUN
ejde-629	8	4	and	and	CCONJ
ejde-629	8	5	main	main	ADJ
ejde-629	8	6	result	result	NOUN
ejde-629	8	7	thin	thin	ADJ
ejde-629	8	8	film	film	NOUN
ejde-629	8	9	growth	growth	NOUN
ejde-629	8	10	processes	process	NOUN
ejde-629	8	11	play	play	VERB
ejde-629	8	12	a	a	DET
ejde-629	8	13	crucial	crucial	ADJ
ejde-629	8	14	role	role	NOUN
ejde-629	8	15	in	in	ADP
ejde-629	8	16	various	various	ADJ
ejde-629	8	17	scientific	scientific	ADJ
ejde-629	8	18	and	and	CCONJ
ejde-629	8	19	technological	technological	ADJ
ejde-629	8	20	applications	application	NOUN
ejde-629	8	21	,	,	PUNCT
ejde-629	8	22	ranging	range	VERB
ejde-629	8	23	from	from	ADP
ejde-629	8	24	semiconductor	semiconductor	NOUN
ejde-629	8	25	manufacturing	manufacturing	NOUN
ejde-629	8	26	to	to	ADP
ejde-629	8	27	material	material	NOUN
ejde-629	8	28	sciences	science	NOUN
ejde-629	8	29	[	[	X
ejde-629	8	30	14	14	NUM
ejde-629	8	31	,	,	PUNCT
ejde-629	8	32	17	17	NUM
ejde-629	8	33	,	,	PUNCT
ejde-629	8	34	23	23	NUM
ejde-629	8	35	]	]	PUNCT
ejde-629	8	36	.	.	PUNCT
ejde-629	9	1	understanding	understand	VERB
ejde-629	9	2	the	the	DET
ejde-629	9	3	dynamics	dynamic	NOUN
ejde-629	9	4	of	of	ADP
ejde-629	9	5	thin	thin	ADJ
ejde-629	9	6	film	film	NOUN
ejde-629	9	7	growth	growth	NOUN
ejde-629	9	8	is	be	AUX
ejde-629	9	9	essential	essential	ADJ
ejde-629	9	10	for	for	ADP
ejde-629	9	11	optimizing	optimize	VERB
ejde-629	9	12	the	the	DET
ejde-629	9	13	quality	quality	NOUN
ejde-629	9	14	,	,	PUNCT
ejde-629	9	15	stability	stability	NOUN
ejde-629	9	16	,	,	PUNCT
ejde-629	9	17	and	and	CCONJ
ejde-629	9	18	functionality	functionality	NOUN
ejde-629	9	19	of	of	ADP
ejde-629	9	20	thin	thin	ADJ
ejde-629	9	21	films	film	NOUN
ejde-629	9	22	in	in	ADP
ejde-629	9	23	these	these	DET
ejde-629	9	24	applications	application	NOUN
ejde-629	9	25	.	.	PUNCT
ejde-629	10	1	mathematical	mathematical	ADJ
ejde-629	10	2	modeling	modeling	NOUN
ejde-629	10	3	provides	provide	VERB
ejde-629	10	4	a	a	DET
ejde-629	10	5	powerful	powerful	ADJ
ejde-629	10	6	tool	tool	NOUN
ejde-629	10	7	to	to	PART
ejde-629	10	8	capture	capture	VERB
ejde-629	10	9	the	the	DET
ejde-629	10	10	intricate	intricate	ADJ
ejde-629	10	11	dynamics	dynamic	NOUN
ejde-629	10	12	involved	involve	VERB
ejde-629	10	13	in	in	ADP
ejde-629	10	14	such	such	ADJ
ejde-629	10	15	processes	process	NOUN
ejde-629	10	16	and	and	CCONJ
ejde-629	10	17	to	to	PART
ejde-629	10	18	develop	develop	VERB
ejde-629	10	19	predictive	predictive	ADJ
ejde-629	10	20	models	model	NOUN
ejde-629	10	21	that	that	PRON
ejde-629	10	22	guide	guide	VERB
ejde-629	10	23	experimental	experimental	ADJ
ejde-629	10	24	design	design	NOUN
ejde-629	10	25	and	and	CCONJ
ejde-629	10	26	optimization	optimization	NOUN
ejde-629	10	27	.	.	PUNCT
ejde-629	11	1	in	in	ADP
ejde-629	11	2	recent	recent	ADJ
ejde-629	11	3	years	year	NOUN
ejde-629	11	4	,	,	PUNCT
ejde-629	11	5	there	there	PRON
ejde-629	11	6	has	have	AUX
ejde-629	11	7	been	be	AUX
ejde-629	11	8	a	a	DET
ejde-629	11	9	growing	grow	VERB
ejde-629	11	10	interest	interest	NOUN
ejde-629	11	11	in	in	ADP
ejde-629	11	12	utilizing	utilize	VERB
ejde-629	11	13	fractional	fractional	ADJ
ejde-629	11	14	calculus	calculus	NOUN
ejde-629	11	15	to	to	PART
ejde-629	11	16	describe	describe	VERB
ejde-629	11	17	and	and	CCONJ
ejde-629	11	18	analyze	analyze	VERB
ejde-629	11	19	complex	complex	ADJ
ejde-629	11	20	phenomena	phenomenon	NOUN
ejde-629	11	21	that	that	PRON
ejde-629	11	22	exhibit	exhibit	VERB
ejde-629	11	23	non	non	ADJ
ejde-629	11	24	-	-	ADJ
ejde-629	11	25	local	local	ADJ
ejde-629	11	26	and	and	CCONJ
ejde-629	11	27	memory	memory	NOUN
ejde-629	11	28	effects	effect	NOUN
ejde-629	11	29	.	.	PUNCT
ejde-629	12	1	in	in	ADP
ejde-629	12	2	this	this	DET
ejde-629	12	3	article	article	NOUN
ejde-629	12	4	,	,	PUNCT
ejde-629	12	5	we	we	PRON
ejde-629	12	6	focus	focus	VERB
ejde-629	12	7	on	on	ADP
ejde-629	12	8	boundary	boundary	ADJ
ejde-629	12	9	value	value	NOUN
ejde-629	12	10	problems	problem	NOUN
ejde-629	12	11	of	of	ADP
ejde-629	12	12	fourth	fourth	ADJ
ejde-629	12	13	-	-	PUNCT
ejde-629	12	14	order	order	NOUN
ejde-629	12	15	parabolic	parabolic	ADJ
ejde-629	12	16	equation	equation	NOUN
ejde-629	12	17	modeling	model	VERB
ejde-629	12	18	thin	thin	ADJ
ejde-629	12	19	film	film	NOUN
ejde-629	12	20	growth	growth	NOUN
ejde-629	12	21	with	with	ADP
ejde-629	12	22	time	time	NOUN
ejde-629	12	23	fractional	fractional	ADJ
ejde-629	12	24	derivative	derivative	NOUN
ejde-629	12	25	,	,	PUNCT
ejde-629	12	26	cd	cd	PROPN
ejde-629	12	27	α	α	PROPN
ejde-629	12	28	t	t	NOUN
ejde-629	12	29	u(t	u(t	PROPN
ejde-629	12	30	)	)	PUNCT
ejde-629	13	1	+	+	NUM
ejde-629	13	2	∆2u	∆2u	NOUN
ejde-629	13	3	=	=	SYM
ejde-629	13	4	∇	∇	X
ejde-629	13	5	·	·	PUNCT
ejde-629	13	6	f(∇u	f(∇u	NUM
ejde-629	13	7	)	)	PUNCT
ejde-629	13	8	,	,	PUNCT
ejde-629	13	9	x	x	PUNCT
ejde-629	13	10	∈	∈	PROPN
ejde-629	13	11	ω	ω	PROPN
ejde-629	13	12	,	,	PUNCT
ejde-629	13	13	t	t	X
ejde-629	13	14	>	>	X
ejde-629	13	15	0	0	PROPN
ejde-629	13	16	,	,	PUNCT
ejde-629	13	17	∂νu|∂ω	∂νu|∂ω	NOUN
ejde-629	13	18	=	=	PUNCT
ejde-629	13	19	∂ν∆u|∂ω	∂ν∆u|∂ω	NOUN
ejde-629	13	20	=	=	SYM
ejde-629	13	21	0	0	NUM
ejde-629	13	22	,	,	PUNCT
ejde-629	13	23	t	t	X
ejde-629	13	24	>	>	X
ejde-629	13	25	0	0	PROPN
ejde-629	13	26	,	,	PUNCT
ejde-629	13	27	u(x	u(x	NOUN
ejde-629	13	28	,	,	PUNCT
ejde-629	13	29	0	0	NUM
ejde-629	13	30	)	)	PUNCT
ejde-629	13	31	=	=	SYM
ejde-629	13	32	φ(x	φ(x	NOUN
ejde-629	13	33	)	)	PUNCT
ejde-629	13	34	,	,	PUNCT
ejde-629	13	35	x	x	PUNCT
ejde-629	13	36	∈	∈	PROPN
ejde-629	13	37	ω	ω	PROPN
ejde-629	13	38	.	.	PUNCT
ejde-629	13	39	(	(	PUNCT
ejde-629	13	40	1.1	1.1	NUM
ejde-629	13	41	)	)	PUNCT
ejde-629	13	42	here	here	ADV
ejde-629	13	43	ω	ω	PROPN
ejde-629	13	44	∈	∈	PROPN
ejde-629	13	45	rn	rn	PROPN
ejde-629	13	46	with	with	ADP
ejde-629	13	47	n	n	PRON
ejde-629	13	48	≥	≥	NUM
ejde-629	13	49	2	2	NUM
ejde-629	13	50	is	be	AUX
ejde-629	13	51	a	a	DET
ejde-629	13	52	bounded	bounded	ADJ
ejde-629	13	53	smooth	smooth	ADJ
ejde-629	13	54	domain	domain	NOUN
ejde-629	13	55	,	,	PUNCT
ejde-629	13	56	∂ω	∂ω	ADJ
ejde-629	13	57	denotes	denote	VERB
ejde-629	13	58	the	the	DET
ejde-629	13	59	boundary	boundary	NOUN
ejde-629	13	60	of	of	ADP
ejde-629	13	61	ω	ω	PROPN
ejde-629	13	62	and	and	CCONJ
ejde-629	13	63	ν	ν	NOUN
ejde-629	13	64	is	be	AUX
ejde-629	13	65	the	the	DET
ejde-629	13	66	unit	unit	NOUN
ejde-629	13	67	outer	outer	ADJ
ejde-629	13	68	vector	vector	NOUN
ejde-629	13	69	normal	normal	ADJ
ejde-629	13	70	to	to	ADP
ejde-629	13	71	ω	ω	NUM
ejde-629	13	72	,	,	PUNCT
ejde-629	13	73	cdα	cdα	PROPN
ejde-629	13	74	t	t	PROPN
ejde-629	13	75	is	be	AUX
ejde-629	13	76	the	the	DET
ejde-629	13	77	caputo	caputo	PROPN
ejde-629	13	78	derivative	derivative	NOUN
ejde-629	13	79	with	with	ADP
ejde-629	13	80	order	order	NOUN
ejde-629	13	81	α	α	X
ejde-629	13	82	∈	∈	PROPN
ejde-629	13	83	(	(	PUNCT
ejde-629	13	84	0	0	NUM
ejde-629	13	85	,	,	PUNCT
ejde-629	13	86	1	1	NUM
ejde-629	13	87	)	)	PUNCT
ejde-629	13	88	,	,	PUNCT
ejde-629	13	89	which	which	PRON
ejde-629	13	90	is	be	AUX
ejde-629	13	91	defined	define	VERB
ejde-629	13	92	by	by	ADP
ejde-629	13	93	cd	cd	PROPN
ejde-629	13	94	α	α	PROPN
ejde-629	13	95	t	t	NOUN
ejde-629	13	96	u(t	u(t	PROPN
ejde-629	13	97	)	)	PUNCT
ejde-629	13	98	=	=	SYM
ejde-629	14	1	1	1	NUM
ejde-629	14	2	γ(1−	γ(1−	NOUN
ejde-629	14	3	α	α	NUM
ejde-629	14	4	)	)	PUNCT
ejde-629	14	5	d	d	NOUN
ejde-629	14	6	dt	dt	X
ejde-629	15	1	∫	∫	PROPN
ejde-629	15	2	t	t	PROPN
ejde-629	15	3	0	0	NUM
ejde-629	15	4	(	(	PUNCT
ejde-629	15	5	t−	t−	PROPN
ejde-629	15	6	s)−α(u(s)−	s)−α(u(s)−	PROPN
ejde-629	15	7	u(0	u(0	PROPN
ejde-629	15	8	)	)	PUNCT
ejde-629	15	9	)	)	PUNCT
ejde-629	15	10	ds	ds	PROPN
ejde-629	15	11	,	,	PUNCT
ejde-629	15	12	2020	2020	NUM
ejde-629	15	13	mathematics	mathematic	NOUN
ejde-629	15	14	subject	subject	ADJ
ejde-629	15	15	classification	classification	NOUN
ejde-629	15	16	.	.	PUNCT
ejde-629	16	1	35g25	35g25	NUM
ejde-629	16	2	,	,	PUNCT
ejde-629	16	3	35k90	35k90	NUM
ejde-629	16	4	.	.	PUNCT
ejde-629	17	1	key	key	ADJ
ejde-629	17	2	words	word	NOUN
ejde-629	17	3	and	and	CCONJ
ejde-629	17	4	phrases	phrase	NOUN
ejde-629	17	5	.	.	PUNCT
ejde-629	18	1	thin	thin	ADJ
ejde-629	18	2	-	-	PUNCT
ejde-629	18	3	film	film	NOUN
ejde-629	18	4	equation	equation	NOUN
ejde-629	18	5	;	;	PUNCT
ejde-629	18	6	caputo	caputo	PROPN
ejde-629	18	7	fractional	fractional	PROPN
ejde-629	18	8	derivative	derivative	ADJ
ejde-629	18	9	;	;	PUNCT
ejde-629	18	10	mild	mild	ADJ
ejde-629	18	11	solution	solution	NOUN
ejde-629	18	12	;	;	PUNCT
ejde-629	18	13	mittag	mittag	ADJ
ejde-629	18	14	-	-	PUNCT
ejde-629	18	15	leffler	leffler	NOUN
ejde-629	18	16	functions	function	NOUN
ejde-629	18	17	.	.	PUNCT
ejde-629	19	1	©	©	ADP
ejde-629	19	2	2024	2024	NUM
ejde-629	19	3	.	.	PUNCT
ejde-629	20	1	this	this	DET
ejde-629	20	2	work	work	NOUN
ejde-629	20	3	is	be	AUX
ejde-629	20	4	licensed	license	VERB
ejde-629	20	5	under	under	ADP
ejde-629	20	6	a	a	DET
ejde-629	20	7	cc	cc	NOUN
ejde-629	20	8	by	by	ADP
ejde-629	20	9	4.0	4.0	NUM
ejde-629	20	10	license	license	NOUN
ejde-629	20	11	.	.	PUNCT
ejde-629	21	1	submitted	submit	VERB
ejde-629	21	2	march	march	PROPN
ejde-629	21	3	30	30	NUM
ejde-629	21	4	,	,	PUNCT
ejde-629	21	5	2024	2024	NUM
ejde-629	21	6	.	.	PUNCT
ejde-629	22	1	published	publish	VERB
ejde-629	22	2	october	october	PROPN
ejde-629	22	3	4	4	NUM
ejde-629	22	4	,	,	PUNCT
ejde-629	22	5	2024	2024	NUM
ejde-629	22	6	.	.	PUNCT
ejde-629	23	1	1	1	NUM
ejde-629	23	2	2	2	NUM
ejde-629	23	3	q.	q.	PROPN
ejde-629	23	4	liu	liu	PROPN
ejde-629	23	5	,	,	PUNCT
ejde-629	23	6	w.	w.	PROPN
ejde-629	23	7	zhu	zhu	PROPN
ejde-629	23	8	,	,	PUNCT
ejde-629	23	9	h.	h.	PROPN
ejde-629	23	10	ye	ye	PROPN
ejde-629	23	11	ejde-2024/58	ejde-2024/58	ADJ
ejde-629	23	12	where	where	SCONJ
ejde-629	23	13	the	the	DET
ejde-629	23	14	gamma	gamma	NOUN
ejde-629	23	15	function	function	NOUN
ejde-629	23	16	defined	define	VERB
ejde-629	23	17	by	by	ADP
ejde-629	23	18	γ(λ	γ(λ	PROPN
ejde-629	23	19	)	)	PUNCT
ejde-629	23	20	:	:	PUNCT
ejde-629	23	21	=	=	SYM
ejde-629	23	22	∫∞	∫∞	NOUN
ejde-629	23	23	0	0	PUNCT
ejde-629	24	1	tλ−1e−tdt	tλ−1e−tdt	PROPN
ejde-629	24	2	.	.	PUNCT
ejde-629	25	1	here	here	ADV
ejde-629	25	2	the	the	DET
ejde-629	25	3	term	term	NOUN
ejde-629	25	4	u	u	NOUN
ejde-629	25	5	represents	represent	VERB
ejde-629	25	6	the	the	DET
ejde-629	25	7	scaled	scale	VERB
ejde-629	25	8	film	film	NOUN
ejde-629	25	9	height	height	NOUN
ejde-629	25	10	,	,	PUNCT
ejde-629	25	11	and	and	CCONJ
ejde-629	25	12	∆2u	∆2u	NOUN
ejde-629	25	13	denotes	denote	VERB
ejde-629	25	14	the	the	DET
ejde-629	25	15	capillarity	capillarity	NOUN
ejde-629	25	16	-	-	PUNCT
ejde-629	25	17	driven	drive	VERB
ejde-629	25	18	surface	surface	NOUN
ejde-629	25	19	diffusion	diffusion	NOUN
ejde-629	25	20	whereas	whereas	SCONJ
ejde-629	25	21	∇	∇	X
ejde-629	25	22	·	·	PUNCT
ejde-629	25	23	f(∇u	f(∇u	NUM
ejde-629	25	24	)	)	PUNCT
ejde-629	25	25	denotes	denote	VERB
ejde-629	25	26	the	the	DET
ejde-629	25	27	upward	upward	ADJ
ejde-629	25	28	hopping	hopping	NOUN
ejde-629	25	29	of	of	ADP
ejde-629	25	30	atoms	atom	NOUN
ejde-629	25	31	.	.	PUNCT
ejde-629	26	1	throughout	throughout	ADP
ejde-629	26	2	this	this	DET
ejde-629	26	3	paper	paper	NOUN
ejde-629	26	4	,	,	PUNCT
ejde-629	26	5	we	we	PRON
ejde-629	26	6	will	will	AUX
ejde-629	26	7	assume	assume	VERB
ejde-629	26	8	that	that	SCONJ
ejde-629	26	9	f	f	PROPN
ejde-629	26	10	∈	∈	PROPN
ejde-629	26	11	c1(rn	c1(rn	PROPN
ejde-629	26	12	,	,	PUNCT
ejde-629	26	13	rn	rn	PROPN
ejde-629	26	14	)	)	PUNCT
ejde-629	26	15	with	with	ADP
ejde-629	26	16	f(0	f(0	NOUN
ejde-629	26	17	)	)	PUNCT
ejde-629	26	18	=	=	PUNCT
ejde-629	26	19	df(0	df(0	NOUN
ejde-629	26	20	)	)	PUNCT
ejde-629	26	21	=	=	SYM
ejde-629	26	22	0	0	NUM
ejde-629	26	23	and	and	CCONJ
ejde-629	26	24	for	for	ADP
ejde-629	26	25	some	some	DET
ejde-629	26	26	β	β	X
ejde-629	26	27	>	>	X
ejde-629	26	28	1	1	NUM
ejde-629	26	29	,	,	PUNCT
ejde-629	26	30	and	and	CCONJ
ejde-629	26	31	f	f	PROPN
ejde-629	26	32	satisfies	satisfy	VERB
ejde-629	26	33	the	the	DET
ejde-629	26	34	following	follow	VERB
ejde-629	26	35	growth	growth	NOUN
ejde-629	26	36	condition	condition	NOUN
ejde-629	26	37	|f	|f	PROPN
ejde-629	27	1	′(ξ1)−	′(ξ1)−	PROPN
ejde-629	27	2	f	f	PROPN
ejde-629	27	3	′(ξ2)|	′(ξ2)|	NOUN
ejde-629	27	4	≤	≤	NOUN
ejde-629	27	5	c(|ξ1|β−1	c(|ξ1|β−1	PRON
ejde-629	27	6	+	+	NOUN
ejde-629	27	7	|ξ2|β−1)|ξ1	|ξ2|β−1)|ξ1	PROPN
ejde-629	27	8	−	−	PROPN
ejde-629	27	9	ξ2|	ξ2|	PROPN
ejde-629	27	10	(	(	PUNCT
ejde-629	27	11	1.2	1.2	NUM
ejde-629	27	12	)	)	PUNCT
ejde-629	27	13	for	for	ADP
ejde-629	27	14	any	any	DET
ejde-629	27	15	ξ1	ξ1	NOUN
ejde-629	27	16	,	,	PUNCT
ejde-629	27	17	ξ2	ξ2	PROPN
ejde-629	27	18	∈	∈	PROPN
ejde-629	27	19	rn	rn	PROPN
ejde-629	27	20	.	.	PUNCT
ejde-629	28	1	as	as	ADP
ejde-629	28	2	a	a	DET
ejde-629	28	3	simple	simple	ADJ
ejde-629	28	4	example	example	NOUN
ejde-629	28	5	of	of	ADP
ejde-629	28	6	(	(	PUNCT
ejde-629	28	7	1.2	1.2	NUM
ejde-629	28	8	)	)	PUNCT
ejde-629	28	9	,	,	PUNCT
ejde-629	28	10	we	we	PRON
ejde-629	28	11	can	can	AUX
ejde-629	28	12	take	take	VERB
ejde-629	28	13	f(ξ	f(ξ	NOUN
ejde-629	28	14	)	)	PUNCT
ejde-629	28	15	=	=	SYM
ejde-629	28	16	|ξ|βξ	|ξ|βξ	ADJ
ejde-629	28	17	.	.	PUNCT
ejde-629	29	1	when	when	SCONJ
ejde-629	29	2	α	α	PRON
ejde-629	29	3	=	=	SYM
ejde-629	29	4	1	1	NUM
ejde-629	29	5	,	,	PUNCT
ejde-629	29	6	the	the	DET
ejde-629	29	7	fractional	fractional	ADJ
ejde-629	29	8	time	time	NOUN
ejde-629	29	9	caputo	caputo	PROPN
ejde-629	29	10	derivative	derivative	NOUN
ejde-629	29	11	is	be	AUX
ejde-629	29	12	replaced	replace	VERB
ejde-629	29	13	with	with	ADP
ejde-629	29	14	the	the	DET
ejde-629	29	15	classical	classical	ADJ
ejde-629	29	16	integer	integer	NOUN
ejde-629	29	17	derivative	derivative	PROPN
ejde-629	29	18	ut	ut	PROPN
ejde-629	29	19	.	.	PUNCT
ejde-629	30	1	the	the	DET
ejde-629	30	2	problem	problem	NOUN
ejde-629	30	3	(	(	PUNCT
ejde-629	30	4	1.1	1.1	NUM
ejde-629	30	5	)	)	PUNCT
ejde-629	30	6	becomes	become	VERB
ejde-629	30	7	the	the	DET
ejde-629	30	8	usual	usual	ADJ
ejde-629	30	9	thin	thin	ADJ
ejde-629	30	10	film	film	NOUN
ejde-629	30	11	growth	growth	NOUN
ejde-629	30	12	model	model	NOUN
ejde-629	30	13	,	,	PUNCT
ejde-629	30	14	which	which	PRON
ejde-629	30	15	is	be	AUX
ejde-629	30	16	well	well	ADV
ejde-629	30	17	studied	study	VERB
ejde-629	30	18	by	by	ADP
ejde-629	30	19	many	many	ADJ
ejde-629	30	20	researchers	researcher	NOUN
ejde-629	30	21	.	.	PUNCT
ejde-629	31	1	king	king	PROPN
ejde-629	31	2	et	et	PROPN
ejde-629	31	3	al	al	PROPN
ejde-629	31	4	.	.	PUNCT
ejde-629	32	1	[	[	X
ejde-629	32	2	9	9	NUM
ejde-629	32	3	]	]	PUNCT
ejde-629	32	4	proved	prove	VERB
ejde-629	32	5	the	the	DET
ejde-629	32	6	existence	existence	NOUN
ejde-629	32	7	,	,	PUNCT
ejde-629	32	8	uniqueness	uniqueness	NOUN
ejde-629	32	9	,	,	PUNCT
ejde-629	32	10	regularity	regularity	NOUN
ejde-629	32	11	and	and	CCONJ
ejde-629	32	12	large	large	ADJ
ejde-629	32	13	time	time	NOUN
ejde-629	32	14	behavior	behavior	NOUN
ejde-629	32	15	of	of	ADP
ejde-629	32	16	solutions	solution	NOUN
ejde-629	32	17	in	in	ADP
ejde-629	32	18	sobolev	sobolev	NOUN
ejde-629	32	19	function	function	NOUN
ejde-629	32	20	space	space	NOUN
ejde-629	32	21	.	.	PUNCT
ejde-629	33	1	using	use	VERB
ejde-629	33	2	kato	kato	PROPN
ejde-629	33	3	’s	’s	PART
ejde-629	33	4	method	method	NOUN
ejde-629	33	5	,	,	PUNCT
ejde-629	33	6	sandjo	sandjo	PROPN
ejde-629	33	7	et	et	PROPN
ejde-629	33	8	al	al	PROPN
ejde-629	33	9	.	.	PUNCT
ejde-629	34	1	[	[	X
ejde-629	34	2	16	16	NUM
ejde-629	34	3	]	]	PUNCT
ejde-629	34	4	established	establish	VERB
ejde-629	34	5	existence	existence	NOUN
ejde-629	34	6	,	,	PUNCT
ejde-629	34	7	uniqueness	uniqueness	NOUN
ejde-629	34	8	and	and	CCONJ
ejde-629	34	9	regularity	regularity	NOUN
ejde-629	34	10	of	of	ADP
ejde-629	34	11	the	the	DET
ejde-629	34	12	solution	solution	NOUN
ejde-629	34	13	in	in	ADP
ejde-629	34	14	spaces	space	NOUN
ejde-629	34	15	of	of	ADP
ejde-629	34	16	c0([0	c0([0	PROPN
ejde-629	34	17	,	,	PUNCT
ejde-629	34	18	t	t	X
ejde-629	34	19	]	]	X
ejde-629	34	20	;	;	PUNCT
ejde-629	34	21	lp(ω	lp(ω	NUM
ejde-629	34	22	)	)	PUNCT
ejde-629	34	23	)	)	PUNCT
ejde-629	34	24	with	with	ADP
ejde-629	34	25	p	p	PROPN
ejde-629	34	26	=	=	PROPN
ejde-629	34	27	nβ	nβ	ADJ
ejde-629	34	28	2−β	2−β	NUM
ejde-629	34	29	,	,	PUNCT
ejde-629	34	30	1	1	NUM
ejde-629	34	31	<	<	X
ejde-629	34	32	β	β	X
ejde-629	34	33	<	<	X
ejde-629	34	34	2	2	NUM
ejde-629	34	35	.	.	PUNCT
ejde-629	35	1	furthermore	furthermore	ADV
ejde-629	35	2	,	,	PUNCT
ejde-629	35	3	they	they	PRON
ejde-629	35	4	illustrated	illustrate	VERB
ejde-629	35	5	the	the	DET
ejde-629	35	6	qualitative	qualitative	ADJ
ejde-629	35	7	behavior	behavior	NOUN
ejde-629	35	8	of	of	ADP
ejde-629	35	9	the	the	DET
ejde-629	35	10	approximate	approximate	ADJ
ejde-629	35	11	solution	solution	NOUN
ejde-629	35	12	through	through	ADP
ejde-629	35	13	some	some	DET
ejde-629	35	14	numerical	numerical	ADJ
ejde-629	35	15	simulations	simulation	NOUN
ejde-629	35	16	.	.	PUNCT
ejde-629	36	1	ishige	ishige	PROPN
ejde-629	36	2	et	et	PROPN
ejde-629	36	3	al	al	PROPN
ejde-629	36	4	.	.	PUNCT
ejde-629	37	1	[	[	X
ejde-629	37	2	6	6	NUM
ejde-629	37	3	]	]	PUNCT
ejde-629	37	4	give	give	VERB
ejde-629	37	5	sufficient	sufficient	ADJ
ejde-629	37	6	conditions	condition	NOUN
ejde-629	37	7	on	on	ADP
ejde-629	37	8	the	the	DET
ejde-629	37	9	existence	existence	NOUN
ejde-629	37	10	of	of	ADP
ejde-629	37	11	global	global	ADJ
ejde-629	37	12	solutions	solution	NOUN
ejde-629	37	13	,	,	PUNCT
ejde-629	37	14	the	the	DET
ejde-629	37	15	maximal	maximal	ADJ
ejde-629	37	16	existence	existence	NOUN
ejde-629	37	17	time	time	NOUN
ejde-629	37	18	and	and	CCONJ
ejde-629	37	19	blow	blow	VERB
ejde-629	37	20	up	up	ADP
ejde-629	37	21	rate	rate	NOUN
ejde-629	37	22	for	for	ADP
ejde-629	37	23	0	0	NUM
ejde-629	37	24	<	<	X
ejde-629	37	25	β	β	X
ejde-629	37	26	≤	≤	ADV
ejde-629	37	27	2	2	NUM
ejde-629	37	28	.	.	PUNCT
ejde-629	37	29	y.	y.	PROPN
ejde-629	37	30	feng	feng	PROPN
ejde-629	37	31	et	et	PROPN
ejde-629	37	32	al	al	PROPN
ejde-629	37	33	.	.	PUNCT
ejde-629	38	1	[	[	X
ejde-629	38	2	5	5	NUM
ejde-629	38	3	]	]	PUNCT
ejde-629	38	4	studied	study	VERB
ejde-629	38	5	the	the	DET
ejde-629	38	6	existence	existence	NOUN
ejde-629	38	7	of	of	ADP
ejde-629	38	8	local	local	ADJ
ejde-629	38	9	mild	mild	ADJ
ejde-629	38	10	solutions	solution	NOUN
ejde-629	38	11	for	for	ADP
ejde-629	38	12	any	any	DET
ejde-629	38	13	initial	initial	ADJ
ejde-629	38	14	data	datum	NOUN
ejde-629	38	15	lies	lie	VERB
ejde-629	38	16	in	in	ADP
ejde-629	38	17	l2	l2	NOUN
ejde-629	38	18	on	on	ADP
ejde-629	38	19	the	the	DET
ejde-629	38	20	two	two	NUM
ejde-629	38	21	-	-	PUNCT
ejde-629	38	22	dimensional	dimensional	ADJ
ejde-629	38	23	torus	torus	NOUN
ejde-629	38	24	with	with	ADP
ejde-629	38	25	and	and	CCONJ
ejde-629	38	26	without	without	ADP
ejde-629	38	27	advection	advection	NOUN
ejde-629	38	28	.	.	PUNCT
ejde-629	39	1	we	we	PRON
ejde-629	39	2	refer	refer	VERB
ejde-629	39	3	the	the	DET
ejde-629	39	4	interested	interested	ADJ
ejde-629	39	5	reader	reader	NOUN
ejde-629	39	6	to	to	ADP
ejde-629	39	7	the	the	DET
ejde-629	39	8	references	reference	NOUN
ejde-629	39	9	therein	therein	ADV
ejde-629	39	10	.	.	PUNCT
ejde-629	40	1	fractional	fractional	ADJ
ejde-629	40	2	models	model	NOUN
ejde-629	40	3	extend	extend	VERB
ejde-629	40	4	the	the	DET
ejde-629	40	5	classical	classical	ADJ
ejde-629	40	6	model	model	NOUN
ejde-629	40	7	with	with	ADP
ejde-629	40	8	non	non	ADJ
ejde-629	40	9	-	-	ADJ
ejde-629	40	10	integer	integer	ADJ
ejde-629	40	11	orders	order	NOUN
ejde-629	40	12	differentiation	differentiation	NOUN
ejde-629	40	13	and	and	CCONJ
ejde-629	40	14	integration	integration	NOUN
ejde-629	40	15	,	,	PUNCT
ejde-629	40	16	allowing	allow	VERB
ejde-629	40	17	the	the	DET
ejde-629	40	18	incorporation	incorporation	NOUN
ejde-629	40	19	of	of	ADP
ejde-629	40	20	memory	memory	NOUN
ejde-629	40	21	and	and	CCONJ
ejde-629	40	22	long	long	ADJ
ejde-629	40	23	-	-	PUNCT
ejde-629	40	24	range	range	NOUN
ejde-629	40	25	dependencies	dependency	NOUN
ejde-629	40	26	into	into	ADP
ejde-629	40	27	models	model	NOUN
ejde-629	40	28	.	.	PUNCT
ejde-629	41	1	there	there	PRON
ejde-629	41	2	are	be	VERB
ejde-629	41	3	many	many	ADJ
ejde-629	41	4	numerical	numerical	ADJ
ejde-629	41	5	simulations	simulation	NOUN
ejde-629	41	6	for	for	ADP
ejde-629	41	7	the	the	DET
ejde-629	41	8	time	time	NOUN
ejde-629	41	9	fractional	fractional	ADJ
ejde-629	41	10	thin	thin	ADJ
ejde-629	41	11	film	film	NOUN
ejde-629	41	12	growth	growth	NOUN
ejde-629	41	13	equations	equation	NOUN
ejde-629	41	14	.	.	PUNCT
ejde-629	42	1	t.	t.	PROPN
ejde-629	42	2	tang	tang	PROPN
ejde-629	42	3	et	et	PROPN
ejde-629	42	4	al	al	PROPN
ejde-629	42	5	.	.	PUNCT
ejde-629	43	1	[	[	X
ejde-629	43	2	18	18	NUM
ejde-629	43	3	]	]	PUNCT
ejde-629	43	4	proved	prove	VERB
ejde-629	43	5	the	the	DET
ejde-629	43	6	time	time	NOUN
ejde-629	43	7	-	-	PUNCT
ejde-629	43	8	fractional	fractional	ADJ
ejde-629	43	9	molecular	molecular	ADJ
ejde-629	43	10	beam	beam	NOUN
ejde-629	43	11	epitaxy	epitaxy	NOUN
ejde-629	43	12	models	model	NOUN
ejde-629	43	13	admit	admit	VERB
ejde-629	43	14	an	an	DET
ejde-629	43	15	energy	energy	NOUN
ejde-629	43	16	dissipation	dissipation	NOUN
ejde-629	43	17	law	law	NOUN
ejde-629	43	18	as	as	ADP
ejde-629	43	19	integral	integral	ADJ
ejde-629	43	20	cases	case	NOUN
ejde-629	43	21	and	and	CCONJ
ejde-629	43	22	proposed	propose	VERB
ejde-629	43	23	a	a	DET
ejde-629	43	24	class	class	NOUN
ejde-629	43	25	of	of	ADP
ejde-629	43	26	finite	finite	ADJ
ejde-629	43	27	difference	difference	NOUN
ejde-629	43	28	schemes	scheme	NOUN
ejde-629	43	29	inherited	inherit	VERB
ejde-629	43	30	the	the	DET
ejde-629	43	31	theoretical	theoretical	ADJ
ejde-629	43	32	energy	energy	NOUN
ejde-629	43	33	stability	stability	NOUN
ejde-629	43	34	.	.	PUNCT
ejde-629	44	1	chen	chen	PROPN
ejde-629	44	2	et	et	PROPN
ejde-629	44	3	al	al	PROPN
ejde-629	44	4	.	.	PUNCT
ejde-629	45	1	[	[	X
ejde-629	45	2	4	4	X
ejde-629	45	3	]	]	PUNCT
ejde-629	45	4	developed	develop	VERB
ejde-629	45	5	an	an	DET
ejde-629	45	6	efficient	efficient	ADJ
ejde-629	45	7	and	and	CCONJ
ejde-629	45	8	accurate	accurate	ADJ
ejde-629	45	9	,	,	PUNCT
ejde-629	45	10	full	full	ADJ
ejde-629	45	11	discrete	discrete	ADJ
ejde-629	45	12	,	,	PUNCT
ejde-629	45	13	linear	linear	PROPN
ejde-629	45	14	numerical	numerical	ADJ
ejde-629	45	15	approximation	approximation	NOUN
ejde-629	45	16	for	for	ADP
ejde-629	45	17	the	the	DET
ejde-629	45	18	time	time	NOUN
ejde-629	45	19	-	-	PUNCT
ejde-629	45	20	fractional	fractional	ADJ
ejde-629	45	21	thin	thin	ADJ
ejde-629	45	22	film	film	NOUN
ejde-629	45	23	model	model	NOUN
ejde-629	45	24	with	with	ADP
ejde-629	45	25	the	the	DET
ejde-629	45	26	classical	classical	ADJ
ejde-629	45	27	caputo	caputo	PROPN
ejde-629	45	28	fractional	fractional	PROPN
ejde-629	45	29	derivative	derivative	NOUN
ejde-629	45	30	of	of	ADP
ejde-629	45	31	order	order	NOUN
ejde-629	45	32	α	α	NOUN
ejde-629	45	33	and	and	CCONJ
ejde-629	45	34	shown	show	VERB
ejde-629	45	35	the	the	DET
ejde-629	45	36	models	model	NOUN
ejde-629	45	37	possessed	possess	VERB
ejde-629	45	38	an	an	DET
ejde-629	45	39	energy	energy	NOUN
ejde-629	45	40	dissipation	dissipation	NOUN
ejde-629	45	41	law	law	NOUN
ejde-629	45	42	.	.	PUNCT
ejde-629	46	1	wang	wang	PROPN
ejde-629	46	2	et	et	PROPN
ejde-629	46	3	al	al	PROPN
ejde-629	46	4	.	.	PUNCT
ejde-629	47	1	[	[	X
ejde-629	47	2	20	20	NUM
ejde-629	47	3	]	]	PUNCT
ejde-629	47	4	proposed	propose	VERB
ejde-629	47	5	a	a	DET
ejde-629	47	6	variable	variable	ADJ
ejde-629	47	7	-	-	PUNCT
ejde-629	47	8	step	step	NOUN
ejde-629	47	9	l1	l1	PROPN
ejde-629	47	10	scheme	scheme	NOUN
ejde-629	47	11	for	for	ADP
ejde-629	47	12	the	the	DET
ejde-629	47	13	time	time	NOUN
ejde-629	47	14	-	-	PUNCT
ejde-629	47	15	fractional	fractional	ADJ
ejde-629	47	16	molecular	molecular	ADJ
ejde-629	47	17	beam	beam	NOUN
ejde-629	47	18	epitaxy	epitaxy	NOUN
ejde-629	47	19	model	model	NOUN
ejde-629	47	20	and	and	CCONJ
ejde-629	47	21	also	also	ADV
ejde-629	47	22	investigated	investigate	VERB
ejde-629	47	23	the	the	DET
ejde-629	47	24	stability	stability	NOUN
ejde-629	47	25	and	and	CCONJ
ejde-629	47	26	convergence	convergence	NOUN
ejde-629	47	27	of	of	ADP
ejde-629	47	28	the	the	DET
ejde-629	47	29	stabilized	stabilize	VERB
ejde-629	47	30	convex	convex	NOUN
ejde-629	47	31	splitting	splitting	NOUN
ejde-629	47	32	scheme	scheme	NOUN
ejde-629	47	33	.	.	PUNCT
ejde-629	48	1	however	however	ADV
ejde-629	48	2	,	,	PUNCT
ejde-629	48	3	to	to	ADP
ejde-629	48	4	the	the	DET
ejde-629	48	5	best	good	ADJ
ejde-629	48	6	of	of	ADP
ejde-629	48	7	our	our	PRON
ejde-629	48	8	knowledge	knowledge	NOUN
ejde-629	48	9	,	,	PUNCT
ejde-629	48	10	the	the	DET
ejde-629	48	11	well	well	NOUN
ejde-629	48	12	-	-	PUNCT
ejde-629	48	13	posedness	posedness	NOUN
ejde-629	48	14	for	for	ADP
ejde-629	48	15	the	the	DET
ejde-629	48	16	solutions	solution	NOUN
ejde-629	48	17	of	of	ADP
ejde-629	48	18	the	the	DET
ejde-629	48	19	time	time	NOUN
ejde-629	48	20	fractional	fractional	ADJ
ejde-629	48	21	thin	thin	ADJ
ejde-629	48	22	film	film	NOUN
ejde-629	48	23	growth	growth	NOUN
ejde-629	48	24	equation	equation	NOUN
ejde-629	48	25	is	be	AUX
ejde-629	48	26	not	not	PART
ejde-629	48	27	clear	clear	ADJ
ejde-629	48	28	,	,	PUNCT
ejde-629	48	29	which	which	PRON
ejde-629	48	30	is	be	AUX
ejde-629	48	31	the	the	DET
ejde-629	48	32	main	main	ADJ
ejde-629	48	33	motivation	motivation	NOUN
ejde-629	48	34	of	of	ADP
ejde-629	48	35	the	the	DET
ejde-629	48	36	present	present	ADJ
ejde-629	48	37	work	work	NOUN
ejde-629	48	38	.	.	PUNCT
ejde-629	49	1	we	we	PRON
ejde-629	49	2	refer	refer	VERB
ejde-629	49	3	[	[	X
ejde-629	49	4	19	19	NUM
ejde-629	49	5	]	]	PUNCT
ejde-629	49	6	for	for	ADP
ejde-629	49	7	well	well	INTJ
ejde-629	49	8	posedness	posedness	NOUN
ejde-629	49	9	of	of	ADP
ejde-629	49	10	the	the	DET
ejde-629	49	11	linear	linear	ADJ
ejde-629	49	12	and	and	CCONJ
ejde-629	49	13	semilinear	semilinear	ADJ
ejde-629	49	14	time	time	NOUN
ejde-629	49	15	fractional	fractional	ADJ
ejde-629	49	16	order	order	NOUN
ejde-629	49	17	cauchy	cauchy	NOUN
ejde-629	49	18	problem	problem	NOUN
ejde-629	49	19	with	with	ADP
ejde-629	49	20	almost	almost	ADV
ejde-629	49	21	sectorial	sectorial	ADJ
ejde-629	49	22	operators	operator	NOUN
ejde-629	49	23	,	,	PUNCT
ejde-629	49	24	and	and	CCONJ
ejde-629	49	25	[	[	X
ejde-629	49	26	22	22	NUM
ejde-629	49	27	]	]	PUNCT
ejde-629	49	28	for	for	ADP
ejde-629	49	29	well	well	INTJ
ejde-629	49	30	posedness	posedness	NOUN
ejde-629	49	31	of	of	ADP
ejde-629	49	32	the	the	DET
ejde-629	49	33	time	time	NOUN
ejde-629	49	34	fractional	fractional	ADJ
ejde-629	49	35	order	order	NOUN
ejde-629	49	36	cahn	cahn	NOUN
ejde-629	49	37	-	-	PUNCT
ejde-629	49	38	hilliard	hilliard	NOUN
ejde-629	49	39	equation	equation	NOUN
ejde-629	49	40	in	in	ADP
ejde-629	49	41	r3	r3	PROPN
ejde-629	49	42	.	.	PUNCT
ejde-629	50	1	in	in	ADP
ejde-629	50	2	this	this	DET
ejde-629	50	3	article	article	NOUN
ejde-629	50	4	,	,	PUNCT
ejde-629	50	5	we	we	PRON
ejde-629	50	6	focus	focus	VERB
ejde-629	50	7	on	on	ADP
ejde-629	50	8	the	the	DET
ejde-629	50	9	existence	existence	NOUN
ejde-629	50	10	and	and	CCONJ
ejde-629	50	11	uniqueness	uniqueness	NOUN
ejde-629	50	12	of	of	ADP
ejde-629	50	13	mild	mild	ADJ
ejde-629	50	14	solutions	solution	NOUN
ejde-629	50	15	on	on	ADP
ejde-629	50	16	problem	problem	NOUN
ejde-629	50	17	(	(	PUNCT
ejde-629	50	18	1.1	1.1	NUM
ejde-629	50	19	)	)	PUNCT
ejde-629	50	20	.	.	PUNCT
ejde-629	51	1	because	because	SCONJ
ejde-629	51	2	of	of	ADP
ejde-629	51	3	the	the	DET
ejde-629	51	4	observation	observation	NOUN
ejde-629	51	5	that	that	SCONJ
ejde-629	51	6	the	the	DET
ejde-629	51	7	biharmonic	biharmonic	NOUN
ejde-629	51	8	operator	operator	NOUN
ejde-629	51	9	can	can	AUX
ejde-629	51	10	be	be	AUX
ejde-629	51	11	regarded	regard	VERB
ejde-629	51	12	as	as	ADP
ejde-629	51	13	a	a	DET
ejde-629	51	14	sectorial	sectorial	ADJ
ejde-629	51	15	operator	operator	NOUN
ejde-629	51	16	on	on	ADP
ejde-629	51	17	some	some	DET
ejde-629	51	18	spaces	space	NOUN
ejde-629	51	19	,	,	PUNCT
ejde-629	51	20	we	we	PRON
ejde-629	51	21	follow	follow	VERB
ejde-629	51	22	some	some	DET
ejde-629	51	23	ideas	idea	NOUN
ejde-629	51	24	in	in	ADP
ejde-629	51	25	[	[	X
ejde-629	51	26	3	3	NUM
ejde-629	51	27	]	]	PUNCT
ejde-629	51	28	,	,	PUNCT
ejde-629	51	29	properly	properly	ADV
ejde-629	51	30	adapted	adapt	VERB
ejde-629	51	31	to	to	ADP
ejde-629	51	32	our	our	PRON
ejde-629	51	33	problem	problem	NOUN
ejde-629	51	34	.	.	PUNCT
ejde-629	52	1	we	we	PRON
ejde-629	52	2	denote	denote	VERB
ejde-629	52	3	a	a	DET
ejde-629	52	4	=	=	X
ejde-629	52	5	∆2	∆2	PROPN
ejde-629	52	6	defined	define	VERB
ejde-629	52	7	on	on	ADP
ejde-629	52	8	lp(ω	lp(ω	PROPN
ejde-629	52	9	)	)	PUNCT
ejde-629	52	10	,	,	PUNCT
ejde-629	52	11	1	1	NUM
ejde-629	52	12	<	<	X
ejde-629	52	13	p	p	X
ejde-629	52	14	<	<	X
ejde-629	52	15	∞	∞	PROPN
ejde-629	52	16	with	with	ADP
ejde-629	52	17	its	its	PRON
ejde-629	52	18	domain	domain	NOUN
ejde-629	52	19	d(a	d(a	PROPN
ejde-629	52	20	)	)	PUNCT
ejde-629	52	21	=	=	PRON
ejde-629	52	22	{	{	PUNCT
ejde-629	52	23	u	u	NOUN
ejde-629	52	24	∈	∈	PROPN
ejde-629	52	25	w	w	PROPN
ejde-629	52	26	4,p(ω	4,p(ω	PROPN
ejde-629	52	27	)	)	PUNCT
ejde-629	52	28	:	:	PUNCT
ejde-629	52	29	∂νu|∂ω	∂νu|∂ω	NOUN
ejde-629	53	1	=	=	PUNCT
ejde-629	53	2	∂ν∆u|∂ω	∂ν∆u|∂ω	NOUN
ejde-629	53	3	=	=	SYM
ejde-629	53	4	0	0	NUM
ejde-629	53	5	}	}	PUNCT
ejde-629	53	6	.	.	PUNCT
ejde-629	54	1	it	it	PRON
ejde-629	54	2	is	be	AUX
ejde-629	54	3	clear	clear	ADJ
ejde-629	54	4	[	[	X
ejde-629	54	5	15	15	NUM
ejde-629	54	6	]	]	PUNCT
ejde-629	54	7	that	that	SCONJ
ejde-629	54	8	the	the	DET
ejde-629	54	9	following	follow	VERB
ejde-629	54	10	homogeneous	homogeneous	ADJ
ejde-629	54	11	boundary	boundary	ADJ
ejde-629	54	12	value	value	NOUN
ejde-629	54	13	problem	problem	NOUN
ejde-629	54	14	is	be	AUX
ejde-629	54	15	normally	normally	ADV
ejde-629	54	16	elliptic	elliptic	ADJ
ejde-629	54	17	in	in	ADP
ejde-629	54	18	ω	ω	NUM
ejde-629	54	19	,	,	PUNCT
ejde-629	54	20	∂tu	∂tu	ADJ
ejde-629	54	21	=	=	SYM
ejde-629	54	22	−au	−au	NOUN
ejde-629	54	23	,	,	PUNCT
ejde-629	54	24	x	x	X
ejde-629	54	25	∈	∈	PROPN
ejde-629	54	26	ω	ω	PROPN
ejde-629	54	27	,	,	PUNCT
ejde-629	54	28	t	t	X
ejde-629	54	29	>	>	X
ejde-629	54	30	0	0	NUM
ejde-629	54	31	,	,	PUNCT
ejde-629	54	32	u(x	u(x	NOUN
ejde-629	54	33	,	,	PUNCT
ejde-629	54	34	0	0	NUM
ejde-629	54	35	)	)	PUNCT
ejde-629	54	36	=	=	SYM
ejde-629	54	37	φ(x	φ(x	NOUN
ejde-629	54	38	)	)	PUNCT
ejde-629	54	39	,	,	PUNCT
ejde-629	54	40	x	x	PUNCT
ejde-629	54	41	∈	∈	PROPN
ejde-629	54	42	ω	ω	PROPN
ejde-629	54	43	.	.	PUNCT
ejde-629	55	1	(	(	PUNCT
ejde-629	55	2	1.3	1.3	NUM
ejde-629	55	3	)	)	PUNCT
ejde-629	55	4	ejde-2024/58	ejde-2024/58	ADJ
ejde-629	55	5	equations	equation	NOUN
ejde-629	55	6	modeling	model	VERB
ejde-629	55	7	thin	thin	ADJ
ejde-629	55	8	film	film	NOUN
ejde-629	55	9	growth	growth	NOUN
ejde-629	55	10	3	3	NUM
ejde-629	55	11	hence	hence	ADV
ejde-629	55	12	,	,	PUNCT
ejde-629	55	13	the	the	DET
ejde-629	55	14	fourth	fourth	ADJ
ejde-629	55	15	-	-	PUNCT
ejde-629	55	16	order	order	NOUN
ejde-629	55	17	operator	operator	NOUN
ejde-629	55	18	−∆2	−∆2	NOUN
ejde-629	55	19	with	with	ADP
ejde-629	55	20	corresponding	correspond	VERB
ejde-629	55	21	neumann	neumann	PROPN
ejde-629	55	22	boundary	boundary	PROPN
ejde-629	55	23	(	(	PUNCT
ejde-629	55	24	∂	∂	NUM
ejde-629	55	25	∂ν	∂ν	PROPN
ejde-629	55	26	,	,	PUNCT
ejde-629	55	27	∂∆	∂∆	NOUN
ejde-629	55	28	∂ν	∂ν	PROPN
ejde-629	55	29	)	)	PUNCT
ejde-629	55	30	is	be	AUX
ejde-629	55	31	the	the	DET
ejde-629	55	32	infinitesimal	infinitesimal	ADJ
ejde-629	55	33	generator	generator	NOUN
ejde-629	55	34	of	of	ADP
ejde-629	55	35	an	an	DET
ejde-629	55	36	analytic	analytic	ADJ
ejde-629	55	37	semigroup	semigroup	NOUN
ejde-629	55	38	t	t	PROPN
ejde-629	55	39	(	(	PUNCT
ejde-629	55	40	t	t	PROPN
ejde-629	55	41	)	)	PUNCT
ejde-629	55	42	=	=	VERB
ejde-629	56	1	e−t∆2	e−t∆2	PROPN
ejde-629	56	2	in	in	ADP
ejde-629	56	3	lp(ω	lp(ω	NOUN
ejde-629	56	4	)	)	PUNCT
ejde-629	56	5	.	.	PUNCT
ejde-629	57	1	for	for	ADP
ejde-629	57	2	a	a	DET
ejde-629	57	3	detailed	detailed	ADJ
ejde-629	57	4	discussion	discussion	NOUN
ejde-629	57	5	on	on	ADP
ejde-629	57	6	these	these	DET
ejde-629	57	7	results	result	NOUN
ejde-629	57	8	,	,	PUNCT
ejde-629	57	9	we	we	PRON
ejde-629	57	10	refer	refer	VERB
ejde-629	57	11	the	the	DET
ejde-629	57	12	reader	reader	NOUN
ejde-629	57	13	to	to	ADP
ejde-629	57	14	[	[	X
ejde-629	57	15	1	1	NUM
ejde-629	57	16	,	,	PUNCT
ejde-629	57	17	2	2	NUM
ejde-629	57	18	]	]	PUNCT
ejde-629	57	19	.	.	PUNCT
ejde-629	58	1	the	the	DET
ejde-629	58	2	time	time	NOUN
ejde-629	58	3	fractional	fractional	ADJ
ejde-629	58	4	version	version	NOUN
ejde-629	58	5	of	of	ADP
ejde-629	58	6	(	(	PUNCT
ejde-629	58	7	1.3	1.3	NUM
ejde-629	58	8	)	)	PUNCT
ejde-629	58	9	with	with	ADP
ejde-629	58	10	lower	low	ADJ
ejde-629	58	11	order	order	NOUN
ejde-629	58	12	term	term	NOUN
ejde-629	58	13	can	can	AUX
ejde-629	58	14	be	be	AUX
ejde-629	58	15	written	write	VERB
ejde-629	58	16	as	as	ADP
ejde-629	58	17	cd	cd	PROPN
ejde-629	58	18	α	α	PROPN
ejde-629	58	19	t	t	NOUN
ejde-629	58	20	u	u	X
ejde-629	58	21	=	=	PROPN
ejde-629	58	22	−au+	−au+	PROPN
ejde-629	58	23	f	f	PROPN
ejde-629	58	24	(	(	PUNCT
ejde-629	58	25	u	u	NOUN
ejde-629	58	26	)	)	PUNCT
ejde-629	58	27	,	,	PUNCT
ejde-629	58	28	x	x	PUNCT
ejde-629	58	29	∈	∈	PROPN
ejde-629	58	30	ω	ω	PROPN
ejde-629	58	31	,	,	PUNCT
ejde-629	58	32	t	t	PROPN
ejde-629	58	33	>	>	X
ejde-629	58	34	0	0	NUM
ejde-629	58	35	u(x	u(x	NOUN
ejde-629	58	36	,	,	PUNCT
ejde-629	58	37	0	0	NUM
ejde-629	58	38	)	)	PUNCT
ejde-629	58	39	=	=	SYM
ejde-629	58	40	φ(x	φ(x	NOUN
ejde-629	58	41	)	)	PUNCT
ejde-629	58	42	,	,	PUNCT
ejde-629	58	43	x	x	PUNCT
ejde-629	58	44	∈	∈	PROPN
ejde-629	58	45	ω	ω	PROPN
ejde-629	58	46	.	.	PUNCT
ejde-629	59	1	(	(	PUNCT
ejde-629	59	2	1.4	1.4	NUM
ejde-629	59	3	)	)	PUNCT
ejde-629	59	4	we	we	PRON
ejde-629	59	5	formally	formally	ADV
ejde-629	59	6	give	give	VERB
ejde-629	59	7	a	a	DET
ejde-629	59	8	mild	mild	ADJ
ejde-629	59	9	solution	solution	NOUN
ejde-629	59	10	for	for	ADP
ejde-629	59	11	(	(	PUNCT
ejde-629	59	12	1.4	1.4	NUM
ejde-629	59	13	)	)	PUNCT
ejde-629	59	14	,	,	PUNCT
ejde-629	59	15	where	where	SCONJ
ejde-629	59	16	the	the	DET
ejde-629	59	17	rigorous	rigorous	ADJ
ejde-629	59	18	deduction	deduction	NOUN
ejde-629	59	19	could	could	AUX
ejde-629	59	20	be	be	AUX
ejde-629	59	21	found	find	VERB
ejde-629	59	22	in	in	ADP
ejde-629	59	23	[	[	X
ejde-629	59	24	3	3	NUM
ejde-629	59	25	,	,	PUNCT
ejde-629	59	26	8	8	NUM
ejde-629	59	27	,	,	PUNCT
ejde-629	59	28	10	10	NUM
ejde-629	59	29	,	,	PUNCT
ejde-629	59	30	19	19	NUM
ejde-629	59	31	]	]	PUNCT
ejde-629	59	32	.	.	PUNCT
ejde-629	60	1	we	we	PRON
ejde-629	60	2	denote	denote	VERB
ejde-629	60	3	by	by	ADP
ejde-629	60	4	l	l	PROPN
ejde-629	60	5	laplace	laplace	NOUN
ejde-629	60	6	transform	transform	NOUN
ejde-629	60	7	operator	operator	NOUN
ejde-629	60	8	.	.	PUNCT
ejde-629	61	1	by	by	ADP
ejde-629	61	2	the	the	DET
ejde-629	61	3	convolution	convolution	NOUN
ejde-629	61	4	property	property	NOUN
ejde-629	61	5	of	of	ADP
ejde-629	61	6	laplace	laplace	NOUN
ejde-629	61	7	transform	transform	NOUN
ejde-629	61	8	,	,	PUNCT
ejde-629	61	9	we	we	PRON
ejde-629	61	10	have	have	VERB
ejde-629	61	11	l	l	NOUN
ejde-629	61	12	(	(	PUNCT
ejde-629	61	13	cdα	cdα	PROPN
ejde-629	61	14	t	t	PROPN
ejde-629	61	15	u	u	NOUN
ejde-629	61	16	)	)	PUNCT
ejde-629	61	17	=	=	PUNCT
ejde-629	62	1	λαl(u)−	λαl(u)−	NOUN
ejde-629	62	2	λα−1φ	λα−1φ	NOUN
ejde-629	62	3	,	,	PUNCT
ejde-629	62	4	as	as	ADP
ejde-629	62	5	in	in	ADP
ejde-629	62	6	[	[	X
ejde-629	62	7	10	10	NUM
ejde-629	62	8	]	]	PUNCT
ejde-629	62	9	.	.	PUNCT
ejde-629	63	1	so	so	ADV
ejde-629	63	2	taking	take	VERB
ejde-629	63	3	the	the	DET
ejde-629	63	4	laplace	laplace	NOUN
ejde-629	63	5	transform	transform	NOUN
ejde-629	63	6	to	to	ADP
ejde-629	63	7	(	(	PUNCT
ejde-629	63	8	1.4	1.4	NUM
ejde-629	63	9	)	)	PUNCT
ejde-629	63	10	gives	give	VERB
ejde-629	63	11	l(u	l(u	PRON
ejde-629	63	12	)	)	PUNCT
ejde-629	64	1	=	=	PUNCT
ejde-629	65	1	λα−1(λα	λα−1(λα	NOUN
ejde-629	65	2	+	+	NOUN
ejde-629	65	3	a)−1φ+	a)−1φ+	NOUN
ejde-629	65	4	(	(	PUNCT
ejde-629	65	5	λα	λα	PROPN
ejde-629	65	6	+	+	ADJ
ejde-629	65	7	a)−1l(f	a)−1l(f	PROPN
ejde-629	65	8	(	(	PUNCT
ejde-629	65	9	u	u	NOUN
ejde-629	65	10	)	)	PUNCT
ejde-629	65	11	)	)	PUNCT
ejde-629	65	12	.	.	PUNCT
ejde-629	66	1	application	application	NOUN
ejde-629	66	2	of	of	ADP
ejde-629	66	3	laplace	laplace	NOUN
ejde-629	66	4	inversion	inversion	NOUN
ejde-629	66	5	[	[	X
ejde-629	66	6	3	3	X
ejde-629	66	7	]	]	PUNCT
ejde-629	66	8	implies	imply	VERB
ejde-629	66	9	u(t	u(t	NOUN
ejde-629	66	10	)	)	PUNCT
ejde-629	67	1	=	=	SYM
ejde-629	67	2	eα	eα	X
ejde-629	67	3	(	(	PUNCT
ejde-629	67	4	−tαa)φ+	−tαa)φ+	PROPN
ejde-629	67	5	∫	∫	PROPN
ejde-629	67	6	t	t	PROPN
ejde-629	67	7	0	0	NUM
ejde-629	67	8	(	(	PUNCT
ejde-629	67	9	t−	t−	PROPN
ejde-629	67	10	s)α−1eα	s)α−1eα	PROPN
ejde-629	67	11	,	,	PUNCT
ejde-629	67	12	α	α	PROPN
ejde-629	67	13	(	(	PUNCT
ejde-629	67	14	−(t−	−(t−	NOUN
ejde-629	67	15	s)αa)f	s)αa)f	PROPN
ejde-629	67	16	(	(	PUNCT
ejde-629	67	17	u)(s)ds	u)(s)ds	PROPN
ejde-629	67	18	.	.	PUNCT
ejde-629	68	1	where	where	SCONJ
ejde-629	68	2	eα(−tαa	eα(−tαa	NOUN
ejde-629	68	3	)	)	PUNCT
ejde-629	68	4	and	and	CCONJ
ejde-629	68	5	eα	eα	NOUN
ejde-629	68	6	,	,	PUNCT
ejde-629	68	7	α(−tαa	α(−tαa	PROPN
ejde-629	68	8	)	)	PUNCT
ejde-629	68	9	are	be	AUX
ejde-629	68	10	the	the	DET
ejde-629	68	11	mittag	mittag	ADJ
ejde-629	68	12	-	-	PUNCT
ejde-629	68	13	leffler	leffler	NOUN
ejde-629	68	14	operators	operator	NOUN
ejde-629	68	15	(	(	PUNCT
ejde-629	68	16	see	see	VERB
ejde-629	68	17	section	section	NOUN
ejde-629	68	18	2	2	NUM
ejde-629	68	19	)	)	PUNCT
ejde-629	68	20	.	.	PUNCT
ejde-629	69	1	this	this	DET
ejde-629	69	2	formal	formal	ADJ
ejde-629	69	3	computation	computation	NOUN
ejde-629	69	4	then	then	ADV
ejde-629	69	5	motivates	motivate	VERB
ejde-629	69	6	the	the	DET
ejde-629	69	7	definition	definition	NOUN
ejde-629	69	8	of	of	ADP
ejde-629	69	9	the	the	DET
ejde-629	69	10	mild	mild	ADJ
ejde-629	69	11	solution	solution	NOUN
ejde-629	69	12	of	of	ADP
ejde-629	69	13	(	(	PUNCT
ejde-629	69	14	1.1	1.1	NUM
ejde-629	69	15	)	)	PUNCT
ejde-629	69	16	as	as	SCONJ
ejde-629	69	17	follows	follow	VERB
ejde-629	69	18	:	:	PUNCT
ejde-629	69	19	definition	definition	NOUN
ejde-629	69	20	1.1	1.1	NUM
ejde-629	69	21	.	.	PUNCT
ejde-629	70	1	let	let	VERB
ejde-629	70	2	0	0	NUM
ejde-629	70	3	<	<	X
ejde-629	70	4	α	α	X
ejde-629	70	5	<	<	X
ejde-629	70	6	1	1	NUM
ejde-629	70	7	and	and	CCONJ
ejde-629	70	8	t	t	X
ejde-629	70	9	>	>	X
ejde-629	70	10	0	0	PUNCT
ejde-629	70	11	.	.	PUNCT
ejde-629	71	1	(	(	PUNCT
ejde-629	71	2	i	i	NOUN
ejde-629	71	3	)	)	PUNCT
ejde-629	71	4	a	a	DET
ejde-629	71	5	function	function	NOUN
ejde-629	71	6	u	u	NOUN
ejde-629	71	7	such	such	ADJ
ejde-629	71	8	that	that	SCONJ
ejde-629	71	9	u	u	PROPN
ejde-629	71	10	∈	∈	PROPN
ejde-629	71	11	c([0	c([0	NOUN
ejde-629	71	12	,	,	PUNCT
ejde-629	71	13	t	t	X
ejde-629	71	14	]	]	PUNCT
ejde-629	71	15	;	;	PUNCT
ejde-629	71	16	l	l	X
ejde-629	71	17	βn	βn	X
ejde-629	71	18	2−β	2−β	NUM
ejde-629	71	19	(	(	PUNCT
ejde-629	71	20	ω	ω	NOUN
ejde-629	71	21	)	)	PUNCT
ejde-629	71	22	)	)	PUNCT
ejde-629	71	23	defined	define	VERB
ejde-629	71	24	by	by	ADP
ejde-629	71	25	u(x	u(x	NOUN
ejde-629	71	26	,	,	PUNCT
ejde-629	71	27	t	t	NOUN
ejde-629	71	28	)	)	PUNCT
ejde-629	71	29	=	=	PUNCT
ejde-629	71	30	eα(−tαa)φ+	eα(−tαa)φ+	PROPN
ejde-629	71	31	∫	∫	PROPN
ejde-629	71	32	t	t	PROPN
ejde-629	71	33	0	0	NUM
ejde-629	71	34	(	(	PUNCT
ejde-629	71	35	t−	t−	PROPN
ejde-629	71	36	s)α−1eα	s)α−1eα	PROPN
ejde-629	71	37	,	,	PUNCT
ejde-629	71	38	α(−(t−	α(−(t−	NOUN
ejde-629	71	39	s)αa)∇	s)αa)∇	NOUN
ejde-629	71	40	·	·	PUNCT
ejde-629	71	41	f(∇u	f(∇u	NUM
ejde-629	71	42	)	)	PUNCT
ejde-629	71	43	ds	ds	PROPN
ejde-629	71	44	,	,	PUNCT
ejde-629	71	45	(	(	PUNCT
ejde-629	71	46	1.5	1.5	NUM
ejde-629	71	47	)	)	PUNCT
ejde-629	71	48	is	be	AUX
ejde-629	71	49	called	call	VERB
ejde-629	71	50	a	a	DET
ejde-629	71	51	local	local	ADJ
ejde-629	71	52	mild	mild	ADJ
ejde-629	71	53	solution	solution	NOUN
ejde-629	71	54	of	of	ADP
ejde-629	71	55	(	(	PUNCT
ejde-629	71	56	1.1	1.1	NUM
ejde-629	71	57	)	)	PUNCT
ejde-629	71	58	.	.	PUNCT
ejde-629	72	1	(	(	PUNCT
ejde-629	72	2	ii	ii	NOUN
ejde-629	72	3	)	)	PUNCT
ejde-629	72	4	if	if	SCONJ
ejde-629	72	5	t	t	NOUN
ejde-629	72	6	=	=	SYM
ejde-629	72	7	∞	∞	PROPN
ejde-629	72	8	,	,	PUNCT
ejde-629	72	9	we	we	PRON
ejde-629	72	10	say	say	VERB
ejde-629	72	11	that	that	SCONJ
ejde-629	72	12	u	u	PROPN
ejde-629	72	13	is	be	AUX
ejde-629	72	14	a	a	DET
ejde-629	72	15	global	global	ADJ
ejde-629	72	16	mild	mild	ADJ
ejde-629	72	17	solution	solution	NOUN
ejde-629	72	18	of	of	ADP
ejde-629	72	19	(	(	PUNCT
ejde-629	72	20	1.1	1.1	NUM
ejde-629	72	21	)	)	PUNCT
ejde-629	72	22	.	.	PUNCT
ejde-629	73	1	we	we	PRON
ejde-629	73	2	are	be	AUX
ejde-629	73	3	now	now	ADV
ejde-629	73	4	in	in	ADP
ejde-629	73	5	a	a	DET
ejde-629	73	6	position	position	NOUN
ejde-629	73	7	to	to	PART
ejde-629	73	8	state	state	VERB
ejde-629	73	9	the	the	DET
ejde-629	73	10	main	main	ADJ
ejde-629	73	11	result	result	NOUN
ejde-629	73	12	of	of	ADP
ejde-629	73	13	this	this	DET
ejde-629	73	14	article	article	NOUN
ejde-629	73	15	.	.	PUNCT
ejde-629	74	1	theorem	theorem	VERB
ejde-629	74	2	1.2	1.2	NUM
ejde-629	74	3	.	.	PUNCT
ejde-629	75	1	suppose	suppose	VERB
ejde-629	75	2	ω	ω	PROPN
ejde-629	75	3	⊆	⊆	NUM
ejde-629	75	4	rn	rn	PROPN
ejde-629	75	5	is	be	AUX
ejde-629	75	6	a	a	DET
ejde-629	75	7	bounded	bounded	ADJ
ejde-629	75	8	domain	domain	NOUN
ejde-629	75	9	with	with	ADP
ejde-629	75	10	c4	c4	NOUN
ejde-629	75	11	boundary	boundary	NOUN
ejde-629	75	12	,	,	PUNCT
ejde-629	75	13	0	0	PUNCT
ejde-629	75	14	<	<	X
ejde-629	75	15	α	α	X
ejde-629	75	16	<	<	X
ejde-629	75	17	1	1	NUM
ejde-629	75	18	<	<	X
ejde-629	75	19	β	β	X
ejde-629	75	20	<	<	X
ejde-629	75	21	2	2	NUM
ejde-629	75	22	and	and	CCONJ
ejde-629	75	23	φ	φ	NUM
ejde-629	75	24	∈	∈	PROPN
ejde-629	75	25	l	l	NOUN
ejde-629	75	26	βn	βn	X
ejde-629	75	27	2−β	2−β	NUM
ejde-629	75	28	(	(	PUNCT
ejde-629	75	29	ω	ω	NOUN
ejde-629	75	30	)	)	PUNCT
ejde-629	75	31	.	.	PUNCT
ejde-629	76	1	then	then	ADV
ejde-629	76	2	there	there	PRON
ejde-629	76	3	exists	exist	VERB
ejde-629	76	4	t	t	PROPN
ejde-629	76	5	>	>	X
ejde-629	76	6	0	0	NUM
ejde-629	76	7	such	such	ADJ
ejde-629	76	8	that	that	SCONJ
ejde-629	76	9	(	(	PUNCT
ejde-629	76	10	1.1	1.1	NUM
ejde-629	76	11	)	)	PUNCT
ejde-629	76	12	admits	admit	VERB
ejde-629	76	13	a	a	DET
ejde-629	76	14	unique	unique	ADJ
ejde-629	76	15	mild	mild	ADJ
ejde-629	76	16	solution	solution	NOUN
ejde-629	76	17	u	u	PROPN
ejde-629	76	18	∈	∈	PROPN
ejde-629	76	19	c([0	c([0	NOUN
ejde-629	76	20	,	,	PUNCT
ejde-629	76	21	t	t	X
ejde-629	76	22	]	]	PUNCT
ejde-629	76	23	;	;	PUNCT
ejde-629	76	24	l	l	X
ejde-629	76	25	βn	βn	X
ejde-629	76	26	2−β	2−β	NUM
ejde-629	76	27	(	(	PUNCT
ejde-629	76	28	ω	ω	NOUN
ejde-629	76	29	)	)	PUNCT
ejde-629	76	30	)	)	PUNCT
ejde-629	77	1	satisfying	satisfy	VERB
ejde-629	77	2	max	max	PROPN
ejde-629	77	3	{	{	PUNCT
ejde-629	77	4	sup	sup	NOUN
ejde-629	77	5	0≤t≤t	0≤t≤t	NUM
ejde-629	77	6	t	t	NOUN
ejde-629	77	7	α	α	PROPN
ejde-629	77	8	2β−	2β−	PROPN
ejde-629	77	9	αγ	αγ	NUM
ejde-629	77	10	4β2	4β2	NUM
ejde-629	77	11	∥∇u(t)∥	∥∇u(t)∥	NOUN
ejde-629	77	12	β2n	β2n	PUNCT
ejde-629	77	13	γ	γ	NOUN
ejde-629	77	14	,	,	PUNCT
ejde-629	77	15	sup	sup	NOUN
ejde-629	77	16	0≤t≤t	0≤t≤t	NUM
ejde-629	77	17	t	t	NOUN
ejde-629	77	18	α	α	NOUN
ejde-629	77	19	2	2	NUM
ejde-629	77	20	∥∇2u(t)∥	∥∇2u(t)∥	NOUN
ejde-629	77	21	βn	βn	VERB
ejde-629	77	22	2−β	2−β	NUM
ejde-629	77	23	}	}	PUNCT
ejde-629	77	24	<	<	X
ejde-629	77	25	∞	∞	PROPN
ejde-629	77	26	,	,	PUNCT
ejde-629	77	27	where	where	SCONJ
ejde-629	77	28	0	0	PUNCT
ejde-629	77	29	<	<	X
ejde-629	77	30	γ	γ	X
ejde-629	77	31	<	<	X
ejde-629	77	32	min{2β	min{2β	PROPN
ejde-629	77	33	,	,	PUNCT
ejde-629	77	34	β(n+1)−2	β(n+1)−2	ADJ
ejde-629	77	35	}	}	PUNCT
ejde-629	77	36	.	.	PUNCT
ejde-629	78	1	furthermore	furthermore	ADV
ejde-629	78	2	,	,	PUNCT
ejde-629	78	3	if	if	SCONJ
ejde-629	78	4	∥φ∥	∥φ∥	VERB
ejde-629	78	5	βn	βn	VERB
ejde-629	78	6	2−β	2−β	NOUN
ejde-629	78	7	is	be	AUX
ejde-629	78	8	sufficiently	sufficiently	ADV
ejde-629	78	9	small	small	ADJ
ejde-629	78	10	,	,	PUNCT
ejde-629	78	11	the	the	DET
ejde-629	78	12	solution	solution	NOUN
ejde-629	78	13	u	u	NOUN
ejde-629	78	14	can	can	AUX
ejde-629	78	15	be	be	AUX
ejde-629	78	16	extended	extend	VERB
ejde-629	78	17	to	to	PART
ejde-629	78	18	be	be	AUX
ejde-629	78	19	global	global	ADJ
ejde-629	78	20	,	,	PUNCT
ejde-629	78	21	that	that	ADV
ejde-629	78	22	is	is	ADV
ejde-629	78	23	,	,	PUNCT
ejde-629	78	24	t	t	PROPN
ejde-629	78	25	=	=	SYM
ejde-629	78	26	∞.	∞.	PROPN
ejde-629	78	27	to	to	PART
ejde-629	78	28	explain	explain	VERB
ejde-629	78	29	the	the	DET
ejde-629	78	30	meaning	meaning	NOUN
ejde-629	78	31	of	of	ADP
ejde-629	78	32	the	the	DET
ejde-629	78	33	result	result	NOUN
ejde-629	78	34	,	,	PUNCT
ejde-629	78	35	we	we	PRON
ejde-629	78	36	take	take	VERB
ejde-629	78	37	f(ξ	f(ξ	NOUN
ejde-629	78	38	)	)	PUNCT
ejde-629	78	39	=	=	SYM
ejde-629	78	40	|ξ|βξ	|ξ|βξ	ADJ
ejde-629	78	41	in	in	ADP
ejde-629	78	42	(	(	PUNCT
ejde-629	78	43	1.1)1	1.1)1	NUM
ejde-629	78	44	as	as	ADP
ejde-629	78	45	an	an	DET
ejde-629	78	46	example	example	NOUN
ejde-629	78	47	.	.	PUNCT
ejde-629	79	1	notice	notice	VERB
ejde-629	79	2	that	that	SCONJ
ejde-629	79	3	a	a	DET
ejde-629	79	4	smooth	smooth	ADJ
ejde-629	79	5	function	function	NOUN
ejde-629	79	6	u(x	u(x	NOUN
ejde-629	79	7	,	,	PUNCT
ejde-629	79	8	t	t	PROPN
ejde-629	79	9	)	)	PUNCT
ejde-629	79	10	solves	solve	VERB
ejde-629	79	11	the	the	DET
ejde-629	79	12	equation	equation	NOUN
ejde-629	79	13	in	in	ADP
ejde-629	79	14	(	(	PUNCT
ejde-629	79	15	1.1	1.1	NUM
ejde-629	79	16	)	)	PUNCT
ejde-629	79	17	for	for	ADP
ejde-629	79	18	t	t	PROPN
ejde-629	79	19	>	>	X
ejde-629	79	20	0	0	PUNCT
ejde-629	80	1	if	if	SCONJ
ejde-629	80	2	and	and	CCONJ
ejde-629	80	3	only	only	ADV
ejde-629	80	4	if	if	SCONJ
ejde-629	80	5	uλ(x	uλ(x	NUM
ejde-629	80	6	,	,	PUNCT
ejde-629	80	7	t	t	PROPN
ejde-629	80	8	)	)	PUNCT
ejde-629	80	9	=	=	SYM
ejde-629	81	1	λ	λ	NOUN
ejde-629	81	2	2α	2α	NOUN
ejde-629	81	3	β	β	X
ejde-629	81	4	−αu(λαx	−αu(λαx	NUM
ejde-629	81	5	,	,	PUNCT
ejde-629	81	6	λ4	λ4	PROPN
ejde-629	81	7	t	t	PROPN
ejde-629	81	8	)	)	PUNCT
ejde-629	81	9	does	do	VERB
ejde-629	81	10	so	so	ADV
ejde-629	81	11	too	too	ADV
ejde-629	81	12	with	with	ADP
ejde-629	81	13	each	each	PRON
ejde-629	81	14	given	give	VERB
ejde-629	81	15	constant	constant	ADJ
ejde-629	81	16	λ	λ	NOUN
ejde-629	81	17	.	.	PUNCT
ejde-629	82	1	in	in	ADP
ejde-629	82	2	addition	addition	NOUN
ejde-629	82	3	,	,	PUNCT
ejde-629	82	4	for	for	ADP
ejde-629	82	5	the	the	DET
ejde-629	82	6	initial	initial	ADJ
ejde-629	82	7	data	datum	NOUN
ejde-629	82	8	φ	φ	NOUN
ejde-629	82	9	,	,	PUNCT
ejde-629	82	10	under	under	ADP
ejde-629	82	11	the	the	DET
ejde-629	82	12	transformation	transformation	NOUN
ejde-629	82	13	φ	φ	PROPN
ejde-629	82	14	7→	7→	NUM
ejde-629	82	15	φλ	φλ	PROPN
ejde-629	82	16	,	,	PUNCT
ejde-629	82	17	the	the	DET
ejde-629	82	18	l	l	NOUN
ejde-629	82	19	βn	βn	X
ejde-629	82	20	2−β	2−β	NUM
ejde-629	82	21	(	(	PUNCT
ejde-629	82	22	ω	ω	NOUN
ejde-629	82	23	)	)	PUNCT
ejde-629	82	24	norm	norm	NOUN
ejde-629	82	25	is	be	AUX
ejde-629	82	26	invariant	invariant	ADJ
ejde-629	82	27	.	.	PUNCT
ejde-629	83	1	therefore	therefore	ADV
ejde-629	83	2	,	,	PUNCT
ejde-629	83	3	we	we	PRON
ejde-629	83	4	expect	expect	VERB
ejde-629	83	5	the	the	DET
ejde-629	83	6	global	global	ADJ
ejde-629	83	7	existence	existence	NOUN
ejde-629	83	8	and	and	CCONJ
ejde-629	83	9	uniqueness	uniqueness	NOUN
ejde-629	83	10	of	of	ADP
ejde-629	83	11	solutions	solution	NOUN
ejde-629	83	12	when	when	SCONJ
ejde-629	83	13	the	the	DET
ejde-629	83	14	initial	initial	ADJ
ejde-629	83	15	data	data	NOUN
ejde-629	83	16	is	be	AUX
ejde-629	83	17	sufficiently	sufficiently	ADV
ejde-629	83	18	small	small	ADJ
ejde-629	83	19	in	in	ADP
ejde-629	83	20	the	the	DET
ejde-629	83	21	critical	critical	ADJ
ejde-629	83	22	space	space	NOUN
ejde-629	83	23	l	l	NOUN
ejde-629	83	24	βn	βn	X
ejde-629	83	25	2−β	2−β	NUM
ejde-629	83	26	(	(	PUNCT
ejde-629	83	27	ω	ω	NOUN
ejde-629	83	28	)	)	PUNCT
ejde-629	83	29	.	.	PUNCT
ejde-629	84	1	4	4	NUM
ejde-629	84	2	q.	q.	PROPN
ejde-629	84	3	liu	liu	PROPN
ejde-629	84	4	,	,	PUNCT
ejde-629	84	5	w.	w.	PROPN
ejde-629	84	6	zhu	zhu	PROPN
ejde-629	84	7	,	,	PUNCT
ejde-629	84	8	h.	h.	PROPN
ejde-629	84	9	ye	ye	PROPN
ejde-629	84	10	ejde-2024/58	ejde-2024/58	ADJ
ejde-629	84	11	it	it	PRON
ejde-629	84	12	is	be	AUX
ejde-629	84	13	worth	worth	ADJ
ejde-629	84	14	mentioning	mention	VERB
ejde-629	84	15	that	that	SCONJ
ejde-629	84	16	the	the	DET
ejde-629	84	17	singularity	singularity	NOUN
ejde-629	84	18	together	together	ADV
ejde-629	84	19	with	with	ADP
ejde-629	84	20	strong	strong	ADJ
ejde-629	84	21	nonlinearity	nonlinearity	NOUN
ejde-629	84	22	arising	arise	VERB
ejde-629	84	23	from	from	ADP
ejde-629	84	24	the	the	DET
ejde-629	84	25	time	time	NOUN
ejde-629	84	26	fractional	fractional	ADJ
ejde-629	84	27	derivative	derivative	ADJ
ejde-629	84	28	cd	cd	PROPN
ejde-629	84	29	α	α	PROPN
ejde-629	84	30	t	t	NOUN
ejde-629	84	31	u	u	NOUN
ejde-629	84	32	and	and	CCONJ
ejde-629	84	33	the	the	DET
ejde-629	84	34	nonlinear	nonlinear	ADJ
ejde-629	84	35	term	term	NOUN
ejde-629	84	36	∇	∇	X
ejde-629	84	37	·	·	PUNCT
ejde-629	84	38	f(∇u	f(∇u	NUM
ejde-629	84	39	)	)	PUNCT
ejde-629	84	40	make	make	VERB
ejde-629	84	41	its	its	PRON
ejde-629	84	42	mathematical	mathematical	ADJ
ejde-629	84	43	analysis	analysis	NOUN
ejde-629	84	44	more	more	ADV
ejde-629	84	45	difficult	difficult	ADJ
ejde-629	84	46	in	in	ADP
ejde-629	84	47	comparison	comparison	NOUN
ejde-629	84	48	with	with	ADP
ejde-629	84	49	the	the	DET
ejde-629	84	50	fourth	fourth	ADJ
ejde-629	84	51	-	-	PUNCT
ejde-629	84	52	order	order	NOUN
ejde-629	84	53	parabolic	parabolic	ADJ
ejde-629	84	54	equation	equation	NOUN
ejde-629	84	55	(	(	PUNCT
ejde-629	84	56	1.3)1	1.3)1	NOUN
ejde-629	84	57	.	.	NOUN
ejde-629	85	1	for	for	ADP
ejde-629	85	2	example	example	NOUN
ejde-629	85	3	,	,	PUNCT
ejde-629	85	4	the	the	DET
ejde-629	85	5	mittag	mittag	ADJ
ejde-629	85	6	-	-	PUNCT
ejde-629	85	7	leffler	leffler	NOUN
ejde-629	85	8	operators	operator	NOUN
ejde-629	85	9	eα(−tαa	eα(−tαa	VERB
ejde-629	85	10	)	)	PUNCT
ejde-629	85	11	and	and	CCONJ
ejde-629	85	12	eα	eα	NOUN
ejde-629	85	13	,	,	PUNCT
ejde-629	85	14	α(−tαa	α(−tαa	PROPN
ejde-629	85	15	)	)	PUNCT
ejde-629	85	16	do	do	AUX
ejde-629	85	17	not	not	PART
ejde-629	85	18	satisfy	satisfy	VERB
ejde-629	85	19	the	the	DET
ejde-629	85	20	semigroup	semigroup	ADJ
ejde-629	85	21	properties	property	NOUN
ejde-629	85	22	.	.	PUNCT
ejde-629	86	1	so	so	ADV
ejde-629	86	2	we	we	PRON
ejde-629	86	3	need	need	VERB
ejde-629	86	4	to	to	PART
ejde-629	86	5	overcome	overcome	VERB
ejde-629	86	6	these	these	DET
ejde-629	86	7	essential	essential	ADJ
ejde-629	86	8	difficulties	difficulty	NOUN
ejde-629	86	9	to	to	PART
ejde-629	86	10	get	get	VERB
ejde-629	86	11	some	some	DET
ejde-629	86	12	a	a	DET
ejde-629	86	13	priori	priori	ADJ
ejde-629	86	14	estimates	estimate	NOUN
ejde-629	86	15	and	and	CCONJ
ejde-629	86	16	extend	extend	VERB
ejde-629	86	17	the	the	DET
ejde-629	86	18	local	local	ADJ
ejde-629	86	19	solution	solution	NOUN
ejde-629	86	20	to	to	ADP
ejde-629	86	21	a	a	DET
ejde-629	86	22	global	global	ADJ
ejde-629	86	23	one	one	NUM
ejde-629	86	24	.	.	PUNCT
ejde-629	87	1	for	for	ADP
ejde-629	87	2	more	more	ADJ
ejde-629	87	3	details	detail	NOUN
ejde-629	87	4	,	,	PUNCT
ejde-629	87	5	one	one	PRON
ejde-629	87	6	can	can	AUX
ejde-629	87	7	refer	refer	VERB
ejde-629	87	8	to	to	ADP
ejde-629	87	9	section	section	NOUN
ejde-629	87	10	3	3	NUM
ejde-629	87	11	.	.	PUNCT
ejde-629	88	1	this	this	DET
ejde-629	88	2	article	article	NOUN
ejde-629	88	3	is	be	AUX
ejde-629	88	4	organized	organize	VERB
ejde-629	88	5	as	as	SCONJ
ejde-629	88	6	follows	follow	VERB
ejde-629	88	7	.	.	PUNCT
ejde-629	89	1	in	in	ADP
ejde-629	89	2	the	the	DET
ejde-629	89	3	next	next	ADJ
ejde-629	89	4	section	section	NOUN
ejde-629	89	5	,	,	PUNCT
ejde-629	89	6	we	we	PRON
ejde-629	89	7	introduce	introduce	VERB
ejde-629	89	8	some	some	DET
ejde-629	89	9	elementary	elementary	ADJ
ejde-629	89	10	properties	property	NOUN
ejde-629	89	11	of	of	ADP
ejde-629	89	12	mittag	mittag	ADJ
ejde-629	89	13	-	-	PUNCT
ejde-629	89	14	leffler	leffler	NOUN
ejde-629	89	15	operators	operator	NOUN
ejde-629	89	16	,	,	PUNCT
ejde-629	89	17	which	which	PRON
ejde-629	89	18	are	be	AUX
ejde-629	89	19	essential	essential	ADJ
ejde-629	89	20	throughout	throughout	ADP
ejde-629	89	21	the	the	DET
ejde-629	89	22	whole	whole	ADJ
ejde-629	89	23	paper	paper	NOUN
ejde-629	89	24	and	and	CCONJ
ejde-629	89	25	give	give	VERB
ejde-629	89	26	the	the	DET
ejde-629	89	27	main	main	ADJ
ejde-629	89	28	results	result	NOUN
ejde-629	89	29	of	of	ADP
ejde-629	89	30	this	this	DET
ejde-629	89	31	paper	paper	NOUN
ejde-629	89	32	.	.	PUNCT
ejde-629	90	1	in	in	ADP
ejde-629	90	2	section	section	NOUN
ejde-629	90	3	3	3	NUM
ejde-629	90	4	,	,	PUNCT
ejde-629	90	5	we	we	PRON
ejde-629	90	6	establish	establish	VERB
ejde-629	90	7	the	the	DET
ejde-629	90	8	existence	existence	NOUN
ejde-629	90	9	and	and	CCONJ
ejde-629	90	10	uniqueness	uniqueness	NOUN
ejde-629	90	11	of	of	ADP
ejde-629	90	12	mild	mild	ADJ
ejde-629	90	13	solutions	solution	NOUN
ejde-629	90	14	using	use	VERB
ejde-629	90	15	appropriate	appropriate	ADJ
ejde-629	90	16	functional	functional	ADJ
ejde-629	90	17	spaces	space	NOUN
ejde-629	90	18	and	and	CCONJ
ejde-629	90	19	banach	banach	ADV
ejde-629	90	20	fixed	fix	VERB
ejde-629	90	21	pointed	point	VERB
ejde-629	90	22	theorem	theorem	VERB
ejde-629	90	23	.	.	PROPN
ejde-629	91	1	2	2	X
ejde-629	91	2	.	.	X
ejde-629	91	3	a	a	DET
ejde-629	91	4	priori	priori	ADJ
ejde-629	91	5	estimates	estimate	NOUN
ejde-629	91	6	throughout	throughout	ADP
ejde-629	91	7	this	this	DET
ejde-629	91	8	paper	paper	NOUN
ejde-629	91	9	,	,	PUNCT
ejde-629	91	10	c	c	PROPN
ejde-629	91	11	stands	stand	VERB
ejde-629	91	12	for	for	ADP
ejde-629	91	13	a	a	DET
ejde-629	91	14	generic	generic	ADJ
ejde-629	91	15	positive	positive	ADJ
ejde-629	91	16	constant	constant	NOUN
ejde-629	91	17	which	which	PRON
ejde-629	91	18	may	may	AUX
ejde-629	91	19	vary	vary	VERB
ejde-629	91	20	from	from	ADP
ejde-629	91	21	line	line	NOUN
ejde-629	91	22	to	to	ADP
ejde-629	91	23	line	line	NOUN
ejde-629	91	24	.	.	PUNCT
ejde-629	92	1	for	for	ADP
ejde-629	92	2	the	the	DET
ejde-629	92	3	analytic	analytic	ADJ
ejde-629	92	4	semigroup	semigroup	PROPN
ejde-629	92	5	t	t	PROPN
ejde-629	92	6	(	(	PUNCT
ejde-629	92	7	t	t	PROPN
ejde-629	92	8	)	)	PUNCT
ejde-629	92	9	,	,	PUNCT
ejde-629	92	10	we	we	PRON
ejde-629	92	11	have	have	VERB
ejde-629	92	12	the	the	DET
ejde-629	92	13	lp	lp	ADJ
ejde-629	92	14	−	−	PROPN
ejde-629	92	15	lq	lq	NOUN
ejde-629	92	16	estimates	estimate	NOUN
ejde-629	92	17	,	,	PUNCT
ejde-629	92	18	which	which	PRON
ejde-629	92	19	are	be	AUX
ejde-629	92	20	state	state	NOUN
ejde-629	92	21	as	as	SCONJ
ejde-629	92	22	follows	follow	VERB
ejde-629	92	23	.	.	PUNCT
ejde-629	93	1	proposition	proposition	NOUN
ejde-629	93	2	2.1	2.1	NUM
ejde-629	93	3	(	(	PUNCT
ejde-629	93	4	[	[	X
ejde-629	93	5	15	15	NUM
ejde-629	93	6	,	,	PUNCT
ejde-629	93	7	21	21	NUM
ejde-629	93	8	]	]	PUNCT
ejde-629	93	9	)	)	PUNCT
ejde-629	93	10	.	.	PUNCT
ejde-629	94	1	let	let	VERB
ejde-629	94	2	1	1	NUM
ejde-629	94	3	<	<	X
ejde-629	94	4	q	q	X
ejde-629	94	5	≤	≤	NUM
ejde-629	94	6	p	p	NOUN
ejde-629	94	7	<	<	X
ejde-629	94	8	∞	∞	PROPN
ejde-629	94	9	and	and	CCONJ
ejde-629	94	10	j	j	PROPN
ejde-629	94	11	=	=	SYM
ejde-629	94	12	0	0	NUM
ejde-629	94	13	,	,	PUNCT
ejde-629	94	14	1	1	NUM
ejde-629	94	15	,	,	PUNCT
ejde-629	94	16	2	2	NUM
ejde-629	94	17	,	,	PUNCT
ejde-629	94	18	3	3	NUM
ejde-629	94	19	.	.	X
ejde-629	95	1	for	for	ADP
ejde-629	95	2	u	u	PROPN
ejde-629	95	3	∈	∈	PROPN
ejde-629	95	4	lq(ω	lq(ω	NOUN
ejde-629	95	5	)	)	PUNCT
ejde-629	95	6	,	,	PUNCT
ejde-629	95	7	we	we	PRON
ejde-629	95	8	have	have	VERB
ejde-629	95	9	∥∇jt	∥∇jt	X
ejde-629	95	10	(	(	PUNCT
ejde-629	95	11	t)u∥lp(ω	t)u∥lp(ω	PROPN
ejde-629	95	12	)	)	PUNCT
ejde-629	95	13	≤	≤	PUNCT
ejde-629	96	1	c	c	X
ejde-629	96	2	t−	t−	PROPN
ejde-629	96	3	n	n	PROPN
ejde-629	96	4	4	4	NUM
ejde-629	96	5	(	(	PUNCT
ejde-629	96	6	1	1	NUM
ejde-629	96	7	q−	q−	PROPN
ejde-629	96	8	1	1	NUM
ejde-629	96	9	p	p	NOUN
ejde-629	96	10	)	)	PUNCT
ejde-629	96	11	−	−	PROPN
ejde-629	96	12	j	j	PROPN
ejde-629	96	13	4	4	NUM
ejde-629	96	14	∥u∥lq(ω	∥u∥lq(ω	PROPN
ejde-629	96	15	)	)	PUNCT
ejde-629	96	16	,	,	PUNCT
ejde-629	96	17	t	t	X
ejde-629	96	18	>	>	X
ejde-629	96	19	0	0	X
ejde-629	96	20	.	.	PUNCT
ejde-629	97	1	let	let	VERB
ejde-629	97	2	us	we	PRON
ejde-629	97	3	recall	recall	VERB
ejde-629	97	4	some	some	DET
ejde-629	97	5	properties	property	NOUN
ejde-629	97	6	of	of	ADP
ejde-629	97	7	mittag	mittag	ADJ
ejde-629	97	8	-	-	PUNCT
ejde-629	97	9	leffler	leffler	NOUN
ejde-629	97	10	operators	operator	NOUN
ejde-629	97	11	.	.	PUNCT
ejde-629	98	1	for	for	ADP
ejde-629	98	2	α	α	DET
ejde-629	98	3	∈	∈	PROPN
ejde-629	98	4	(	(	PUNCT
ejde-629	98	5	0	0	NUM
ejde-629	98	6	,	,	PUNCT
ejde-629	98	7	1	1	NUM
ejde-629	98	8	)	)	PUNCT
ejde-629	98	9	,	,	PUNCT
ejde-629	98	10	we	we	PRON
ejde-629	98	11	denote	denote	VERB
ejde-629	98	12	the	the	DET
ejde-629	98	13	entire	entire	ADJ
ejde-629	98	14	function	function	NOUN
ejde-629	98	15	mα	mα	PROPN
ejde-629	98	16	:	:	PUNCT
ejde-629	98	17	c	c	X
ejde-629	98	18	→	→	SYM
ejde-629	98	19	c	c	X
ejde-629	98	20	the	the	DET
ejde-629	98	21	mainardi	mainardi	PROPN
ejde-629	98	22	function	function	NOUN
ejde-629	98	23	by	by	ADP
ejde-629	98	24	mα(z	mα(z	NOUN
ejde-629	98	25	)	)	PUNCT
ejde-629	98	26	:	:	PUNCT
ejde-629	99	1	=	=	NOUN
ejde-629	99	2	∞∑	∞∑	NUM
ejde-629	99	3	n=0	n=0	NUM
ejde-629	99	4	(	(	PUNCT
ejde-629	99	5	−z)n	−z)n	NOUN
ejde-629	99	6	n!γ(1−	n!γ(1−	PROPN
ejde-629	99	7	α(1	α(1	PROPN
ejde-629	99	8	+	+	CCONJ
ejde-629	99	9	n	n	CCONJ
ejde-629	99	10	)	)	PUNCT
ejde-629	99	11	)	)	PUNCT
ejde-629	99	12	,	,	PUNCT
ejde-629	99	13	which	which	PRON
ejde-629	99	14	is	be	AUX
ejde-629	99	15	a	a	DET
ejde-629	99	16	particular	particular	ADJ
ejde-629	99	17	case	case	NOUN
ejde-629	99	18	of	of	ADP
ejde-629	99	19	the	the	DET
ejde-629	99	20	wright	wright	PROPN
ejde-629	99	21	type	type	NOUN
ejde-629	99	22	function	function	NOUN
ejde-629	99	23	introduced	introduce	VERB
ejde-629	99	24	by	by	ADP
ejde-629	99	25	mainardi	mainardi	PROPN
ejde-629	99	26	in	in	ADP
ejde-629	99	27	[	[	X
ejde-629	99	28	12	12	NUM
ejde-629	99	29	]	]	PUNCT
ejde-629	99	30	to	to	PART
ejde-629	99	31	characterize	characterize	VERB
ejde-629	99	32	the	the	DET
ejde-629	99	33	fundamental	fundamental	ADJ
ejde-629	99	34	solutions	solution	NOUN
ejde-629	99	35	for	for	ADP
ejde-629	99	36	some	some	DET
ejde-629	99	37	standard	standard	ADJ
ejde-629	99	38	boundary	boundary	ADJ
ejde-629	99	39	value	value	NOUN
ejde-629	99	40	problems	problem	NOUN
ejde-629	99	41	in	in	ADP
ejde-629	99	42	physics	physics	NOUN
ejde-629	99	43	.	.	PUNCT
ejde-629	100	1	the	the	DET
ejde-629	100	2	following	follow	VERB
ejde-629	100	3	classical	classical	ADJ
ejde-629	100	4	result	result	NOUN
ejde-629	100	5	gives	give	VERB
ejde-629	100	6	some	some	DET
ejde-629	100	7	essential	essential	ADJ
ejde-629	100	8	relations	relation	NOUN
ejde-629	100	9	used	use	VERB
ejde-629	100	10	in	in	ADP
ejde-629	100	11	this	this	DET
ejde-629	100	12	article	article	NOUN
ejde-629	100	13	to	to	PART
ejde-629	100	14	obtain	obtain	VERB
ejde-629	100	15	the	the	DET
ejde-629	100	16	main	main	ADJ
ejde-629	100	17	estimates	estimate	NOUN
ejde-629	100	18	.	.	PUNCT
ejde-629	101	1	proposition	proposition	NOUN
ejde-629	101	2	2.2	2.2	NUM
ejde-629	101	3	(	(	PUNCT
ejde-629	101	4	[	[	X
ejde-629	101	5	19	19	NUM
ejde-629	101	6	]	]	NUM
ejde-629	101	7	)	)	PUNCT
ejde-629	101	8	.	.	PUNCT
ejde-629	102	1	let	let	VERB
ejde-629	102	2	0	0	PUNCT
ejde-629	102	3	<	<	X
ejde-629	102	4	α	α	X
ejde-629	102	5	<	<	X
ejde-629	102	6	1	1	NUM
ejde-629	102	7	and	and	CCONJ
ejde-629	102	8	−1	−1	NOUN
ejde-629	102	9	<	<	X
ejde-629	102	10	γ	γ	X
ejde-629	102	11	<	<	X
ejde-629	102	12	∞.	∞.	PROPN
ejde-629	102	13	if	if	SCONJ
ejde-629	102	14	we	we	PRON
ejde-629	102	15	restrict	restrict	VERB
ejde-629	102	16	mα	mα	PROPN
ejde-629	102	17	to	to	ADP
ejde-629	102	18	the	the	DET
ejde-629	102	19	positive	positive	ADJ
ejde-629	102	20	real	real	ADJ
ejde-629	102	21	line	line	NOUN
ejde-629	102	22	,	,	PUNCT
ejde-629	102	23	then	then	ADV
ejde-629	102	24	it	it	PRON
ejde-629	102	25	holds	hold	VERB
ejde-629	102	26	that	that	SCONJ
ejde-629	102	27	mα	mα	PROPN
ejde-629	102	28	∈	∈	PROPN
ejde-629	102	29	s([0,∞	s([0,∞	PROPN
ejde-629	102	30	)	)	PUNCT
ejde-629	102	31	)	)	PUNCT
ejde-629	102	32	,	,	PUNCT
ejde-629	102	33	mα(t	mα(t	X
ejde-629	102	34	)	)	PUNCT
ejde-629	102	35	≥	≥	NOUN
ejde-629	102	36	0	0	NUM
ejde-629	102	37	for	for	ADP
ejde-629	102	38	all	all	DET
ejde-629	102	39	t	t	PROPN
ejde-629	102	40	≥	≥	NOUN
ejde-629	102	41	0	0	NUM
ejde-629	102	42	and	and	CCONJ
ejde-629	102	43	∫	∫	PROPN
ejde-629	103	1	∞	∞	PROPN
ejde-629	103	2	0	0	PUNCT
ejde-629	103	3	tγmα(t	tγmα(t	NOUN
ejde-629	103	4	)	)	PUNCT
ejde-629	103	5	dt	dt	NOUN
ejde-629	103	6	=	=	SYM
ejde-629	103	7	γ(γ	γ(γ	NOUN
ejde-629	103	8	+	+	CCONJ
ejde-629	103	9	1	1	X
ejde-629	103	10	)	)	PUNCT
ejde-629	103	11	γ(αγ	γ(αγ	PROPN
ejde-629	103	12	+	+	CCONJ
ejde-629	103	13	1	1	X
ejde-629	103	14	)	)	PUNCT
ejde-629	103	15	,	,	PUNCT
ejde-629	103	16	where	where	SCONJ
ejde-629	103	17	s([0,∞	s([0,∞	NOUN
ejde-629	103	18	)	)	PUNCT
ejde-629	103	19	)	)	PUNCT
ejde-629	103	20	is	be	AUX
ejde-629	103	21	the	the	DET
ejde-629	103	22	schwartz	schwartz	PROPN
ejde-629	103	23	space	space	NOUN
ejde-629	103	24	on	on	ADP
ejde-629	103	25	[	[	X
ejde-629	103	26	0,∞	0,∞	NOUN
ejde-629	103	27	)	)	PUNCT
ejde-629	103	28	.	.	PUNCT
ejde-629	104	1	now	now	ADV
ejde-629	104	2	,	,	PUNCT
ejde-629	104	3	for	for	ADP
ejde-629	104	4	each	each	DET
ejde-629	104	5	α	α	NOUN
ejde-629	104	6	∈	∈	PROPN
ejde-629	104	7	(	(	PUNCT
ejde-629	104	8	0	0	NUM
ejde-629	104	9	,	,	PUNCT
ejde-629	104	10	1	1	NUM
ejde-629	104	11	)	)	PUNCT
ejde-629	104	12	,	,	PUNCT
ejde-629	104	13	we	we	PRON
ejde-629	104	14	define	define	VERB
ejde-629	104	15	the	the	DET
ejde-629	104	16	mittag	mittag	ADJ
ejde-629	104	17	-	-	PUNCT
ejde-629	104	18	leffler	leffler	NOUN
ejde-629	104	19	families	family	NOUN
ejde-629	104	20	eα(−tαa	eα(−tαa	VERB
ejde-629	104	21	)	)	PUNCT
ejde-629	105	1	=	=	SYM
ejde-629	105	2	∫	∫	PROPN
ejde-629	106	1	∞	∞	NUM
ejde-629	106	2	0	0	PUNCT
ejde-629	107	1	mα(s)t	mα(s)t	PROPN
ejde-629	107	2	(	(	PUNCT
ejde-629	107	3	st	st	PROPN
ejde-629	107	4	α	α	PROPN
ejde-629	107	5	)	)	PUNCT
ejde-629	107	6	ds	ds	PROPN
ejde-629	107	7	,	,	PUNCT
ejde-629	107	8	eα	eα	NOUN
ejde-629	107	9	,	,	PUNCT
ejde-629	107	10	α(−tαa	α(−tαa	PROPN
ejde-629	107	11	)	)	PUNCT
ejde-629	107	12	=	=	PUNCT
ejde-629	108	1	∫	∫	PROPN
ejde-629	108	2	∞	∞	NUM
ejde-629	108	3	0	0	NUM
ejde-629	109	1	αsmα(s)t	αsmα(s)t	NOUN
ejde-629	109	2	(	(	PUNCT
ejde-629	109	3	st	st	PROPN
ejde-629	109	4	α	α	NOUN
ejde-629	109	5	)	)	PUNCT
ejde-629	109	6	ds	ds	NOUN
ejde-629	109	7	.	.	PUNCT
ejde-629	110	1	it	it	PRON
ejde-629	110	2	is	be	AUX
ejde-629	110	3	interesting	interesting	ADJ
ejde-629	110	4	to	to	PART
ejde-629	110	5	notice	notice	VERB
ejde-629	110	6	that	that	SCONJ
ejde-629	110	7	the	the	DET
ejde-629	110	8	mainardi	mainardi	PROPN
ejde-629	110	9	functions	function	NOUN
ejde-629	110	10	act	act	VERB
ejde-629	110	11	as	as	ADP
ejde-629	110	12	a	a	DET
ejde-629	110	13	bridge	bridge	NOUN
ejde-629	110	14	between	between	ADP
ejde-629	110	15	the	the	DET
ejde-629	110	16	fractional	fractional	ADJ
ejde-629	110	17	and	and	CCONJ
ejde-629	110	18	the	the	DET
ejde-629	110	19	classical	classical	ADJ
ejde-629	110	20	abstract	abstract	ADJ
ejde-629	110	21	theories	theory	NOUN
ejde-629	110	22	,	,	PUNCT
ejde-629	110	23	for	for	SCONJ
ejde-629	110	24	more	more	ADJ
ejde-629	110	25	details	detail	NOUN
ejde-629	110	26	see	see	VERB
ejde-629	110	27	[	[	X
ejde-629	110	28	19	19	NUM
ejde-629	110	29	,	,	PUNCT
ejde-629	110	30	11	11	NUM
ejde-629	110	31	,	,	PUNCT
ejde-629	110	32	3	3	NUM
ejde-629	110	33	]	]	PUNCT
ejde-629	110	34	.	.	PUNCT
ejde-629	111	1	the	the	DET
ejde-629	111	2	next	next	ADJ
ejde-629	111	3	result	result	NOUN
ejde-629	111	4	comprises	comprise	VERB
ejde-629	111	5	the	the	DET
ejde-629	111	6	main	main	ADJ
ejde-629	111	7	assertions	assertion	NOUN
ejde-629	111	8	about	about	ADP
ejde-629	111	9	the	the	DET
ejde-629	111	10	theory	theory	NOUN
ejde-629	111	11	of	of	ADP
ejde-629	111	12	abstract	abstract	ADJ
ejde-629	111	13	fractional	fractional	ADJ
ejde-629	111	14	calculus	calculus	NOUN
ejde-629	111	15	.	.	PUNCT
ejde-629	112	1	ejde-2024/58	ejde-2024/58	ADJ
ejde-629	112	2	equations	equation	NOUN
ejde-629	112	3	modeling	model	VERB
ejde-629	112	4	thin	thin	ADJ
ejde-629	112	5	film	film	NOUN
ejde-629	112	6	growth	growth	NOUN
ejde-629	112	7	5	5	NUM
ejde-629	112	8	proposition	proposition	NOUN
ejde-629	112	9	2.3	2.3	NUM
ejde-629	112	10	(	(	PUNCT
ejde-629	112	11	[	[	X
ejde-629	112	12	19	19	NUM
ejde-629	112	13	]	]	NUM
ejde-629	112	14	)	)	PUNCT
ejde-629	112	15	.	.	PUNCT
ejde-629	113	1	eα(−tαa	eα(−tαa	NOUN
ejde-629	113	2	)	)	PUNCT
ejde-629	113	3	and	and	CCONJ
ejde-629	113	4	eα	eα	NOUN
ejde-629	113	5	,	,	PUNCT
ejde-629	113	6	α(−tαa	α(−tαa	PROPN
ejde-629	113	7	)	)	PUNCT
ejde-629	113	8	are	be	AUX
ejde-629	113	9	well	well	ADV
ejde-629	113	10	defined	define	VERB
ejde-629	113	11	from	from	ADP
ejde-629	113	12	lp(ω	lp(ω	PRON
ejde-629	113	13	)	)	PUNCT
ejde-629	113	14	to	to	ADP
ejde-629	113	15	lp(ω	lp(ω	NUM
ejde-629	113	16	)	)	PUNCT
ejde-629	113	17	,	,	PUNCT
ejde-629	114	1	p	p	PROPN
ejde-629	114	2	∈	∈	PROPN
ejde-629	114	3	(	(	PUNCT
ejde-629	114	4	1,∞	1,∞	NUM
ejde-629	114	5	)	)	PUNCT
ejde-629	114	6	.	.	PUNCT
ejde-629	115	1	moreover	moreover	ADV
ejde-629	115	2	,	,	PUNCT
ejde-629	115	3	for	for	ADP
ejde-629	115	4	t	t	PROPN
ejde-629	115	5	≥	≥	NOUN
ejde-629	115	6	0	0	NUM
ejde-629	115	7	,	,	PUNCT
ejde-629	115	8	eα(−tαa	eα(−tαa	NOUN
ejde-629	115	9	)	)	PUNCT
ejde-629	115	10	and	and	CCONJ
ejde-629	115	11	eα	eα	NOUN
ejde-629	115	12	,	,	PUNCT
ejde-629	115	13	α(−tαa	α(−tαa	PROPN
ejde-629	115	14	)	)	PUNCT
ejde-629	115	15	are	be	AUX
ejde-629	115	16	uniformly	uniformly	ADV
ejde-629	115	17	continuous	continuous	ADJ
ejde-629	115	18	in	in	ADP
ejde-629	115	19	the	the	DET
ejde-629	115	20	uniform	uniform	ADJ
ejde-629	115	21	operator	operator	NOUN
ejde-629	115	22	topology	topology	NOUN
ejde-629	115	23	on	on	ADP
ejde-629	115	24	lp(ω	lp(ω	PROPN
ejde-629	115	25	)	)	PUNCT
ejde-629	115	26	.	.	PUNCT
ejde-629	116	1	our	our	PRON
ejde-629	116	2	proof	proof	NOUN
ejde-629	116	3	relies	rely	VERB
ejde-629	116	4	on	on	ADP
ejde-629	116	5	the	the	DET
ejde-629	116	6	well	well	ADV
ejde-629	116	7	-	-	PUNCT
ejde-629	116	8	known	know	VERB
ejde-629	116	9	weierstrass	weierstrass	NOUN
ejde-629	116	10	m	m	NOUN
ejde-629	116	11	-	-	NOUN
ejde-629	116	12	test	test	NOUN
ejde-629	116	13	in	in	ADP
ejde-629	116	14	banach	banach	NOUN
ejde-629	116	15	space	space	NOUN
ejde-629	116	16	and	and	CCONJ
ejde-629	116	17	lp	lp	ADJ
ejde-629	116	18	−	−	PROPN
ejde-629	116	19	lq	lq	ADP
ejde-629	116	20	estimates	estimate	NOUN
ejde-629	116	21	for	for	ADP
ejde-629	116	22	mittag	mittag	ADJ
ejde-629	116	23	-	-	PUNCT
ejde-629	116	24	leffler	leffler	NOUN
ejde-629	116	25	operators	operator	NOUN
ejde-629	116	26	.	.	PUNCT
ejde-629	117	1	lemma	lemma	PROPN
ejde-629	117	2	2.4	2.4	NUM
ejde-629	117	3	(	(	PUNCT
ejde-629	117	4	weierstrass	weierstrass	PROPN
ejde-629	117	5	m	m	NOUN
ejde-629	117	6	-	-	NOUN
ejde-629	117	7	test	test	NOUN
ejde-629	117	8	[	[	X
ejde-629	117	9	7	7	NUM
ejde-629	117	10	]	]	NUM
ejde-629	117	11	)	)	PUNCT
ejde-629	117	12	.	.	PUNCT
ejde-629	118	1	let	let	VERB
ejde-629	118	2	x	x	PRON
ejde-629	118	3	denote	denote	VERB
ejde-629	118	4	a	a	DET
ejde-629	118	5	banach	banach	NOUN
ejde-629	118	6	space	space	NOUN
ejde-629	118	7	equipped	equip	VERB
ejde-629	118	8	with	with	ADP
ejde-629	118	9	the	the	DET
ejde-629	118	10	norm	norm	NOUN
ejde-629	118	11	∥	∥	X
ejde-629	118	12	·	·	PUNCT
ejde-629	119	1	∥x	∥x	PROPN
ejde-629	119	2	.	.	PUNCT
ejde-629	120	1	suppose	suppose	VERB
ejde-629	120	2	{	{	PUNCT
ejde-629	120	3	ωj}j≥0	ωj}j≥0	ADJ
ejde-629	120	4	is	be	AUX
ejde-629	120	5	a	a	DET
ejde-629	120	6	sequence	sequence	NOUN
ejde-629	120	7	of	of	ADP
ejde-629	120	8	continuous	continuous	ADJ
ejde-629	120	9	functions	function	NOUN
ejde-629	120	10	from	from	ADP
ejde-629	120	11	[	[	X
ejde-629	120	12	0	0	NUM
ejde-629	120	13	,	,	PUNCT
ejde-629	120	14	t	t	NOUN
ejde-629	120	15	]	]	PUNCT
ejde-629	120	16	to	to	ADP
ejde-629	120	17	x	x	SYM
ejde-629	120	18	such	such	ADJ
ejde-629	120	19	that	that	DET
ejde-629	120	20	sup	sup	NOUN
ejde-629	120	21	0≤t≤t	0≤t≤t	NUM
ejde-629	120	22	∥ωj(t)∥x	∥ωj(t)∥x	PROPN
ejde-629	120	23	≤	≤	PROPN
ejde-629	120	24	mj	mj	PROPN
ejde-629	120	25	,	,	PUNCT
ejde-629	120	26	j	j	PROPN
ejde-629	120	27	=	=	SYM
ejde-629	120	28	0	0	NUM
ejde-629	120	29	,	,	PUNCT
ejde-629	120	30	1	1	NUM
ejde-629	120	31	,	,	PUNCT
ejde-629	120	32	2	2	NUM
ejde-629	120	33	,	,	PUNCT
ejde-629	120	34	.	.	PUNCT
ejde-629	120	35	.	.	PUNCT
ejde-629	120	36	.	.	PUNCT
ejde-629	121	1	where	where	SCONJ
ejde-629	121	2	0	0	NUM
ejde-629	121	3	<	<	X
ejde-629	121	4	t	t	X
ejde-629	121	5	≤	≤	NUM
ejde-629	121	6	∞	∞	PROPN
ejde-629	121	7	and	and	CCONJ
ejde-629	121	8	the	the	DET
ejde-629	121	9	sequence	sequence	NOUN
ejde-629	121	10	{	{	PUNCT
ejde-629	121	11	mj}j≥0	mj}j≥0	NOUN
ejde-629	121	12	satisfies	satisfie	NOUN
ejde-629	121	13	∑∞	∑∞	X
ejde-629	121	14	j=0	j=0	PROPN
ejde-629	121	15	mj	mj	PROPN
ejde-629	121	16	<	<	X
ejde-629	121	17	∞	∞	PROPN
ejde-629	121	18	,	,	PUNCT
ejde-629	121	19	then	then	ADV
ejde-629	121	20	the	the	DET
ejde-629	121	21	sequence	sequence	NOUN
ejde-629	121	22	{	{	PUNCT
ejde-629	121	23	ωj}j≥0	ωj}j≥0	PRON
ejde-629	121	24	converges	converge	VERB
ejde-629	121	25	uniformly	uniformly	ADV
ejde-629	121	26	on	on	ADP
ejde-629	121	27	[	[	X
ejde-629	121	28	0	0	NUM
ejde-629	121	29	,	,	PUNCT
ejde-629	121	30	t	t	X
ejde-629	121	31	]	]	PUNCT
ejde-629	121	32	,	,	PUNCT
ejde-629	121	33	that	that	ADV
ejde-629	121	34	is	is	ADV
ejde-629	121	35	,	,	PUNCT
ejde-629	121	36	∞∑	∞∑	PROPN
ejde-629	121	37	j=0	j=0	PROPN
ejde-629	121	38	ωj	ωj	ADP
ejde-629	121	39	∈	∈	PROPN
ejde-629	121	40	c([0	c([0	NOUN
ejde-629	121	41	,	,	PUNCT
ejde-629	121	42	t	t	X
ejde-629	121	43	]	]	PUNCT
ejde-629	121	44	;	;	PUNCT
ejde-629	121	45	x	x	X
ejde-629	121	46	)	)	PUNCT
ejde-629	121	47	.	.	PUNCT
ejde-629	122	1	using	use	VERB
ejde-629	122	2	proposition	proposition	NOUN
ejde-629	122	3	2.1	2.1	NUM
ejde-629	122	4	,	,	PUNCT
ejde-629	122	5	we	we	PRON
ejde-629	122	6	can	can	AUX
ejde-629	122	7	obtain	obtain	VERB
ejde-629	122	8	similar	similar	ADJ
ejde-629	122	9	lp	lp	ADJ
ejde-629	122	10	−lq	−lq	PROPN
ejde-629	122	11	estimates	estimate	NOUN
ejde-629	122	12	for	for	ADP
ejde-629	122	13	both	both	DET
ejde-629	122	14	families	family	NOUN
ejde-629	122	15	of	of	ADP
ejde-629	122	16	mittag	mittag	ADJ
ejde-629	122	17	-	-	PUNCT
ejde-629	122	18	leffler	leffler	NOUN
ejde-629	122	19	operators	operator	NOUN
ejde-629	122	20	,	,	PUNCT
ejde-629	122	21	which	which	PRON
ejde-629	122	22	also	also	ADV
ejde-629	122	23	depend	depend	VERB
ejde-629	122	24	on	on	ADP
ejde-629	122	25	the	the	DET
ejde-629	122	26	exponent	exponent	NOUN
ejde-629	122	27	of	of	ADP
ejde-629	122	28	differentiation	differentiation	NOUN
ejde-629	122	29	α	α	NOUN
ejde-629	122	30	.	.	PUNCT
ejde-629	123	1	proposition	proposition	NOUN
ejde-629	123	2	2.5	2.5	NUM
ejde-629	123	3	.	.	PUNCT
ejde-629	124	1	let	let	VERB
ejde-629	124	2	1	1	NUM
ejde-629	124	3	<	<	X
ejde-629	124	4	q	q	X
ejde-629	124	5	≤	≤	NUM
ejde-629	124	6	p	p	NOUN
ejde-629	124	7	<	<	X
ejde-629	124	8	∞	∞	NUM
ejde-629	124	9	and	and	CCONJ
ejde-629	124	10	1	1	NUM
ejde-629	124	11	q	q	NOUN
ejde-629	124	12	−	−	PROPN
ejde-629	124	13	1	1	NUM
ejde-629	124	14	p	p	NOUN
ejde-629	124	15	<	<	X
ejde-629	124	16	4−j	4−j	PROPN
ejde-629	124	17	n	n	NOUN
ejde-629	124	18	with	with	ADP
ejde-629	124	19	any	any	DET
ejde-629	124	20	nonnegative	nonnegative	ADJ
ejde-629	124	21	integer	integer	NOUN
ejde-629	124	22	j	j	PROPN
ejde-629	124	23	<	<	X
ejde-629	124	24	4	4	X
ejde-629	124	25	.	.	X
ejde-629	125	1	for	for	ADP
ejde-629	125	2	u	u	PROPN
ejde-629	125	3	∈	∈	PROPN
ejde-629	125	4	lq(ω	lq(ω	NOUN
ejde-629	125	5	)	)	PUNCT
ejde-629	125	6	,	,	PUNCT
ejde-629	125	7	we	we	PRON
ejde-629	125	8	have	have	VERB
ejde-629	125	9	∥∇jeα(−tαa)u∥lp(ω	∥∇jeα(−tαa)u∥lp(ω	PROPN
ejde-629	125	10	)	)	PUNCT
ejde-629	125	11	≤	≤	PUNCT
ejde-629	126	1	ct−	ct−	PROPN
ejde-629	126	2	nα	nα	PRON
ejde-629	126	3	4	4	NUM
ejde-629	126	4	(	(	PUNCT
ejde-629	126	5	1	1	NUM
ejde-629	126	6	q−	q−	PROPN
ejde-629	126	7	1	1	NUM
ejde-629	126	8	p	p	NOUN
ejde-629	126	9	)	)	PUNCT
ejde-629	126	10	−	−	PROPN
ejde-629	126	11	jα	jα	PROPN
ejde-629	126	12	4	4	NUM
ejde-629	126	13	∥u∥lq(ω	∥u∥lq(ω	NOUN
ejde-629	126	14	)	)	PUNCT
ejde-629	126	15	,	,	PUNCT
ejde-629	126	16	t	t	X
ejde-629	126	17	>	>	X
ejde-629	126	18	0	0	PROPN
ejde-629	126	19	.	.	PUNCT
ejde-629	127	1	(	(	PUNCT
ejde-629	127	2	2.1	2.1	NUM
ejde-629	127	3	)	)	PUNCT
ejde-629	127	4	proof	proof	NOUN
ejde-629	127	5	.	.	PUNCT
ejde-629	128	1	noting	note	VERB
ejde-629	128	2	that	that	SCONJ
ejde-629	128	3	if	if	SCONJ
ejde-629	128	4	0	0	NUM
ejde-629	128	5	≤	≤	NUM
ejde-629	128	6	1	1	NUM
ejde-629	128	7	q	q	NOUN
ejde-629	128	8	−	−	PROPN
ejde-629	128	9	1	1	NUM
ejde-629	128	10	p	p	NOUN
ejde-629	128	11	<	<	X
ejde-629	128	12	4−j	4−j	PROPN
ejde-629	128	13	n	n	NOUN
ejde-629	128	14	with	with	ADP
ejde-629	128	15	j	j	PROPN
ejde-629	128	16	<	<	X
ejde-629	128	17	4	4	NUM
ejde-629	128	18	,	,	PUNCT
ejde-629	128	19	we	we	PRON
ejde-629	128	20	have	have	VERB
ejde-629	128	21	−n	−n	ADV
ejde-629	128	22	4	4	NUM
ejde-629	128	23	(	(	PUNCT
ejde-629	128	24	1	1	NUM
ejde-629	128	25	q	q	NOUN
ejde-629	128	26	−	−	PROPN
ejde-629	128	27	1	1	NUM
ejde-629	128	28	p	p	NOUN
ejde-629	128	29	)	)	PUNCT
ejde-629	128	30	−	−	PROPN
ejde-629	129	1	j	j	PROPN
ejde-629	129	2	4	4	NUM
ejde-629	129	3	>	>	SYM
ejde-629	129	4	−1	−1	NOUN
ejde-629	129	5	.	.	PUNCT
ejde-629	130	1	by	by	ADP
ejde-629	130	2	proposition	proposition	NOUN
ejde-629	130	3	2.1	2.1	NUM
ejde-629	130	4	and	and	CCONJ
ejde-629	130	5	2.2	2.2	NUM
ejde-629	130	6	,	,	PUNCT
ejde-629	130	7	we	we	PRON
ejde-629	130	8	obtain	obtain	VERB
ejde-629	130	9	∥∇jeα(−tαa)u∥lp(ω	∥∇jeα(−tαa)u∥lp(ω	PROPN
ejde-629	130	10	)	)	PUNCT
ejde-629	130	11	≤	≤	NUM
ejde-629	131	1	∫	∫	PROPN
ejde-629	131	2	∞	∞	NUM
ejde-629	131	3	0	0	NUM
ejde-629	131	4	mα(s)∥∇jt	mα(s)∥∇jt	X
ejde-629	132	1	(	(	PUNCT
ejde-629	132	2	stα)u∥lp(ω	stα)u∥lp(ω	NOUN
ejde-629	132	3	)	)	PUNCT
ejde-629	132	4	ds	ds	ADJ
ejde-629	132	5	≤	≤	NUM
ejde-629	132	6	c	c	PROPN
ejde-629	132	7	(	(	PUNCT
ejde-629	132	8	∫	∫	PROPN
ejde-629	132	9	∞	∞	NUM
ejde-629	132	10	0	0	PUNCT
ejde-629	132	11	mα(s)s	mα(s)s	PROPN
ejde-629	132	12	−n	−n	SYM
ejde-629	132	13	4	4	NUM
ejde-629	132	14	(	(	PUNCT
ejde-629	132	15	1	1	NUM
ejde-629	132	16	q−	q−	PROPN
ejde-629	132	17	1	1	NUM
ejde-629	132	18	p	p	NOUN
ejde-629	132	19	)	)	PUNCT
ejde-629	132	20	−	−	PROPN
ejde-629	133	1	j	j	NOUN
ejde-629	133	2	4	4	NUM
ejde-629	133	3	ds	ds	NOUN
ejde-629	133	4	)	)	PUNCT
ejde-629	133	5	(	(	PUNCT
ejde-629	133	6	t−	t−	PROPN
ejde-629	133	7	nα	nα	VERB
ejde-629	133	8	4	4	NUM
ejde-629	133	9	(	(	PUNCT
ejde-629	133	10	1	1	NUM
ejde-629	133	11	q−	q−	PROPN
ejde-629	133	12	1	1	NUM
ejde-629	133	13	p	p	NOUN
ejde-629	133	14	)	)	PUNCT
ejde-629	133	15	−	−	PROPN
ejde-629	133	16	jα	jα	PROPN
ejde-629	133	17	4	4	NUM
ejde-629	133	18	∥u∥lq(ω	∥u∥lq(ω	NOUN
ejde-629	133	19	)	)	PUNCT
ejde-629	133	20	)	)	PUNCT
ejde-629	134	1	≤	≤	NOUN
ejde-629	134	2	ct−	ct−	PUNCT
ejde-629	134	3	nα	nα	PRON
ejde-629	134	4	4	4	NUM
ejde-629	134	5	(	(	PUNCT
ejde-629	134	6	1	1	NUM
ejde-629	134	7	q−	q−	PROPN
ejde-629	134	8	1	1	NUM
ejde-629	134	9	p	p	NOUN
ejde-629	134	10	)	)	PUNCT
ejde-629	134	11	−	−	PROPN
ejde-629	134	12	jα	jα	PROPN
ejde-629	134	13	4	4	NUM
ejde-629	134	14	∥u∥lq(ω	∥u∥lq(ω	NOUN
ejde-629	134	15	)	)	PUNCT
ejde-629	134	16	.	.	PUNCT
ejde-629	135	1	the	the	DET
ejde-629	135	2	proof	proof	NOUN
ejde-629	135	3	is	be	AUX
ejde-629	135	4	complete	complete	ADJ
ejde-629	135	5	.	.	PUNCT
ejde-629	136	1	□	□	PUNCT
ejde-629	136	2	proposition	proposition	NOUN
ejde-629	136	3	2.6	2.6	NUM
ejde-629	136	4	.	.	PUNCT
ejde-629	137	1	let	let	VERB
ejde-629	137	2	1	1	NUM
ejde-629	137	3	<	<	X
ejde-629	137	4	q	q	X
ejde-629	137	5	≤	≤	NUM
ejde-629	138	1	p	p	NOUN
ejde-629	138	2	<	<	X
ejde-629	138	3	∞	∞	NUM
ejde-629	138	4	and	and	CCONJ
ejde-629	138	5	1	1	NUM
ejde-629	138	6	q	q	NOUN
ejde-629	138	7	−	−	PROPN
ejde-629	138	8	1	1	NUM
ejde-629	138	9	p	p	X
ejde-629	138	10	<	<	X
ejde-629	138	11	8−j	8−j	NUM
ejde-629	138	12	n	n	NOUN
ejde-629	138	13	with	with	ADP
ejde-629	138	14	a	a	DET
ejde-629	138	15	nonnegative	nonnegative	ADJ
ejde-629	138	16	integer	integer	NOUN
ejde-629	138	17	j	j	PROPN
ejde-629	138	18	<	<	X
ejde-629	138	19	4	4	X
ejde-629	138	20	.	.	PUNCT
ejde-629	139	1	then	then	ADV
ejde-629	139	2	we	we	PRON
ejde-629	139	3	have	have	VERB
ejde-629	139	4	∥∇jeα	∥∇jeα	NOUN
ejde-629	139	5	,	,	PUNCT
ejde-629	139	6	α(−tαa)u∥lp(ω	α(−tαa)u∥lp(ω	ADJ
ejde-629	139	7	)	)	PUNCT
ejde-629	139	8	≤	≤	NOUN
ejde-629	139	9	ct−	ct−	PROPN
ejde-629	139	10	nα	nα	PRON
ejde-629	139	11	4	4	NUM
ejde-629	139	12	(	(	PUNCT
ejde-629	139	13	1	1	NUM
ejde-629	139	14	q−	q−	PROPN
ejde-629	139	15	1	1	NUM
ejde-629	139	16	p	p	NOUN
ejde-629	139	17	)	)	PUNCT
ejde-629	139	18	−	−	PROPN
ejde-629	139	19	jα	jα	PROPN
ejde-629	139	20	4	4	NUM
ejde-629	139	21	∥u∥lq(ω	∥u∥lq(ω	NOUN
ejde-629	139	22	)	)	PUNCT
ejde-629	139	23	,	,	PUNCT
ejde-629	139	24	t	t	X
ejde-629	139	25	>	>	X
ejde-629	139	26	0	0	X
ejde-629	139	27	.	.	PUNCT
ejde-629	140	1	the	the	DET
ejde-629	140	2	proof	proof	NOUN
ejde-629	140	3	of	of	ADP
ejde-629	140	4	the	the	DET
ejde-629	140	5	above	above	ADJ
ejde-629	140	6	propostion	propostion	NOUN
ejde-629	140	7	is	be	AUX
ejde-629	140	8	similar	similar	ADJ
ejde-629	140	9	to	to	ADP
ejde-629	140	10	that	that	PRON
ejde-629	140	11	of	of	ADP
ejde-629	140	12	proposition	proposition	NOUN
ejde-629	140	13	2.5	2.5	NUM
ejde-629	140	14	,	,	PUNCT
ejde-629	140	15	so	so	SCONJ
ejde-629	140	16	we	we	PRON
ejde-629	140	17	omit	omit	VERB
ejde-629	140	18	it	it	PRON
ejde-629	140	19	.	.	PUNCT
ejde-629	141	1	6	6	NUM
ejde-629	141	2	q.	q.	PROPN
ejde-629	141	3	liu	liu	PROPN
ejde-629	141	4	,	,	PUNCT
ejde-629	141	5	w.	w.	PROPN
ejde-629	141	6	zhu	zhu	PROPN
ejde-629	141	7	,	,	PUNCT
ejde-629	141	8	h.	h.	PROPN
ejde-629	141	9	ye	ye	PROPN
ejde-629	141	10	ejde-2024/58	ejde-2024/58	ADJ
ejde-629	141	11	3	3	NUM
ejde-629	141	12	.	.	PUNCT
ejde-629	141	13	proof	proof	NOUN
ejde-629	141	14	of	of	ADP
ejde-629	141	15	theorem	theorem	ADJ
ejde-629	141	16	1.2	1.2	NUM
ejde-629	141	17	in	in	ADP
ejde-629	141	18	this	this	DET
ejde-629	141	19	section	section	NOUN
ejde-629	141	20	,	,	PUNCT
ejde-629	141	21	based	base	VERB
ejde-629	141	22	on	on	ADP
ejde-629	141	23	the	the	DET
ejde-629	141	24	lp−lq	lp−lq	ADJ
ejde-629	141	25	estimates	estimate	NOUN
ejde-629	141	26	in	in	ADP
ejde-629	141	27	section	section	NOUN
ejde-629	141	28	2	2	NUM
ejde-629	141	29	,	,	PUNCT
ejde-629	141	30	we	we	PRON
ejde-629	141	31	will	will	AUX
ejde-629	141	32	prove	prove	VERB
ejde-629	141	33	theorem	theorem	ADJ
ejde-629	141	34	1.2	1.2	NUM
ejde-629	141	35	by	by	ADP
ejde-629	141	36	using	use	VERB
ejde-629	141	37	the	the	DET
ejde-629	141	38	method	method	NOUN
ejde-629	141	39	of	of	ADP
ejde-629	141	40	successive	successive	ADJ
ejde-629	141	41	approximation	approximation	NOUN
ejde-629	141	42	.	.	PUNCT
ejde-629	142	1	to	to	PART
ejde-629	142	2	simplify	simplify	VERB
ejde-629	142	3	the	the	DET
ejde-629	142	4	notation	notation	NOUN
ejde-629	142	5	,	,	PUNCT
ejde-629	142	6	we	we	PRON
ejde-629	142	7	denote	denote	VERB
ejde-629	142	8	the	the	DET
ejde-629	142	9	norm	norm	NOUN
ejde-629	142	10	∥	∥	X
ejde-629	142	11	·	·	PUNCT
ejde-629	142	12	∥lp(ω	∥lp(ω	NOUN
ejde-629	142	13	)	)	PUNCT
ejde-629	142	14	by	by	ADP
ejde-629	142	15	∥	∥	X
ejde-629	142	16	·	·	PUNCT
ejde-629	142	17	∥p	∥p	ADJ
ejde-629	142	18	.	.	PUNCT
ejde-629	142	19	recalling	recall	VERB
ejde-629	142	20	the	the	DET
ejde-629	142	21	integral	integral	ADJ
ejde-629	142	22	equation	equation	NOUN
ejde-629	142	23	(	(	PUNCT
ejde-629	142	24	1.5	1.5	NUM
ejde-629	142	25	)	)	PUNCT
ejde-629	142	26	,	,	PUNCT
ejde-629	142	27	we	we	PRON
ejde-629	142	28	define	define	VERB
ejde-629	142	29	a	a	DET
ejde-629	142	30	sequence	sequence	NOUN
ejde-629	142	31	{	{	PUNCT
ejde-629	142	32	uj}j≥0	uj}j≥0	NOUN
ejde-629	142	33	as	as	SCONJ
ejde-629	142	34	follows	follow	VERB
ejde-629	142	35	,	,	PUNCT
ejde-629	142	36	u0(x	u0(x	SYM
ejde-629	142	37	,	,	PUNCT
ejde-629	142	38	t	t	PROPN
ejde-629	142	39	)	)	PUNCT
ejde-629	142	40	=	=	SYM
ejde-629	143	1	eα(−tαa)φ	eα(−tαa)φ	PROPN
ejde-629	143	2	,	,	PUNCT
ejde-629	143	3	uj(x	uj(x	NUM
ejde-629	143	4	,	,	PUNCT
ejde-629	143	5	t	t	PROPN
ejde-629	143	6	)	)	PUNCT
ejde-629	143	7	=	=	PUNCT
ejde-629	143	8	eα(−tαa)φ+	eα(−tαa)φ+	PROPN
ejde-629	143	9	∫	∫	PROPN
ejde-629	143	10	t	t	PROPN
ejde-629	143	11	0	0	NUM
ejde-629	143	12	(	(	PUNCT
ejde-629	143	13	t−	t−	PROPN
ejde-629	143	14	s)α−1eα	s)α−1eα	PROPN
ejde-629	143	15	,	,	PUNCT
ejde-629	143	16	α(−(t−	α(−(t−	NOUN
ejde-629	143	17	s)αa)∇	s)αa)∇	NOUN
ejde-629	143	18	·	·	PUNCT
ejde-629	144	1	f(∇uj−1	f(∇uj−1	NOUN
ejde-629	144	2	)	)	PUNCT
ejde-629	144	3	ds	ds	NOUN
ejde-629	144	4	(	(	PUNCT
ejde-629	144	5	3.1	3.1	NUM
ejde-629	144	6	)	)	PUNCT
ejde-629	144	7	for	for	ADP
ejde-629	144	8	positive	positive	ADJ
ejde-629	144	9	integers	integer	NOUN
ejde-629	144	10	j	j	PROPN
ejde-629	144	11	and	and	CCONJ
ejde-629	144	12	t	t	PROPN
ejde-629	144	13	>	>	X
ejde-629	144	14	0	0	X
ejde-629	144	15	.	.	PUNCT
ejde-629	145	1	in	in	ADP
ejde-629	145	2	additional	additional	ADJ
ejde-629	145	3	,	,	PUNCT
ejde-629	145	4	we	we	PRON
ejde-629	145	5	define	define	VERB
ejde-629	145	6	r(t)j	r(t)j	NOUN
ejde-629	145	7	=	=	SYM
ejde-629	145	8	max	max	X
ejde-629	145	9	{	{	PUNCT
ejde-629	145	10	sup	sup	NOUN
ejde-629	145	11	0	0	NUM
ejde-629	145	12	<	<	NOUN
ejde-629	145	13	s≤t	s≤t	PROPN
ejde-629	145	14	s	s	NOUN
ejde-629	145	15	α	α	PRON
ejde-629	145	16	2	2	NUM
ejde-629	145	17	∥∇2uj(s)∥	∥∇2uj(s)∥	PROPN
ejde-629	145	18	βn	βn	NOUN
ejde-629	145	19	2−β	2−β	NUM
ejde-629	145	20	,	,	PUNCT
ejde-629	145	21	sup	sup	NOUN
ejde-629	145	22	0	0	NUM
ejde-629	145	23	<	<	NOUN
ejde-629	145	24	s≤t	s≤t	PROPN
ejde-629	145	25	s	s	PART
ejde-629	145	26	α	α	PROPN
ejde-629	145	27	2β−	2β−	PROPN
ejde-629	145	28	αγ	αγ	SYM
ejde-629	145	29	4β2	4β2	NUM
ejde-629	145	30	∥∇uj(s)∥	∥∇uj(s)∥	ADP
ejde-629	145	31	β2n	β2n	PROPN
ejde-629	145	32	γ	γ	X
ejde-629	145	33	}	}	PUNCT
ejde-629	145	34	(	(	PUNCT
ejde-629	145	35	3.2	3.2	NUM
ejde-629	145	36	)	)	PUNCT
ejde-629	145	37	for	for	ADP
ejde-629	145	38	t	t	PROPN
ejde-629	145	39	>	>	X
ejde-629	145	40	0	0	PROPN
ejde-629	145	41	and	and	CCONJ
ejde-629	145	42	j	j	PROPN
ejde-629	145	43	≥	≥	NUM
ejde-629	145	44	0	0	NUM
ejde-629	145	45	,	,	PUNCT
ejde-629	145	46	where	where	SCONJ
ejde-629	145	47	0	0	PUNCT
ejde-629	145	48	<	<	X
ejde-629	145	49	γ	γ	X
ejde-629	145	50	<	<	X
ejde-629	145	51	min{2β	min{2β	PROPN
ejde-629	145	52	,	,	PUNCT
ejde-629	145	53	β(n	β(n	PUNCT
ejde-629	146	1	+	+	PROPN
ejde-629	146	2	1)−	1)−	NUM
ejde-629	146	3	2	2	NUM
ejde-629	146	4	}	}	PUNCT
ejde-629	146	5	.	.	PUNCT
ejde-629	147	1	next	next	ADV
ejde-629	147	2	,	,	PUNCT
ejde-629	147	3	we	we	PRON
ejde-629	147	4	show	show	VERB
ejde-629	147	5	uj(t	uj(t	PUNCT
ejde-629	147	6	)	)	PUNCT
ejde-629	147	7	belongs	belong	VERB
ejde-629	147	8	l	l	PROPN
ejde-629	147	9	βn	βn	X
ejde-629	147	10	2−β	2−β	NUM
ejde-629	147	11	(	(	PUNCT
ejde-629	147	12	ω	ω	NOUN
ejde-629	147	13	)	)	PUNCT
ejde-629	147	14	and	and	CCONJ
ejde-629	147	15	is	be	AUX
ejde-629	147	16	continuous	continuous	ADJ
ejde-629	147	17	under	under	ADP
ejde-629	147	18	some	some	DET
ejde-629	147	19	smallness	smallness	NOUN
ejde-629	147	20	conditions	condition	NOUN
ejde-629	147	21	.	.	PUNCT
ejde-629	148	1	the	the	DET
ejde-629	148	2	proofs	proof	NOUN
ejde-629	148	3	require	require	VERB
ejde-629	148	4	the	the	DET
ejde-629	148	5	following	follow	VERB
ejde-629	148	6	iteration	iteration	NOUN
ejde-629	148	7	lemma	lemma	PROPN
ejde-629	148	8	.	.	PUNCT
ejde-629	149	1	lemma	lemma	PROPN
ejde-629	149	2	3.1	3.1	NUM
ejde-629	149	3	(	(	PUNCT
ejde-629	149	4	[	[	X
ejde-629	149	5	13	13	NUM
ejde-629	149	6	]	]	NUM
ejde-629	149	7	)	)	PUNCT
ejde-629	149	8	.	.	PUNCT
ejde-629	150	1	let	let	VERB
ejde-629	150	2	λ	λ	PROPN
ejde-629	150	3	,	,	PUNCT
ejde-629	150	4	β	β	X
ejde-629	150	5	>	>	X
ejde-629	150	6	0	0	PUNCT
ejde-629	150	7	and	and	CCONJ
ejde-629	150	8	bj	bj	VERB
ejde-629	150	9	be	be	AUX
ejde-629	150	10	a	a	DET
ejde-629	150	11	nonnegative	nonnegative	ADJ
ejde-629	150	12	sequence	sequence	NOUN
ejde-629	150	13	such	such	ADJ
ejde-629	150	14	that	that	PRON
ejde-629	150	15	bj	bj	VERB
ejde-629	150	16	≤	≤	NOUN
ejde-629	150	17	b0	b0	NOUN
ejde-629	150	18	+	+	CCONJ
ejde-629	150	19	λb1+β	λb1+β	PROPN
ejde-629	150	20	j−1	j−1	PROPN
ejde-629	150	21	for	for	ADP
ejde-629	150	22	all	all	DET
ejde-629	150	23	positive	positive	ADJ
ejde-629	150	24	integer	integer	NOUN
ejde-629	150	25	j.	j.	NOUN
ejde-629	151	1	if	if	SCONJ
ejde-629	151	2	2λ(2b0	2λ(2b0	NOUN
ejde-629	151	3	)	)	PUNCT
ejde-629	152	1	β	β	X
ejde-629	152	2	<	<	X
ejde-629	152	3	1	1	NUM
ejde-629	152	4	,	,	PUNCT
ejde-629	152	5	then	then	ADV
ejde-629	152	6	for	for	ADP
ejde-629	152	7	each	each	DET
ejde-629	152	8	nonnegative	nonnegative	ADJ
ejde-629	152	9	integer	integer	PROPN
ejde-629	152	10	j	j	PROPN
ejde-629	152	11	,	,	PUNCT
ejde-629	152	12	we	we	PRON
ejde-629	152	13	have	have	AUX
ejde-629	152	14	bj	bj	VERB
ejde-629	152	15	≤	≤	NUM
ejde-629	152	16	b0	b0	ADP
ejde-629	152	17	1−	1−	NUM
ejde-629	152	18	λ(2b0)β	λ(2b0)β	PROPN
ejde-629	152	19	.	.	PUNCT
ejde-629	153	1	lemma	lemma	PROPN
ejde-629	153	2	3.2	3.2	NUM
ejde-629	153	3	.	.	PUNCT
ejde-629	154	1	for	for	ADP
ejde-629	154	2	any	any	DET
ejde-629	154	3	t	t	PROPN
ejde-629	154	4	>	>	X
ejde-629	154	5	0	0	NUM
ejde-629	154	6	,	,	PUNCT
ejde-629	154	7	there	there	PRON
ejde-629	154	8	exists	exist	VERB
ejde-629	154	9	a	a	DET
ejde-629	154	10	constant	constant	ADJ
ejde-629	154	11	ε0	ε0	NOUN
ejde-629	154	12	>	>	X
ejde-629	154	13	0	0	PUNCT
ejde-629	154	14	independent	independent	ADJ
ejde-629	154	15	of	of	ADP
ejde-629	154	16	t	t	PROPN
ejde-629	154	17	such	such	ADJ
ejde-629	154	18	that	that	SCONJ
ejde-629	154	19	if	if	SCONJ
ejde-629	154	20	r(t	r(t	NOUN
ejde-629	154	21	)	)	PUNCT
ejde-629	154	22	0	0	NUM
ejde-629	155	1	≤	≤	NUM
ejde-629	155	2	ε0	ε0	PROPN
ejde-629	155	3	,	,	PUNCT
ejde-629	155	4	each	each	PRON
ejde-629	155	5	uj(t	uj(t	NUM
ejde-629	155	6	)	)	PUNCT
ejde-629	155	7	is	be	AUX
ejde-629	155	8	well	well	ADV
ejde-629	155	9	defined	define	VERB
ejde-629	155	10	as	as	ADP
ejde-629	155	11	an	an	DET
ejde-629	155	12	element	element	NOUN
ejde-629	155	13	of	of	ADP
ejde-629	155	14	l	l	PROPN
ejde-629	155	15	βn	βn	X
ejde-629	155	16	2−β	2−β	NUM
ejde-629	155	17	(	(	PUNCT
ejde-629	155	18	ω	ω	NOUN
ejde-629	155	19	)	)	PUNCT
ejde-629	155	20	for	for	ADP
ejde-629	155	21	any	any	DET
ejde-629	155	22	t	t	PROPN
ejde-629	155	23	>	>	X
ejde-629	155	24	0	0	NUM
ejde-629	155	25	,	,	PUNCT
ejde-629	155	26	and	and	CCONJ
ejde-629	155	27	r(t	r(t	NOUN
ejde-629	155	28	)	)	PUNCT
ejde-629	155	29	j	j	PROPN
ejde-629	155	30	≤	≤	PROPN
ejde-629	155	31	2r(t	2r(t	NUM
ejde-629	155	32	)	)	PUNCT
ejde-629	155	33	0	0	NUM
ejde-629	155	34	,	,	PUNCT
ejde-629	155	35	j	j	PROPN
ejde-629	155	36	≥	≥	PROPN
ejde-629	155	37	0	0	NUM
ejde-629	155	38	.	.	PUNCT
ejde-629	156	1	(	(	PUNCT
ejde-629	156	2	3.3	3.3	NUM
ejde-629	156	3	)	)	PUNCT
ejde-629	156	4	proof	proof	NOUN
ejde-629	156	5	.	.	PUNCT
ejde-629	157	1	because	because	SCONJ
ejde-629	157	2	f	f	PROPN
ejde-629	157	3	′(ξ	′(ξ	PROPN
ejde-629	157	4	)	)	PUNCT
ejde-629	157	5	behaves	behave	VERB
ejde-629	157	6	like	like	ADP
ejde-629	157	7	|ξ|β	|ξ|β	NOUN
ejde-629	157	8	,	,	PUNCT
ejde-629	157	9	we	we	PRON
ejde-629	157	10	have	have	VERB
ejde-629	157	11	∥f	∥f	PROPN
ejde-629	157	12	′(∇u)∥s	′(∇u)∥s	PROPN
ejde-629	157	13	≤	≤	NOUN
ejde-629	157	14	c∥∇u∥βs	c∥∇u∥βs	PROPN
ejde-629	157	15	.	.	PUNCT
ejde-629	158	1	by	by	ADP
ejde-629	158	2	hölder	hölder	PROPN
ejde-629	158	3	’s	’s	PART
ejde-629	158	4	inequality	inequality	NOUN
ejde-629	158	5	,	,	PUNCT
ejde-629	158	6	it	it	PRON
ejde-629	158	7	is	be	AUX
ejde-629	158	8	easy	easy	ADJ
ejde-629	158	9	to	to	PART
ejde-629	158	10	verify	verify	VERB
ejde-629	158	11	that	that	SCONJ
ejde-629	158	12	∥∇	∥∇	ADJ
ejde-629	158	13	·	·	PUNCT
ejde-629	158	14	f(∇uj(s))∥	f(∇uj(s))∥	NOUN
ejde-629	158	15	βn	βn	VERB
ejde-629	158	16	2−β+γ	2−β+γ	NUM
ejde-629	158	17	=	=	SYM
ejde-629	158	18	∥∇2uj(s	∥∇2uj(s	NOUN
ejde-629	158	19	)	)	PUNCT
ejde-629	158	20	·	·	PUNCT
ejde-629	159	1	f	f	X
ejde-629	159	2	′(∇uj(s))∥	′(∇uj(s))∥	X
ejde-629	159	3	βn	βn	VERB
ejde-629	159	4	2−β+γ	2−β+γ	NUM
ejde-629	159	5	≤	≤	ADV
ejde-629	159	6	∥∇2uj(s)∥	∥∇2uj(s)∥	PROPN
ejde-629	159	7	βn	βn	NOUN
ejde-629	159	8	2−β	2−β	NUM
ejde-629	159	9	∥f	∥f	PROPN
ejde-629	159	10	′(∇uj(s))∥	′(∇uj(s))∥	PROPN
ejde-629	159	11	βn	βn	NOUN
ejde-629	159	12	γ	γ	X
ejde-629	159	13	=	=	PROPN
ejde-629	159	14	s−α+αγ	s−α+αγ	PROPN
ejde-629	159	15	4β	4β	NUM
ejde-629	159	16	(	(	PUNCT
ejde-629	159	17	s	s	AUX
ejde-629	159	18	α	α	PRON
ejde-629	159	19	2	2	NUM
ejde-629	159	20	∥∇2uj(s)∥	∥∇2uj(s)∥	PROPN
ejde-629	159	21	βn	βn	NOUN
ejde-629	159	22	2−β	2−β	NUM
ejde-629	159	23	)	)	PUNCT
ejde-629	159	24	(	(	PUNCT
ejde-629	159	25	s	s	NOUN
ejde-629	159	26	α	α	PRON
ejde-629	159	27	2	2	NUM
ejde-629	159	28	−αγ	−αγ	NOUN
ejde-629	159	29	4β	4β	NOUN
ejde-629	159	30	∥∇uj(s)∥ββ2n	∥∇uj(s)∥ββ2n	PROPN
ejde-629	159	31	γ	γ	X
ejde-629	159	32	)	)	PUNCT
ejde-629	159	33	≤	≤	PUNCT
ejde-629	160	1	s−α+αγ	s−α+αγ	PROPN
ejde-629	160	2	4β	4β	NUM
ejde-629	160	3	(	(	PUNCT
ejde-629	160	4	sup	sup	NOUN
ejde-629	160	5	0	0	NUM
ejde-629	160	6	<	<	NOUN
ejde-629	160	7	s≤t	s≤t	PROPN
ejde-629	160	8	s	s	NOUN
ejde-629	160	9	α	α	PRON
ejde-629	160	10	2	2	NUM
ejde-629	160	11	∥∇2uj(s)∥	∥∇2uj(s)∥	PROPN
ejde-629	160	12	βn	βn	NOUN
ejde-629	160	13	2−β	2−β	NUM
ejde-629	160	14	)	)	PUNCT
ejde-629	160	15	(	(	PUNCT
ejde-629	160	16	sup	sup	NOUN
ejde-629	160	17	0	0	NUM
ejde-629	160	18	<	<	NOUN
ejde-629	160	19	s≤t	s≤t	PROPN
ejde-629	160	20	s	s	PART
ejde-629	160	21	α	α	PROPN
ejde-629	160	22	2β−	2β−	PROPN
ejde-629	160	23	αγ	αγ	SYM
ejde-629	160	24	4β2	4β2	NUM
ejde-629	160	25	∥∇uj(s)∥	∥∇uj(s)∥	ADP
ejde-629	160	26	β2n	β2n	PROPN
ejde-629	160	27	γ	γ	NOUN
ejde-629	160	28	)	)	PUNCT
ejde-629	160	29	β	β	NOUN
ejde-629	160	30	≤	≤	NUM
ejde-629	161	1	s−α+αγ	s−α+αγ	PROPN
ejde-629	161	2	4β	4β	NOUN
ejde-629	161	3	r(t)1+β	r(t)1+β	PRON
ejde-629	161	4	j	j	PROPN
ejde-629	161	5	.	.	PUNCT
ejde-629	162	1	(	(	PUNCT
ejde-629	162	2	3.4	3.4	NUM
ejde-629	162	3	)	)	PUNCT
ejde-629	162	4	applying	apply	VERB
ejde-629	162	5	the	the	DET
ejde-629	162	6	differential	differential	ADJ
ejde-629	162	7	operator	operator	NOUN
ejde-629	162	8	∇	∇	X
ejde-629	162	9	to	to	ADP
ejde-629	162	10	(	(	PUNCT
ejde-629	162	11	3.1	3.1	NUM
ejde-629	162	12	)	)	PUNCT
ejde-629	162	13	,	,	PUNCT
ejde-629	162	14	and	and	CCONJ
ejde-629	162	15	applying	apply	VERB
ejde-629	162	16	propositions	proposition	NOUN
ejde-629	162	17	2.5	2.5	NUM
ejde-629	162	18	and	and	CCONJ
ejde-629	162	19	2.6	2.6	NUM
ejde-629	162	20	,	,	PUNCT
ejde-629	162	21	and	and	CCONJ
ejde-629	162	22	(	(	PUNCT
ejde-629	162	23	3.4	3.4	NUM
ejde-629	162	24	)	)	PUNCT
ejde-629	162	25	,	,	PUNCT
ejde-629	162	26	we	we	PRON
ejde-629	162	27	obtain	obtain	VERB
ejde-629	162	28	that	that	SCONJ
ejde-629	162	29	∥∇uj+1∥	∥∇uj+1∥	PROPN
ejde-629	162	30	β2n	β2n	PUNCT
ejde-629	162	31	γ	γ	X
ejde-629	162	32	ejde-2024/58	ejde-2024/58	ADJ
ejde-629	162	33	equations	equation	NOUN
ejde-629	162	34	modeling	model	VERB
ejde-629	162	35	thin	thin	ADJ
ejde-629	162	36	film	film	NOUN
ejde-629	162	37	growth	growth	NOUN
ejde-629	162	38	7	7	NUM
ejde-629	162	39	≤	≤	NOUN
ejde-629	162	40	∥∇eα(−tαa)φ∥	∥∇eα(−tαa)φ∥	PROPN
ejde-629	162	41	β2n	β2n	PUNCT
ejde-629	162	42	γ	γ	X
ejde-629	162	43	+	+	PROPN
ejde-629	162	44	∫	∫	PROPN
ejde-629	162	45	t	t	PROPN
ejde-629	162	46	0	0	NUM
ejde-629	162	47	(	(	PUNCT
ejde-629	162	48	t−	t−	PROPN
ejde-629	162	49	s)α−1∥∇eα	s)α−1∥∇eα	PROPN
ejde-629	162	50	,	,	PUNCT
ejde-629	162	51	α(−(t−	α(−(t−	NOUN
ejde-629	162	52	s)αa)∇	s)αa)∇	NOUN
ejde-629	162	53	·	·	PUNCT
ejde-629	163	1	f(∇uj)∥	f(∇uj)∥	PROPN
ejde-629	163	2	β2n	β2n	PUNCT
ejde-629	163	3	γ	γ	X
ejde-629	163	4	ds	ds	PROPN
ejde-629	163	5	≤	≤	NUM
ejde-629	163	6	∥∇u0∥	∥∇u0∥	PROPN
ejde-629	163	7	β2n	β2n	ADJ
ejde-629	163	8	γ	γ	PROPN
ejde-629	164	1	+	+	X
ejde-629	164	2	c	c	PROPN
ejde-629	164	3	∫	∫	PROPN
ejde-629	164	4	t	t	PROPN
ejde-629	164	5	0	0	NUM
ejde-629	164	6	(	(	PUNCT
ejde-629	164	7	t−	t−	PROPN
ejde-629	164	8	s	s	PART
ejde-629	164	9	)	)	PUNCT
ejde-629	164	10	α−1	α−1	PROPN
ejde-629	164	11	+	+	SYM
ejde-629	164	12	αγ	αγ	PROPN
ejde-629	164	13	4β2	4β2	NUM
ejde-629	164	14	−	−	NUM
ejde-629	164	15	α	α	NOUN
ejde-629	164	16	2β−αγ	2β−αγ	NOUN
ejde-629	164	17	4β	4β	NOUN
ejde-629	164	18	∥∇	∥∇	ADJ
ejde-629	164	19	·	·	PUNCT
ejde-629	164	20	f(∇uj)∥	f(∇uj)∥	PROPN
ejde-629	164	21	βn	βn	NOUN
ejde-629	164	22	2−β+γ	2−β+γ	NUM
ejde-629	164	23	ds	ds	X
ejde-629	164	24	(	(	PUNCT
ejde-629	164	25	3.5	3.5	NUM
ejde-629	164	26	)	)	PUNCT
ejde-629	164	27	≤	≤	NOUN
ejde-629	164	28	∥∇u0∥	∥∇u0∥	PROPN
ejde-629	164	29	β2n	β2n	PUNCT
ejde-629	164	30	γ	γ	PROPN
ejde-629	164	31	+	+	PROPN
ejde-629	164	32	cr(t)1+β	cr(t)1+β	PROPN
ejde-629	164	33	j	j	PROPN
ejde-629	164	34	∫	∫	PROPN
ejde-629	164	35	t	t	PROPN
ejde-629	164	36	0	0	NUM
ejde-629	164	37	(	(	PUNCT
ejde-629	164	38	t−	t−	PROPN
ejde-629	164	39	s	s	PART
ejde-629	164	40	)	)	PUNCT
ejde-629	164	41	α−1	α−1	PROPN
ejde-629	164	42	+	+	SYM
ejde-629	164	43	αγ	αγ	PROPN
ejde-629	164	44	4β2	4β2	NUM
ejde-629	164	45	−	−	NUM
ejde-629	164	46	α	α	NOUN
ejde-629	164	47	2β−αγ	2β−αγ	NOUN
ejde-629	164	48	4β	4β	NOUN
ejde-629	165	1	s−α+αγ	s−α+αγ	PROPN
ejde-629	165	2	4β	4β	NOUN
ejde-629	165	3	ds	ds	VERB
ejde-629	165	4	≤	≤	PUNCT
ejde-629	165	5	∥∇u0∥	∥∇u0∥	PROPN
ejde-629	165	6	β2n	β2n	ADJ
ejde-629	165	7	γ	γ	X
ejde-629	165	8	+	+	PROPN
ejde-629	165	9	ct	ct	PROPN
ejde-629	165	10	αγ	αγ	NUM
ejde-629	165	11	4β2	4β2	NUM
ejde-629	165	12	−	−	NOUN
ejde-629	166	1	α	α	PROPN
ejde-629	166	2	2β	2β	NOUN
ejde-629	166	3	r(t)1+β	r(t)1+β	PRON
ejde-629	166	4	j	j	NOUN
ejde-629	166	5	,	,	PUNCT
ejde-629	166	6	and	and	CCONJ
ejde-629	166	7	similarly	similarly	ADV
ejde-629	166	8	∥∇2uj+1∥	∥∇2uj+1∥	PROPN
ejde-629	166	9	βn	βn	VERB
ejde-629	166	10	2−β	2−β	NUM
ejde-629	166	11	≤	≤	NOUN
ejde-629	166	12	∥∇2eα(−tαa)φ∥	∥∇2eα(−tαa)φ∥	ADP
ejde-629	166	13	βn	βn	NOUN
ejde-629	166	14	2−β	2−β	NUM
ejde-629	166	15	+	+	CCONJ
ejde-629	166	16	∫	∫	PROPN
ejde-629	166	17	t	t	PROPN
ejde-629	166	18	0	0	NUM
ejde-629	166	19	(	(	PUNCT
ejde-629	166	20	t−	t−	PROPN
ejde-629	166	21	s)α−1∥∇2eα	s)α−1∥∇2eα	NOUN
ejde-629	166	22	,	,	PUNCT
ejde-629	166	23	α(−(t−	α(−(t−	PROPN
ejde-629	166	24	s)αa)∇	s)αa)∇	NOUN
ejde-629	166	25	·	·	PUNCT
ejde-629	167	1	f(∇uj)∥	f(∇uj)∥	PROPN
ejde-629	167	2	βn	βn	VERB
ejde-629	167	3	2−β	2−β	NUM
ejde-629	167	4	ds	ds	ADJ
ejde-629	167	5	≤	≤	NUM
ejde-629	167	6	∥∇2u0∥	∥∇2u0∥	PROPN
ejde-629	167	7	βn	βn	VERB
ejde-629	167	8	2−β	2−β	NUM
ejde-629	168	1	+	+	CCONJ
ejde-629	168	2	c	c	NOUN
ejde-629	168	3	∫	∫	PROPN
ejde-629	168	4	t	t	PROPN
ejde-629	168	5	0	0	NUM
ejde-629	168	6	(	(	PUNCT
ejde-629	168	7	t−	t−	PROPN
ejde-629	168	8	s	s	X
ejde-629	168	9	)	)	PUNCT
ejde-629	168	10	α	α	DET
ejde-629	168	11	2	2	NUM
ejde-629	168	12	−1−αγ	−1−αγ	NOUN
ejde-629	168	13	4β	4β	NOUN
ejde-629	168	14	∥∇	∥∇	ADJ
ejde-629	168	15	·	·	PUNCT
ejde-629	169	1	f(∇uj)∥	f(∇uj)∥	PROPN
ejde-629	169	2	βn	βn	AUX
ejde-629	169	3	2−β+γ	2−β+γ	NUM
ejde-629	169	4	ds	ds	ADJ
ejde-629	169	5	≤	≤	NUM
ejde-629	169	6	∥∇2u0∥	∥∇2u0∥	PROPN
ejde-629	169	7	βn	βn	VERB
ejde-629	169	8	2−β	2−β	PROPN
ejde-629	169	9	+	+	CCONJ
ejde-629	169	10	cr(t)1+β	cr(t)1+β	PROPN
ejde-629	169	11	j	j	PROPN
ejde-629	169	12	∫	∫	PROPN
ejde-629	169	13	t	t	PROPN
ejde-629	169	14	0	0	NUM
ejde-629	169	15	(	(	PUNCT
ejde-629	169	16	t−	t−	PROPN
ejde-629	169	17	s	s	X
ejde-629	169	18	)	)	PUNCT
ejde-629	169	19	α	α	DET
ejde-629	169	20	2	2	NUM
ejde-629	169	21	−1−αγ	−1−αγ	NOUN
ejde-629	169	22	4β	4β	NOUN
ejde-629	170	1	s−α+αγ	s−α+αγ	PROPN
ejde-629	170	2	4β	4β	NOUN
ejde-629	170	3	ds	ds	VERB
ejde-629	170	4	(	(	PUNCT
ejde-629	170	5	3.6	3.6	NUM
ejde-629	170	6	)	)	PUNCT
ejde-629	170	7	≤	≤	NOUN
ejde-629	170	8	∥∇2u0∥	∥∇2u0∥	PROPN
ejde-629	170	9	βn	βn	VERB
ejde-629	170	10	2−β	2−β	NUM
ejde-629	171	1	+	+	CCONJ
ejde-629	171	2	ct−	ct−	NUM
ejde-629	171	3	α	α	SYM
ejde-629	171	4	2	2	NUM
ejde-629	171	5	r(t)1+β	r(t)1+β	NUM
ejde-629	171	6	j	j	PROPN
ejde-629	171	7	.	.	PUNCT
ejde-629	172	1	combining	combine	VERB
ejde-629	172	2	(	(	PUNCT
ejde-629	172	3	3.5	3.5	NUM
ejde-629	172	4	)	)	PUNCT
ejde-629	172	5	and	and	CCONJ
ejde-629	172	6	(	(	PUNCT
ejde-629	172	7	3.6	3.6	NUM
ejde-629	172	8	)	)	PUNCT
ejde-629	172	9	,	,	PUNCT
ejde-629	172	10	for	for	ADP
ejde-629	172	11	any	any	DET
ejde-629	172	12	fixed	fix	VERB
ejde-629	172	13	t	t	PROPN
ejde-629	172	14	>	>	X
ejde-629	172	15	0	0	PROPN
ejde-629	172	16	,	,	PUNCT
ejde-629	172	17	we	we	PRON
ejde-629	172	18	have	have	VERB
ejde-629	172	19	r(t	r(t	NOUN
ejde-629	172	20	)	)	PUNCT
ejde-629	173	1	j+1	j+1	PROPN
ejde-629	173	2	≤	≤	NUM
ejde-629	173	3	r(t	r(t	NOUN
ejde-629	173	4	)	)	PUNCT
ejde-629	173	5	0	0	PUNCT
ejde-629	174	1	+	+	CCONJ
ejde-629	174	2	cr(t	cr(t	NUM
ejde-629	174	3	)	)	PUNCT
ejde-629	175	1	1+β	1+β	NUM
ejde-629	175	2	j	j	NOUN
ejde-629	175	3	,	,	PUNCT
ejde-629	175	4	where	where	SCONJ
ejde-629	175	5	c	c	AUX
ejde-629	175	6	>	>	X
ejde-629	175	7	0	0	NUM
ejde-629	175	8	is	be	AUX
ejde-629	175	9	independent	independent	ADJ
ejde-629	175	10	of	of	ADP
ejde-629	175	11	t	t	PROPN
ejde-629	175	12	.	.	PUNCT
ejde-629	176	1	according	accord	VERB
ejde-629	176	2	to	to	ADP
ejde-629	176	3	lemma	lemma	PROPN
ejde-629	176	4	3.1	3.1	NUM
ejde-629	176	5	,	,	PUNCT
ejde-629	176	6	there	there	PRON
ejde-629	176	7	exists	exist	VERB
ejde-629	176	8	a	a	DET
ejde-629	176	9	constant	constant	ADJ
ejde-629	176	10	ε0	ε0	NOUN
ejde-629	176	11	>	>	X
ejde-629	176	12	0	0	NUM
ejde-629	177	1	such	such	ADJ
ejde-629	177	2	that	that	SCONJ
ejde-629	177	3	r(t	r(t	NOUN
ejde-629	177	4	)	)	PUNCT
ejde-629	177	5	0	0	NUM
ejde-629	177	6	≤	≤	NUM
ejde-629	177	7	ε0	ε0	PROPN
ejde-629	177	8	,	,	PUNCT
ejde-629	177	9	and	and	CCONJ
ejde-629	177	10	2c(2r(t	2c(2r(t	NOUN
ejde-629	177	11	)	)	PUNCT
ejde-629	177	12	0	0	NUM
ejde-629	177	13	)	)	PUNCT
ejde-629	177	14	β	β	X
ejde-629	177	15	<	<	X
ejde-629	177	16	1	1	NUM
ejde-629	177	17	,	,	PUNCT
ejde-629	177	18	which	which	PRON
ejde-629	177	19	yields	yield	VERB
ejde-629	177	20	r(t	r(t	NOUN
ejde-629	177	21	)	)	PUNCT
ejde-629	178	1	j	j	PROPN
ejde-629	178	2	≤	≤	PROPN
ejde-629	178	3	2r(t	2r(t	NUM
ejde-629	178	4	)	)	PUNCT
ejde-629	178	5	0	0	NUM
ejde-629	178	6	,	,	PUNCT
ejde-629	178	7	j	j	PROPN
ejde-629	178	8	≥	≥	NOUN
ejde-629	178	9	0	0	NUM
ejde-629	178	10	.	.	PUNCT
ejde-629	179	1	at	at	ADP
ejde-629	179	2	last	last	ADV
ejde-629	179	3	,	,	PUNCT
ejde-629	179	4	we	we	PRON
ejde-629	179	5	obtain	obtain	VERB
ejde-629	179	6	∥uj+1∥	∥uj+1∥	NUM
ejde-629	179	7	βn	βn	NOUN
ejde-629	179	8	2−β	2−β	NOUN
ejde-629	179	9	≤	≤	NOUN
ejde-629	179	10	∥eα(−tαa)φ∥	∥eα(−tαa)φ∥	VERB
ejde-629	179	11	βn	βn	NOUN
ejde-629	179	12	2−β	2−β	NUM
ejde-629	180	1	+	+	CCONJ
ejde-629	180	2	∫	∫	PROPN
ejde-629	180	3	t	t	PROPN
ejde-629	180	4	0	0	NUM
ejde-629	180	5	(	(	PUNCT
ejde-629	180	6	t−	t−	PROPN
ejde-629	180	7	s)α−1∥eα	s)α−1∥eα	PROPN
ejde-629	180	8	,	,	PUNCT
ejde-629	180	9	α(−(t−	α(−(t−	NOUN
ejde-629	180	10	s)αa)∇	s)αa)∇	NOUN
ejde-629	180	11	·	·	PUNCT
ejde-629	181	1	f(∇uj)∥	f(∇uj)∥	PROPN
ejde-629	181	2	βn	βn	VERB
ejde-629	181	3	2−β	2−β	NUM
ejde-629	181	4	ds	ds	ADJ
ejde-629	181	5	≤	≤	NUM
ejde-629	181	6	r(t	r(t	NOUN
ejde-629	181	7	)	)	PUNCT
ejde-629	181	8	0	0	PUNCT
ejde-629	182	1	+	+	CCONJ
ejde-629	182	2	c	c	X
ejde-629	182	3	∫	∫	PROPN
ejde-629	182	4	t	t	PROPN
ejde-629	182	5	0	0	NUM
ejde-629	182	6	(	(	PUNCT
ejde-629	182	7	t−	t−	PROPN
ejde-629	182	8	s)α−1−αγ	s)α−1−αγ	NOUN
ejde-629	182	9	4β	4β	NOUN
ejde-629	182	10	∥∇	∥∇	ADJ
ejde-629	182	11	·	·	PUNCT
ejde-629	182	12	f(∇uj)∥	f(∇uj)∥	PROPN
ejde-629	182	13	βn	βn	AUX
ejde-629	182	14	2−β+γ	2−β+γ	NUM
ejde-629	182	15	ds	ds	ADJ
ejde-629	182	16	≤	≤	NUM
ejde-629	182	17	r(t	r(t	NOUN
ejde-629	182	18	)	)	PUNCT
ejde-629	182	19	0	0	PUNCT
ejde-629	183	1	+	+	CCONJ
ejde-629	183	2	cr(t	cr(t	NUM
ejde-629	183	3	)	)	PUNCT
ejde-629	184	1	1+β	1+β	NUM
ejde-629	185	1	j	j	NOUN
ejde-629	185	2	∫	∫	PROPN
ejde-629	185	3	t	t	PROPN
ejde-629	185	4	0	0	NUM
ejde-629	186	1	(	(	PUNCT
ejde-629	186	2	t−	t−	PROPN
ejde-629	186	3	s)α−1−αγ	s)α−1−αγ	NOUN
ejde-629	186	4	4β	4β	NOUN
ejde-629	186	5	s−α+αγ	s−α+αγ	PROPN
ejde-629	186	6	4β	4β	NOUN
ejde-629	186	7	ds	ds	VERB
ejde-629	186	8	≤	≤	NUM
ejde-629	186	9	r(t	r(t	NOUN
ejde-629	186	10	)	)	PUNCT
ejde-629	186	11	0	0	PUNCT
ejde-629	187	1	+	+	CCONJ
ejde-629	187	2	cr(t	cr(t	NUM
ejde-629	187	3	)	)	PUNCT
ejde-629	188	1	1+β	1+β	NUM
ejde-629	188	2	j	j	PROPN
ejde-629	188	3	≤	≤	NOUN
ejde-629	188	4	cr(t	cr(t	NUM
ejde-629	188	5	)	)	PUNCT
ejde-629	188	6	0	0	NUM
ejde-629	188	7	,	,	PUNCT
ejde-629	188	8	which	which	PRON
ejde-629	188	9	means	mean	VERB
ejde-629	188	10	uj(t	uj(t	SYM
ejde-629	188	11	)	)	PUNCT
ejde-629	188	12	∈	∈	PROPN
ejde-629	188	13	lp(ω	lp(ω	PROPN
ejde-629	188	14	)	)	PUNCT
ejde-629	188	15	for	for	ADP
ejde-629	188	16	any	any	DET
ejde-629	188	17	0	0	NUM
ejde-629	188	18	<	<	X
ejde-629	188	19	t	t	X
ejde-629	188	20	≤	≤	X
ejde-629	188	21	t	t	PROPN
ejde-629	188	22	and	and	CCONJ
ejde-629	188	23	j	j	PROPN
ejde-629	188	24	≥	≥	PROPN
ejde-629	188	25	0	0	NUM
ejde-629	188	26	.	.	PUNCT
ejde-629	189	1	□	□	PUNCT
ejde-629	189	2	next	next	ADV
ejde-629	189	3	,	,	PUNCT
ejde-629	189	4	we	we	PRON
ejde-629	189	5	shall	shall	AUX
ejde-629	189	6	show	show	VERB
ejde-629	189	7	the	the	DET
ejde-629	189	8	strong	strong	ADJ
ejde-629	189	9	continuity	continuity	NOUN
ejde-629	189	10	of	of	ADP
ejde-629	189	11	uj(t	uj(t	PROPN
ejde-629	189	12	)	)	PUNCT
ejde-629	189	13	for	for	ADP
ejde-629	189	14	t	t	PROPN
ejde-629	189	15	∈	∈	PROPN
ejde-629	190	1	[	[	X
ejde-629	190	2	0	0	NUM
ejde-629	190	3	,	,	PUNCT
ejde-629	190	4	t	t	X
ejde-629	190	5	]	]	PUNCT
ejde-629	190	6	.	.	PUNCT
ejde-629	191	1	lemma	lemma	PROPN
ejde-629	191	2	3.3	3.3	NUM
ejde-629	191	3	.	.	PUNCT
ejde-629	192	1	under	under	ADP
ejde-629	192	2	the	the	DET
ejde-629	192	3	assumption	assumption	NOUN
ejde-629	192	4	r(t	r(t	NOUN
ejde-629	192	5	)	)	PUNCT
ejde-629	192	6	0	0	X
ejde-629	192	7	≤	≤	PROPN
ejde-629	192	8	ε0	ε0	PROPN
ejde-629	192	9	in	in	ADP
ejde-629	192	10	lemma	lemma	PROPN
ejde-629	192	11	3.2	3.2	NUM
ejde-629	192	12	,	,	PUNCT
ejde-629	192	13	for	for	ADP
ejde-629	192	14	any	any	DET
ejde-629	192	15	j	j	PROPN
ejde-629	192	16	≥	≥	NUM
ejde-629	192	17	0	0	NUM
ejde-629	192	18	,	,	PUNCT
ejde-629	192	19	we	we	PRON
ejde-629	192	20	have	have	VERB
ejde-629	192	21	uj	uj	VERB
ejde-629	192	22	∈	∈	PROPN
ejde-629	192	23	c([0	c([0	NOUN
ejde-629	192	24	,	,	PUNCT
ejde-629	192	25	t	t	X
ejde-629	192	26	]	]	PUNCT
ejde-629	192	27	;	;	PUNCT
ejde-629	192	28	l	l	X
ejde-629	192	29	βn	βn	X
ejde-629	192	30	2−β	2−β	NUM
ejde-629	192	31	(	(	PUNCT
ejde-629	192	32	ω	ω	NOUN
ejde-629	192	33	)	)	PUNCT
ejde-629	192	34	)	)	PUNCT
ejde-629	192	35	,	,	PUNCT
ejde-629	192	36	t	t	X
ejde-629	192	37	>	>	X
ejde-629	192	38	0	0	PROPN
ejde-629	192	39	,	,	PUNCT
ejde-629	192	40	j	j	PROPN
ejde-629	192	41	=	=	SYM
ejde-629	192	42	0	0	NUM
ejde-629	192	43	,	,	PUNCT
ejde-629	192	44	1	1	NUM
ejde-629	192	45	,	,	PUNCT
ejde-629	192	46	2	2	NUM
ejde-629	192	47	,	,	PUNCT
ejde-629	192	48	·	·	PUNCT
ejde-629	192	49	·	·	PUNCT
ejde-629	192	50	·	·	PUNCT
ejde-629	192	51	.	.	PUNCT
ejde-629	193	1	8	8	NUM
ejde-629	193	2	q.	q.	PROPN
ejde-629	193	3	liu	liu	PROPN
ejde-629	193	4	,	,	PUNCT
ejde-629	193	5	w.	w.	PROPN
ejde-629	193	6	zhu	zhu	PROPN
ejde-629	193	7	,	,	PUNCT
ejde-629	193	8	h.	h.	PROPN
ejde-629	193	9	ye	ye	PROPN
ejde-629	193	10	ejde-2024/58	ejde-2024/58	ADJ
ejde-629	193	11	proof	proof	NOUN
ejde-629	193	12	.	.	PUNCT
ejde-629	194	1	fixing	fix	VERB
ejde-629	194	2	t0	t0	PROPN
ejde-629	194	3	∈	∈	PROPN
ejde-629	194	4	(	(	PUNCT
ejde-629	194	5	0	0	NUM
ejde-629	194	6	,	,	PUNCT
ejde-629	194	7	t	t	PROPN
ejde-629	194	8	)	)	PUNCT
ejde-629	194	9	,	,	PUNCT
ejde-629	194	10	we	we	PRON
ejde-629	194	11	have	have	VERB
ejde-629	194	12	the	the	DET
ejde-629	194	13	estimate	estimate	NOUN
ejde-629	194	14	∥uj+1(t)−	∥uj+1(t)−	PROPN
ejde-629	194	15	uj+1(t0)∥	uj+1(t0)∥	VERB
ejde-629	194	16	βn	βn	PROPN
ejde-629	194	17	2−β	2−β	NOUN
ejde-629	194	18	≤	≤	NOUN
ejde-629	194	19	∥(eα(−tαa)−	∥(eα(−tαa)−	ADV
ejde-629	194	20	eα(−tα0a))φ∥	eα(−tα0a))φ∥	ADV
ejde-629	194	21	βn	βn	VERB
ejde-629	194	22	2−β	2−β	NUM
ejde-629	195	1	+	+	CCONJ
ejde-629	195	2	∫	∫	PROPN
ejde-629	195	3	t	t	PROPN
ejde-629	195	4	t0	t0	PROPN
ejde-629	195	5	(	(	PUNCT
ejde-629	195	6	t−	t−	PROPN
ejde-629	195	7	s)α−1	s)α−1	PROPN
ejde-629	195	8	∥eα	∥eα	NOUN
ejde-629	195	9	,	,	PUNCT
ejde-629	195	10	α(−(t−	α(−(t−	NOUN
ejde-629	195	11	s)αa)∇	s)αa)∇	NOUN
ejde-629	195	12	·	·	PUNCT
ejde-629	196	1	f(∇uj)∥	f(∇uj)∥	PROPN
ejde-629	196	2	βn	βn	PROPN
ejde-629	196	3	2−β	2−β	NUM
ejde-629	196	4	ds	ds	NOUN
ejde-629	196	5	+	+	CCONJ
ejde-629	196	6	∫	∫	PROPN
ejde-629	196	7	t0	t0	PROPN
ejde-629	196	8	0	0	PUNCT
ejde-629	196	9	∥∥(t−	∥∥(t−	PROPN
ejde-629	196	10	s)α−1eα	s)α−1eα	PROPN
ejde-629	196	11	,	,	PUNCT
ejde-629	196	12	α(−(t−	α(−(t−	NOUN
ejde-629	196	13	s)αa)∇	s)αa)∇	NOUN
ejde-629	196	14	·	·	PUNCT
ejde-629	196	15	f(∇uj	f(∇uj	NUM
ejde-629	196	16	)	)	PUNCT
ejde-629	196	17	−	−	PROPN
ejde-629	197	1	(	(	PUNCT
ejde-629	197	2	t0	t0	PROPN
ejde-629	197	3	−	−	PROPN
ejde-629	197	4	s)α−1eα	s)α−1eα	PROPN
ejde-629	197	5	,	,	PUNCT
ejde-629	197	6	α(−(t0	α(−(t0	NOUN
ejde-629	197	7	−	−	PROPN
ejde-629	197	8	s)αa)∇	s)αa)∇	NOUN
ejde-629	197	9	·	·	PUNCT
ejde-629	197	10	f(∇uj	f(∇uj	NUM
ejde-629	197	11	)	)	PUNCT
ejde-629	197	12	∥∥	∥∥	AUX
ejde-629	197	13	βn	βn	VERB
ejde-629	197	14	2−β	2−β	NUM
ejde-629	197	15	ds	ds	PROPN
ejde-629	197	16	=	=	PROPN
ejde-629	197	17	i1	i1	PROPN
ejde-629	197	18	+	+	CCONJ
ejde-629	197	19	i2	i2	PROPN
ejde-629	197	20	+	+	CCONJ
ejde-629	197	21	i3	i3	NOUN
ejde-629	197	22	,	,	PUNCT
ejde-629	197	23	(	(	PUNCT
ejde-629	197	24	3.7	3.7	NUM
ejde-629	197	25	)	)	PUNCT
ejde-629	197	26	where	where	SCONJ
ejde-629	197	27	t0	t0	PROPN
ejde-629	197	28	<	<	X
ejde-629	197	29	t	t	PROPN
ejde-629	197	30	≤	≤	PROPN
ejde-629	197	31	t	t	PROPN
ejde-629	197	32	.	.	PUNCT
ejde-629	198	1	using	use	VERB
ejde-629	198	2	the	the	DET
ejde-629	198	3	strong	strong	ADJ
ejde-629	198	4	continuity	continuity	NOUN
ejde-629	198	5	of	of	ADP
ejde-629	198	6	eα(−tαa	eα(−tαa	NOUN
ejde-629	198	7	)	)	PUNCT
ejde-629	198	8	on	on	ADP
ejde-629	198	9	lp(ω	lp(ω	PROPN
ejde-629	198	10	)	)	PUNCT
ejde-629	198	11	for	for	ADP
ejde-629	198	12	t	t	PROPN
ejde-629	198	13	∈	∈	PROPN
ejde-629	198	14	[	[	X
ejde-629	198	15	0,∞	0,∞	NOUN
ejde-629	198	16	)	)	PUNCT
ejde-629	198	17	,	,	PUNCT
ejde-629	198	18	we	we	PRON
ejde-629	198	19	deduce	deduce	VERB
ejde-629	198	20	easily	easily	ADV
ejde-629	198	21	that	that	SCONJ
ejde-629	198	22	the	the	DET
ejde-629	198	23	first	first	ADJ
ejde-629	198	24	term	term	NOUN
ejde-629	198	25	i1	i1	PROPN
ejde-629	198	26	goes	go	VERB
ejde-629	198	27	to	to	ADP
ejde-629	198	28	zero	zero	NUM
ejde-629	198	29	as	as	ADP
ejde-629	198	30	t	t	PROPN
ejde-629	198	31	→	→	SYM
ejde-629	198	32	t+0	t+0	NUM
ejde-629	198	33	.	.	PUNCT
ejde-629	199	1	by	by	ADP
ejde-629	199	2	proposition	proposition	NOUN
ejde-629	199	3	2.6	2.6	NUM
ejde-629	199	4	,	,	PUNCT
ejde-629	199	5	the	the	DET
ejde-629	199	6	estimate	estimate	NOUN
ejde-629	199	7	of	of	ADP
ejde-629	199	8	the	the	DET
ejde-629	199	9	second	second	ADJ
ejde-629	199	10	term	term	NOUN
ejde-629	199	11	yields	yield	NOUN
ejde-629	199	12	i2	i2	PROPN
ejde-629	199	13	=	=	SYM
ejde-629	199	14	∫	∫	PROPN
ejde-629	199	15	t	t	PROPN
ejde-629	199	16	t0	t0	PROPN
ejde-629	199	17	(	(	PUNCT
ejde-629	199	18	t−	t−	PROPN
ejde-629	199	19	s)α−1	s)α−1	PROPN
ejde-629	199	20	∥eα	∥eα	NOUN
ejde-629	199	21	,	,	PUNCT
ejde-629	199	22	α(−(t−	α(−(t−	NOUN
ejde-629	199	23	s)αa)∇	s)αa)∇	NOUN
ejde-629	199	24	·	·	PUNCT
ejde-629	200	1	f(∇uj)∥	f(∇uj)∥	PROPN
ejde-629	200	2	βn	βn	VERB
ejde-629	200	3	2−β	2−β	NUM
ejde-629	200	4	ds	ds	NOUN
ejde-629	200	5	≤	≤	NUM
ejde-629	200	6	c	c	PROPN
ejde-629	200	7	∫	∫	PROPN
ejde-629	200	8	t	t	PROPN
ejde-629	200	9	t0	t0	PROPN
ejde-629	200	10	(	(	PUNCT
ejde-629	200	11	t−	t−	PROPN
ejde-629	200	12	s)α−1−αγ	s)α−1−αγ	NOUN
ejde-629	200	13	4β	4β	NOUN
ejde-629	200	14	∥∇	∥∇	ADJ
ejde-629	200	15	·	·	PUNCT
ejde-629	200	16	f(∇uj)∥	f(∇uj)∥	PROPN
ejde-629	200	17	βn	βn	AUX
ejde-629	200	18	2−β+γ	2−β+γ	NUM
ejde-629	200	19	ds	ds	ADJ
ejde-629	200	20	≤	≤	NUM
ejde-629	200	21	cr(t	cr(t	NOUN
ejde-629	200	22	)	)	PUNCT
ejde-629	201	1	1+β	1+β	NUM
ejde-629	201	2	0	0	NUM
ejde-629	202	1	∫	∫	PROPN
ejde-629	202	2	t	t	PROPN
ejde-629	202	3	t0	t0	PROPN
ejde-629	202	4	(	(	PUNCT
ejde-629	202	5	t−	t−	PROPN
ejde-629	202	6	s)α−1−αγ	s)α−1−αγ	NOUN
ejde-629	202	7	4β	4β	NOUN
ejde-629	202	8	s−α+αγ	s−α+αγ	PROPN
ejde-629	202	9	4β	4β	NOUN
ejde-629	202	10	ds	ds	VERB
ejde-629	202	11	≤	≤	NUM
ejde-629	202	12	cr(t	cr(t	NOUN
ejde-629	202	13	)	)	PUNCT
ejde-629	202	14	1+β	1+β	NUM
ejde-629	202	15	0	0	NUM
ejde-629	202	16	(	(	PUNCT
ejde-629	202	17	t−	t−	PROPN
ejde-629	202	18	t0	t0	PROPN
ejde-629	202	19	t0	t0	PROPN
ejde-629	202	20	)	)	PUNCT
ejde-629	203	1	1−α+αγ	1−α+αγ	NUM
ejde-629	203	2	4β	4β	NOUN
ejde-629	203	3	.	.	PUNCT
ejde-629	204	1	obviously	obviously	ADV
ejde-629	204	2	,	,	PUNCT
ejde-629	204	3	this	this	DET
ejde-629	204	4	term	term	NOUN
ejde-629	204	5	vanishes	vanish	VERB
ejde-629	204	6	as	as	ADP
ejde-629	204	7	t	t	PROPN
ejde-629	204	8	→	→	SYM
ejde-629	204	9	t+0	t+0	NUM
ejde-629	204	10	.	.	PUNCT
ejde-629	205	1	for	for	ADP
ejde-629	205	2	the	the	DET
ejde-629	205	3	estimate	estimate	NOUN
ejde-629	205	4	of	of	ADP
ejde-629	205	5	the	the	DET
ejde-629	205	6	third	third	ADJ
ejde-629	205	7	term	term	NOUN
ejde-629	205	8	,	,	PUNCT
ejde-629	205	9	we	we	PRON
ejde-629	205	10	first	first	ADV
ejde-629	205	11	denote	denote	VERB
ejde-629	205	12	g(t	g(t	PROPN
ejde-629	205	13	,	,	PUNCT
ejde-629	205	14	s	s	PART
ejde-629	205	15	)	)	PUNCT
ejde-629	205	16	=	=	SYM
ejde-629	205	17	∥∥(t−	∥∥(t−	NOUN
ejde-629	205	18	s)α−1eα	s)α−1eα	PROPN
ejde-629	205	19	,	,	PUNCT
ejde-629	205	20	α(−(t−	α(−(t−	NOUN
ejde-629	205	21	s)αa)∇	s)αa)∇	NOUN
ejde-629	205	22	·	·	PUNCT
ejde-629	205	23	f(∇uj	f(∇uj	NUM
ejde-629	205	24	)	)	PUNCT
ejde-629	206	1	−	−	PROPN
ejde-629	206	2	(	(	PUNCT
ejde-629	206	3	t0	t0	PROPN
ejde-629	206	4	−	−	PROPN
ejde-629	206	5	s)α−1eα	s)α−1eα	PROPN
ejde-629	206	6	,	,	PUNCT
ejde-629	206	7	α(−(t0	α(−(t0	NOUN
ejde-629	206	8	−	−	PROPN
ejde-629	206	9	s)αa)∇	s)αa)∇	NOUN
ejde-629	206	10	·	·	PUNCT
ejde-629	206	11	f(∇uj	f(∇uj	NUM
ejde-629	206	12	)	)	PUNCT
ejde-629	206	13	∥∥	∥∥	X
ejde-629	206	14	βn	βn	VERB
ejde-629	206	15	2−β	2−β	NUM
ejde-629	206	16	,	,	PUNCT
ejde-629	206	17	where	where	SCONJ
ejde-629	206	18	0	0	PUNCT
ejde-629	206	19	<	<	X
ejde-629	206	20	s	s	X
ejde-629	206	21	<	<	X
ejde-629	206	22	t0	t0	X
ejde-629	206	23	<	<	X
ejde-629	206	24	t.	t.	X
ejde-629	206	25	combining	combine	VERB
ejde-629	206	26	this	this	PRON
ejde-629	206	27	with	with	ADP
ejde-629	206	28	(	(	PUNCT
ejde-629	206	29	3.4	3.4	NUM
ejde-629	206	30	)	)	PUNCT
ejde-629	206	31	,	,	PUNCT
ejde-629	206	32	it	it	PRON
ejde-629	206	33	is	be	AUX
ejde-629	206	34	easy	easy	ADJ
ejde-629	206	35	to	to	PART
ejde-629	206	36	see	see	VERB
ejde-629	206	37	that	that	SCONJ
ejde-629	206	38	g(t	g(t	PROPN
ejde-629	206	39	,	,	PUNCT
ejde-629	206	40	s	s	PART
ejde-629	206	41	)	)	PUNCT
ejde-629	206	42	≤	≤	NOUN
ejde-629	206	43	|(t−	|(t−	NOUN
ejde-629	206	44	s)α−1	s)α−1	NOUN
ejde-629	206	45	−	−	PROPN
ejde-629	206	46	(	(	PUNCT
ejde-629	206	47	t0	t0	PROPN
ejde-629	206	48	−	−	PROPN
ejde-629	206	49	s)α−1|	s)α−1|	NOUN
ejde-629	206	50	·	·	PUNCT
ejde-629	206	51	∥∥eα	∥∥eα	NUM
ejde-629	206	52	,	,	PUNCT
ejde-629	206	53	α(−(t−	α(−(t−	NUM
ejde-629	206	54	s)αa)∇	s)αa)∇	NOUN
ejde-629	206	55	·	·	PUNCT
ejde-629	206	56	f(∇uj(s	f(∇uj(s	NOUN
ejde-629	206	57	)	)	PUNCT
ejde-629	206	58	)	)	PUNCT
ejde-629	207	1	∥∥	∥∥	PROPN
ejde-629	207	2	βn	βn	VERB
ejde-629	207	3	2−β	2−β	NUM
ejde-629	207	4	+	+	CCONJ
ejde-629	207	5	(	(	PUNCT
ejde-629	207	6	t0	t0	PROPN
ejde-629	207	7	−	−	NOUN
ejde-629	207	8	s)α−1	s)α−1	NOUN
ejde-629	207	9	∥∥eα	∥∥eα	ADJ
ejde-629	207	10	,	,	PUNCT
ejde-629	207	11	α(−(t−	α(−(t−	NUM
ejde-629	207	12	s)αa)∇	s)αa)∇	NOUN
ejde-629	207	13	·	·	PUNCT
ejde-629	207	14	f(∇uj(s	f(∇uj(s	NOUN
ejde-629	207	15	)	)	PUNCT
ejde-629	207	16	)	)	PUNCT
ejde-629	208	1	−	−	ADP
ejde-629	208	2	eα	eα	NOUN
ejde-629	208	3	,	,	PUNCT
ejde-629	208	4	α(−(t0	α(−(t0	NOUN
ejde-629	208	5	−	−	PROPN
ejde-629	208	6	s)αa)∇	s)αa)∇	NOUN
ejde-629	208	7	·	·	PUNCT
ejde-629	208	8	f(∇uj(s	f(∇uj(s	NOUN
ejde-629	208	9	)	)	PUNCT
ejde-629	208	10	)	)	PUNCT
ejde-629	208	11	∥∥	∥∥	PRON
ejde-629	208	12	βn	βn	VERB
ejde-629	208	13	2−β	2−β	NUM
ejde-629	208	14	≤	≤	PROPN
ejde-629	208	15	c|(t−	c|(t−	PROPN
ejde-629	208	16	s)α−1	s)α−1	NOUN
ejde-629	208	17	−	−	PROPN
ejde-629	208	18	(	(	PUNCT
ejde-629	208	19	t0	t0	X
ejde-629	208	20	−	−	NOUN
ejde-629	209	1	s)α−1|(t−	s)α−1|(t−	NOUN
ejde-629	209	2	s)−	s)−	PROPN
ejde-629	209	3	αγ	αγ	PROPN
ejde-629	209	4	4β	4β	NOUN
ejde-629	209	5	·	·	PUNCT
ejde-629	209	6	∥∇	∥∇	PUNCT
ejde-629	209	7	·	·	PUNCT
ejde-629	209	8	f(∇uj(s))∥	f(∇uj(s))∥	AUX
ejde-629	209	9	βn	βn	VERB
ejde-629	209	10	2−β+γ	2−β+γ	NUM
ejde-629	209	11	+	+	CCONJ
ejde-629	209	12	(	(	PUNCT
ejde-629	209	13	t0	t0	PROPN
ejde-629	209	14	−	−	NOUN
ejde-629	209	15	s)α−1	s)α−1	NOUN
ejde-629	209	16	∥∥eα	∥∥eα	ADJ
ejde-629	209	17	,	,	PUNCT
ejde-629	209	18	α(−(t−	α(−(t−	NUM
ejde-629	209	19	s)αa)∇	s)αa)∇	NOUN
ejde-629	209	20	·	·	PUNCT
ejde-629	209	21	f(∇uj(s	f(∇uj(s	NOUN
ejde-629	209	22	)	)	PUNCT
ejde-629	209	23	)	)	PUNCT
ejde-629	210	1	−	−	ADP
ejde-629	210	2	eα	eα	NOUN
ejde-629	210	3	,	,	PUNCT
ejde-629	210	4	α(−(t0	α(−(t0	NOUN
ejde-629	210	5	−	−	PROPN
ejde-629	210	6	s)αa)∇	s)αa)∇	NOUN
ejde-629	210	7	·	·	PUNCT
ejde-629	210	8	f(∇uj(s	f(∇uj(s	NOUN
ejde-629	210	9	)	)	PUNCT
ejde-629	210	10	)	)	PUNCT
ejde-629	210	11	∥∥	∥∥	PRON
ejde-629	210	12	βn	βn	VERB
ejde-629	210	13	2−β	2−β	NUM
ejde-629	210	14	≤	≤	PROPN
ejde-629	210	15	c|(t−	c|(t−	PROPN
ejde-629	210	16	s)α−1	s)α−1	NOUN
ejde-629	210	17	−	−	PROPN
ejde-629	210	18	(	(	PUNCT
ejde-629	210	19	t0	t0	X
ejde-629	210	20	−	−	NOUN
ejde-629	211	1	s)α−1|(t−	s)α−1|(t−	NOUN
ejde-629	211	2	s)−	s)−	PROPN
ejde-629	211	3	αγ	αγ	PROPN
ejde-629	211	4	4β	4β	NOUN
ejde-629	212	1	s−α+αγ	s−α+αγ	PROPN
ejde-629	212	2	4β	4β	NOUN
ejde-629	212	3	r(t	r(t	NOUN
ejde-629	212	4	)	)	PUNCT
ejde-629	212	5	0	0	PUNCT
ejde-629	213	1	+	+	CCONJ
ejde-629	213	2	(	(	PUNCT
ejde-629	213	3	t0	t0	PROPN
ejde-629	213	4	−	−	NOUN
ejde-629	213	5	s)α−1	s)α−1	NOUN
ejde-629	213	6	∥∥eα	∥∥eα	ADJ
ejde-629	213	7	,	,	PUNCT
ejde-629	213	8	α(−(t−	α(−(t−	NUM
ejde-629	213	9	s)αa)∇	s)αa)∇	NOUN
ejde-629	213	10	·	·	PUNCT
ejde-629	213	11	f(∇uj(s	f(∇uj(s	NOUN
ejde-629	213	12	)	)	PUNCT
ejde-629	213	13	)	)	PUNCT
ejde-629	214	1	−	−	ADP
ejde-629	214	2	eα	eα	NOUN
ejde-629	214	3	,	,	PUNCT
ejde-629	214	4	α(−(t0	α(−(t0	NOUN
ejde-629	214	5	−	−	PROPN
ejde-629	214	6	s)αa)∇	s)αa)∇	NOUN
ejde-629	214	7	·	·	PUNCT
ejde-629	214	8	f(∇uj(s	f(∇uj(s	NOUN
ejde-629	214	9	)	)	PUNCT
ejde-629	214	10	)	)	PUNCT
ejde-629	214	11	∥∥	∥∥	PROPN
ejde-629	214	12	βn	βn	VERB
ejde-629	214	13	2−β	2−β	NUM
ejde-629	214	14	.	.	PUNCT
ejde-629	215	1	(	(	PUNCT
ejde-629	215	2	3.8	3.8	NUM
ejde-629	215	3	)	)	PUNCT
ejde-629	215	4	ejde-2024/58	ejde-2024/58	ADJ
ejde-629	215	5	equations	equation	NOUN
ejde-629	215	6	modeling	model	VERB
ejde-629	215	7	thin	thin	ADJ
ejde-629	215	8	film	film	NOUN
ejde-629	215	9	growth	growth	NOUN
ejde-629	215	10	9	9	NUM
ejde-629	215	11	then	then	ADV
ejde-629	215	12	combining	combine	VERB
ejde-629	215	13	with	with	ADP
ejde-629	215	14	the	the	DET
ejde-629	215	15	strong	strong	ADJ
ejde-629	215	16	continuity	continuity	NOUN
ejde-629	215	17	of	of	ADP
ejde-629	215	18	eα	eα	PROPN
ejde-629	215	19	,	,	PUNCT
ejde-629	215	20	α(−tαa	α(−tαa	PROPN
ejde-629	215	21	)	)	PUNCT
ejde-629	215	22	on	on	ADP
ejde-629	215	23	l	l	PROPN
ejde-629	215	24	βn	βn	X
ejde-629	215	25	2−β	2−β	NUM
ejde-629	215	26	(	(	PUNCT
ejde-629	215	27	ω	ω	NOUN
ejde-629	215	28	)	)	PUNCT
ejde-629	215	29	for	for	ADP
ejde-629	215	30	t	t	PROPN
ejde-629	215	31	∈	∈	PROPN
ejde-629	215	32	(	(	PUNCT
ejde-629	215	33	0,∞	0,∞	NUM
ejde-629	215	34	)	)	PUNCT
ejde-629	215	35	,	,	PUNCT
ejde-629	215	36	we	we	PRON
ejde-629	215	37	have	have	VERB
ejde-629	215	38	lim	lim	PROPN
ejde-629	215	39	t→t+0	t→t+0	ADP
ejde-629	215	40	g(t	g(t	PROPN
ejde-629	215	41	,	,	PUNCT
ejde-629	215	42	s	s	PART
ejde-629	215	43	)	)	PUNCT
ejde-629	215	44	=	=	SYM
ejde-629	215	45	0	0	NUM
ejde-629	215	46	for	for	ADP
ejde-629	215	47	each	each	DET
ejde-629	215	48	fixed	fix	VERB
ejde-629	215	49	s	s	X
ejde-629	215	50	∈	∈	NOUN
ejde-629	215	51	(	(	PUNCT
ejde-629	215	52	0	0	NUM
ejde-629	215	53	,	,	PUNCT
ejde-629	215	54	t0	t0	NOUN
ejde-629	215	55	)	)	PUNCT
ejde-629	215	56	.	.	PUNCT
ejde-629	216	1	in	in	ADP
ejde-629	216	2	addition	addition	NOUN
ejde-629	216	3	,	,	PUNCT
ejde-629	216	4	the	the	DET
ejde-629	216	5	last	last	ADJ
ejde-629	216	6	term	term	NOUN
ejde-629	216	7	of	of	ADP
ejde-629	216	8	(	(	PUNCT
ejde-629	216	9	3.8	3.8	NUM
ejde-629	216	10	)	)	PUNCT
ejde-629	216	11	is	be	AUX
ejde-629	216	12	integrable	integrable	ADJ
ejde-629	216	13	.	.	PUNCT
ejde-629	217	1	applying	apply	VERB
ejde-629	217	2	dominated	dominate	VERB
ejde-629	217	3	convergence	convergence	NOUN
ejde-629	217	4	theorem	theorem	VERB
ejde-629	217	5	yields	yield	NOUN
ejde-629	217	6	the	the	DET
ejde-629	217	7	third	third	ADJ
ejde-629	217	8	term	term	NOUN
ejde-629	217	9	i3	i3	NOUN
ejde-629	217	10	also	also	ADV
ejde-629	217	11	tends	tend	VERB
ejde-629	217	12	to	to	ADP
ejde-629	217	13	zero	zero	NUM
ejde-629	217	14	as	as	ADP
ejde-629	217	15	t	t	PROPN
ejde-629	217	16	→	→	SYM
ejde-629	217	17	t+0	t+0	NUM
ejde-629	217	18	.	.	PUNCT
ejde-629	218	1	indeed	indeed	ADV
ejde-629	218	2	,	,	PUNCT
ejde-629	218	3	for	for	ADP
ejde-629	218	4	0	0	NUM
ejde-629	218	5	<	<	X
ejde-629	218	6	s	s	X
ejde-629	218	7	<	<	X
ejde-629	218	8	t0	t0	PROPN
ejde-629	218	9	<	<	X
ejde-629	218	10	t	t	PROPN
ejde-629	218	11	,	,	PUNCT
ejde-629	218	12	we	we	PRON
ejde-629	218	13	have	have	VERB
ejde-629	218	14	i3	i3	NOUN
ejde-629	218	15	=	=	SYM
ejde-629	218	16	∫	∫	PROPN
ejde-629	218	17	t0	t0	PROPN
ejde-629	218	18	0	0	PUNCT
ejde-629	219	1	g(t	g(t	PROPN
ejde-629	219	2	,	,	PUNCT
ejde-629	219	3	s	s	X
ejde-629	219	4	)	)	PUNCT
ejde-629	219	5	ds	ds	ADJ
ejde-629	219	6	≤	≤	NUM
ejde-629	219	7	c	c	NOUN
ejde-629	219	8	∫	∫	PROPN
ejde-629	219	9	t0	t0	X
ejde-629	219	10	0	0	PUNCT
ejde-629	220	1	(	(	PUNCT
ejde-629	220	2	t0	t0	NOUN
ejde-629	220	3	−	−	PROPN
ejde-629	220	4	s)α−1−αγ	s)α−1−αγ	NOUN
ejde-629	220	5	4β	4β	PRON
ejde-629	220	6	∥∇	∥∇	ADJ
ejde-629	220	7	·	·	PUNCT
ejde-629	221	1	f(∇uj)∥	f(∇uj)∥	PROPN
ejde-629	221	2	βn	βn	PUNCT
ejde-629	221	3	2−β+γ	2−β+γ	NUM
ejde-629	221	4	ds	ds	ADJ
ejde-629	221	5	,	,	PUNCT
ejde-629	221	6	≤	≤	NUM
ejde-629	221	7	cr(t	cr(t	NOUN
ejde-629	221	8	)	)	PUNCT
ejde-629	222	1	1+β	1+β	NUM
ejde-629	223	1	j	j	NOUN
ejde-629	223	2	∫	∫	PROPN
ejde-629	223	3	t0	t0	PROPN
ejde-629	223	4	0	0	PUNCT
ejde-629	223	5	(	(	PUNCT
ejde-629	223	6	t0	t0	X
ejde-629	223	7	−	−	PROPN
ejde-629	223	8	s)α−1−αγ	s)α−1−αγ	NOUN
ejde-629	223	9	4β	4β	NOUN
ejde-629	223	10	s−α+αγ	s−α+αγ	PROPN
ejde-629	223	11	4β	4β	NOUN
ejde-629	223	12	ds	ds	VERB
ejde-629	223	13	≤	≤	NUM
ejde-629	223	14	cr(t	cr(t	NOUN
ejde-629	223	15	)	)	PUNCT
ejde-629	223	16	1+β	1+β	NUM
ejde-629	223	17	0	0	NUM
ejde-629	223	18	.	.	PUNCT
ejde-629	224	1	similarly	similarly	ADV
ejde-629	224	2	,	,	PUNCT
ejde-629	224	3	we	we	PRON
ejde-629	224	4	can	can	AUX
ejde-629	224	5	also	also	ADV
ejde-629	224	6	prove	prove	VERB
ejde-629	224	7	the	the	DET
ejde-629	224	8	same	same	ADJ
ejde-629	224	9	limit	limit	NOUN
ejde-629	224	10	as	as	ADP
ejde-629	224	11	t	t	PROPN
ejde-629	224	12	→	→	SYM
ejde-629	224	13	t−0	t−0	PROPN
ejde-629	224	14	with	with	ADP
ejde-629	224	15	t0	t0	PROPN
ejde-629	224	16	∈	∈	PROPN
ejde-629	224	17	(	(	PUNCT
ejde-629	224	18	0	0	NUM
ejde-629	224	19	,	,	PUNCT
ejde-629	224	20	t	t	X
ejde-629	224	21	]	]	PUNCT
ejde-629	224	22	.	.	PUNCT
ejde-629	225	1	thus	thus	ADV
ejde-629	225	2	,	,	PUNCT
ejde-629	225	3	lim	lim	PROPN
ejde-629	225	4	t→t0	t→t0	VERB
ejde-629	225	5	∥uj+1(t)−	∥uj+1(t)−	PROPN
ejde-629	225	6	uj+1(t0)∥	uj+1(t0)∥	VERB
ejde-629	225	7	βn	βn	PROPN
ejde-629	225	8	2−β	2−β	NUM
ejde-629	225	9	=	=	SYM
ejde-629	225	10	0	0	NUM
ejde-629	225	11	,	,	PUNCT
ejde-629	225	12	t0	t0	PROPN
ejde-629	225	13	∈	∈	PROPN
ejde-629	225	14	(	(	PUNCT
ejde-629	225	15	0	0	NUM
ejde-629	225	16	,	,	PUNCT
ejde-629	225	17	t	t	X
ejde-629	225	18	]	]	PUNCT
ejde-629	225	19	.	.	PUNCT
ejde-629	226	1	as	as	ADP
ejde-629	226	2	for	for	ADP
ejde-629	226	3	the	the	DET
ejde-629	226	4	continuity	continuity	NOUN
ejde-629	226	5	up	up	ADP
ejde-629	226	6	to	to	ADP
ejde-629	226	7	t	t	NOUN
ejde-629	226	8	=	=	SYM
ejde-629	226	9	0	0	NUM
ejde-629	226	10	of	of	ADP
ejde-629	226	11	uj+1	uj+1	NUM
ejde-629	226	12	,	,	PUNCT
ejde-629	226	13	observe	observe	VERB
ejde-629	226	14	that	that	SCONJ
ejde-629	226	15	∥uj+1(t)−	∥uj+1(t)−	PROPN
ejde-629	226	16	uj+1(0)∥	uj+1(0)∥	PUNCT
ejde-629	227	1	βn	βn	VERB
ejde-629	227	2	2−β	2−β	NUM
ejde-629	227	3	≤	≤	NUM
ejde-629	227	4	∥eα(−tαa)φ−	∥eα(−tαa)φ−	NOUN
ejde-629	227	5	φ∥	φ∥	AUX
ejde-629	227	6	βn	βn	VERB
ejde-629	227	7	2−β	2−β	NUM
ejde-629	228	1	+	+	CCONJ
ejde-629	228	2	∫	∫	PROPN
ejde-629	228	3	t	t	PROPN
ejde-629	228	4	0	0	NUM
ejde-629	228	5	(	(	PUNCT
ejde-629	228	6	t−	t−	PROPN
ejde-629	228	7	s)α−1	s)α−1	NOUN
ejde-629	228	8	∥eα	∥eα	NOUN
ejde-629	228	9	,	,	PUNCT
ejde-629	228	10	α(−(t−	α(−(t−	NOUN
ejde-629	228	11	s)αa)∇	s)αa)∇	NOUN
ejde-629	228	12	·	·	PUNCT
ejde-629	229	1	f(∇uj(s))∥	f(∇uj(s))∥	NOUN
ejde-629	229	2	βn	βn	VERB
ejde-629	229	3	2−β	2−β	NUM
ejde-629	229	4	ds	ds	ADJ
ejde-629	229	5	≤	≤	NUM
ejde-629	229	6	∥eα(−tαa)φ−	∥eα(−tαa)φ−	NOUN
ejde-629	229	7	φ∥	φ∥	X
ejde-629	229	8	βn	βn	VERB
ejde-629	229	9	2−β	2−β	NUM
ejde-629	230	1	+	+	CCONJ
ejde-629	230	2	c	c	NOUN
ejde-629	230	3	∫	∫	PROPN
ejde-629	230	4	t	t	PROPN
ejde-629	230	5	0	0	NUM
ejde-629	230	6	(	(	PUNCT
ejde-629	230	7	t−	t−	PROPN
ejde-629	230	8	s)α−1−αγ	s)α−1−αγ	NOUN
ejde-629	230	9	4β	4β	NOUN
ejde-629	230	10	∥∇	∥∇	ADJ
ejde-629	230	11	·	·	PUNCT
ejde-629	230	12	f(∇uj)∥	f(∇uj)∥	PROPN
ejde-629	230	13	βn	βn	PUNCT
ejde-629	230	14	2−β+γ	2−β+γ	NUM
ejde-629	230	15	dsr	dsr	NOUN
ejde-629	230	16	≤	≤	PUNCT
ejde-629	230	17	∥eα(−tαa)φ−	∥eα(−tαa)φ−	NOUN
ejde-629	230	18	φ∥	φ∥	AUX
ejde-629	230	19	βn	βn	VERB
ejde-629	230	20	2−β	2−β	NUM
ejde-629	230	21	+	+	CCONJ
ejde-629	230	22	cr(t)1+β	cr(t)1+β	PROPN
ejde-629	230	23	j	j	PROPN
ejde-629	230	24	∫	∫	PROPN
ejde-629	230	25	t	t	PROPN
ejde-629	230	26	0	0	NUM
ejde-629	230	27	(	(	PUNCT
ejde-629	230	28	t−	t−	PROPN
ejde-629	230	29	s)α−1−αγ	s)α−1−αγ	NOUN
ejde-629	230	30	4β	4β	NOUN
ejde-629	230	31	s−α+αγ	s−α+αγ	PROPN
ejde-629	230	32	4β	4β	NOUN
ejde-629	230	33	ds	ds	VERB
ejde-629	230	34	≤	≤	NUM
ejde-629	230	35	∥eα(−tαa)φ−	∥eα(−tαa)φ−	NOUN
ejde-629	230	36	φ∥	φ∥	X
ejde-629	230	37	βn	βn	VERB
ejde-629	230	38	2−β	2−β	NUM
ejde-629	230	39	+	+	CCONJ
ejde-629	230	40	cr(t)1+β	cr(t)1+β	PROPN
ejde-629	230	41	0	0	X
ejde-629	230	42	.	.	PUNCT
ejde-629	231	1	obviously	obviously	ADV
ejde-629	231	2	,	,	PUNCT
ejde-629	231	3	if	if	SCONJ
ejde-629	231	4	lim	lim	PROPN
ejde-629	231	5	t→0	t→0	PROPN
ejde-629	231	6	+	+	PROPN
ejde-629	231	7	r(t)0	r(t)0	PROPN
ejde-629	231	8	=	=	SYM
ejde-629	231	9	0	0	PROPN
ejde-629	231	10	,	,	PUNCT
ejde-629	231	11	(	(	PUNCT
ejde-629	231	12	3.9	3.9	NUM
ejde-629	231	13	)	)	PUNCT
ejde-629	231	14	then	then	ADV
ejde-629	231	15	combining	combine	VERB
ejde-629	231	16	with	with	ADP
ejde-629	231	17	the	the	DET
ejde-629	231	18	strong	strong	ADJ
ejde-629	231	19	continuity	continuity	NOUN
ejde-629	231	20	of	of	ADP
ejde-629	231	21	eα(−tαa	eα(−tαa	NOUN
ejde-629	231	22	)	)	PUNCT
ejde-629	231	23	,	,	PUNCT
ejde-629	231	24	we	we	PRON
ejde-629	231	25	obtain	obtain	VERB
ejde-629	231	26	that	that	DET
ejde-629	231	27	lim	lim	PROPN
ejde-629	231	28	t→0	t→0	AUX
ejde-629	231	29	+	+	NUM
ejde-629	231	30	∥uj+1(t)−	∥uj+1(t)−	NUM
ejde-629	231	31	uj+1(0)∥	uj+1(0)∥	NUM
ejde-629	232	1	βn	βn	PROPN
ejde-629	232	2	2−β	2−β	NUM
ejde-629	232	3	=	=	SYM
ejde-629	232	4	0	0	X
ejde-629	232	5	.	.	PUNCT
ejde-629	232	6	to	to	PART
ejde-629	232	7	prove	prove	VERB
ejde-629	232	8	(	(	PUNCT
ejde-629	232	9	3.9	3.9	NUM
ejde-629	232	10	)	)	PUNCT
ejde-629	232	11	,	,	PUNCT
ejde-629	232	12	we	we	PRON
ejde-629	232	13	notice	notice	VERB
ejde-629	232	14	that	that	SCONJ
ejde-629	232	15	since	since	SCONJ
ejde-629	232	16	φ	φ	PROPN
ejde-629	232	17	∈	∈	PROPN
ejde-629	232	18	l	l	X
ejde-629	232	19	βn	βn	X
ejde-629	232	20	2−β	2−β	NUM
ejde-629	232	21	(	(	PUNCT
ejde-629	232	22	ω	ω	NOUN
ejde-629	232	23	)	)	PUNCT
ejde-629	232	24	,	,	PUNCT
ejde-629	232	25	for	for	ADP
ejde-629	232	26	any	any	DET
ejde-629	232	27	ε	ε	PROPN
ejde-629	232	28	>	>	X
ejde-629	232	29	0	0	PROPN
ejde-629	232	30	,	,	PUNCT
ejde-629	232	31	there	there	PRON
ejde-629	232	32	exists	exist	VERB
ejde-629	232	33	φ̃	φ̃	PROPN
ejde-629	232	34	∈	∈	PROPN
ejde-629	232	35	c∞	c∞	NOUN
ejde-629	232	36	0	0	NUM
ejde-629	232	37	(	(	PUNCT
ejde-629	232	38	ω	ω	NOUN
ejde-629	232	39	)	)	PUNCT
ejde-629	232	40	such	such	ADJ
ejde-629	232	41	that	that	SCONJ
ejde-629	232	42	∥φ−	∥φ−	PROPN
ejde-629	232	43	φ̃∥	φ̃∥	NUM
ejde-629	232	44	βn	βn	VERB
ejde-629	232	45	2−β	2−β	NUM
ejde-629	232	46	<	<	X
ejde-629	232	47	ε	ε	PROPN
ejde-629	232	48	.	.	PUNCT
ejde-629	233	1	then	then	ADV
ejde-629	233	2	we	we	PRON
ejde-629	233	3	have	have	VERB
ejde-629	233	4	t	t	PROPN
ejde-629	233	5	α	α	PROPN
ejde-629	233	6	2β−	2β−	PROPN
ejde-629	233	7	αγ	αγ	SYM
ejde-629	233	8	4β2	4β2	NUM
ejde-629	233	9	∥∇u0(t)∥	∥∇u0(t)∥	NOUN
ejde-629	233	10	β2n	β2n	ADV
ejde-629	233	11	γ	γ	X
ejde-629	233	12	=	=	SYM
ejde-629	233	13	t	t	PROPN
ejde-629	233	14	α	α	PROPN
ejde-629	233	15	2β−	2β−	PROPN
ejde-629	233	16	αγ	αγ	NUM
ejde-629	233	17	4β2	4β2	NUM
ejde-629	233	18	∥∇eα(−tαa)φ∥	∥∇eα(−tαa)φ∥	PROPN
ejde-629	233	19	β2n	β2n	ADV
ejde-629	233	20	γ	γ	PROPN
ejde-629	233	21	≤	≤	PROPN
ejde-629	233	22	t	t	PROPN
ejde-629	233	23	α	α	PROPN
ejde-629	233	24	2β−	2β−	PROPN
ejde-629	233	25	αγ	αγ	SYM
ejde-629	233	26	4β2	4β2	NUM
ejde-629	233	27	∥∇eα(−tαa)(φ−	∥∇eα(−tαa)(φ−	PROPN
ejde-629	233	28	φ̃)∥	φ̃)∥	NUM
ejde-629	233	29	β2n	β2n	ADJ
ejde-629	233	30	γ	γ	X
ejde-629	233	31	+	+	X
ejde-629	233	32	t	t	PROPN
ejde-629	233	33	α	α	PROPN
ejde-629	233	34	2β−	2β−	PROPN
ejde-629	233	35	αγ	αγ	SYM
ejde-629	233	36	4β2	4β2	NUM
ejde-629	233	37	∥∇eα(−tαa)φ̃∥	∥∇eα(−tαa)φ̃∥	ADJ
ejde-629	233	38	β2n	β2n	PUNCT
ejde-629	233	39	γ	γ	X
ejde-629	233	40	≤	≤	NOUN
ejde-629	233	41	∥φ−	∥φ−	NUM
ejde-629	233	42	φ̃∥	φ̃∥	NUM
ejde-629	233	43	βn	βn	VERB
ejde-629	233	44	2−β	2−β	NUM
ejde-629	234	1	+	+	CCONJ
ejde-629	234	2	t	t	PROPN
ejde-629	234	3	α	α	NOUN
ejde-629	234	4	4	4	NUM
ejde-629	234	5	∥∇φ̃∥	∥∇φ̃∥	PROPN
ejde-629	234	6	βn	βn	PUNCT
ejde-629	234	7	2−β	2−β	NUM
ejde-629	234	8	≤	≤	NUM
ejde-629	234	9	ε	ε	PROPN
ejde-629	234	10	10	10	NUM
ejde-629	234	11	q.	q.	PROPN
ejde-629	234	12	liu	liu	PROPN
ejde-629	234	13	,	,	PUNCT
ejde-629	234	14	w.	w.	PROPN
ejde-629	234	15	zhu	zhu	PROPN
ejde-629	234	16	,	,	PUNCT
ejde-629	234	17	h.	h.	PROPN
ejde-629	234	18	ye	ye	PROPN
ejde-629	234	19	ejde-2024/58	ejde-2024/58	ADJ
ejde-629	234	20	for	for	ADP
ejde-629	234	21	small	small	ADJ
ejde-629	234	22	t	t	PROPN
ejde-629	234	23	>	>	X
ejde-629	234	24	0	0	PROPN
ejde-629	234	25	,	,	PUNCT
ejde-629	234	26	which	which	PRON
ejde-629	234	27	implies	imply	VERB
ejde-629	234	28	lim	lim	PROPN
ejde-629	235	1	t→0	t→0	PROPN
ejde-629	236	1	+	+	NUM
ejde-629	236	2	t	t	PROPN
ejde-629	236	3	α	α	NUM
ejde-629	236	4	2β−	2β−	PROPN
ejde-629	236	5	αγ	αγ	SYM
ejde-629	236	6	4β2	4β2	NUM
ejde-629	236	7	∥∇u0(t)∥	∥∇u0(t)∥	NOUN
ejde-629	236	8	β2n	β2n	ADV
ejde-629	236	9	γ	γ	X
ejde-629	236	10	=	=	SYM
ejde-629	236	11	0	0	PROPN
ejde-629	236	12	.	.	PUNCT
ejde-629	237	1	(	(	PUNCT
ejde-629	237	2	3.10	3.10	NUM
ejde-629	237	3	)	)	PUNCT
ejde-629	237	4	similarly	similarly	ADV
ejde-629	237	5	,	,	PUNCT
ejde-629	237	6	we	we	PRON
ejde-629	237	7	can	can	AUX
ejde-629	237	8	obtain	obtain	VERB
ejde-629	237	9	lim	lim	NOUN
ejde-629	237	10	t→0	t→0	PROPN
ejde-629	237	11	+	+	NUM
ejde-629	237	12	t	t	PROPN
ejde-629	237	13	α	α	NOUN
ejde-629	237	14	2	2	NUM
ejde-629	237	15	∥∇2u0(t)∥	∥∇2u0(t)∥	NOUN
ejde-629	237	16	βn	βn	VERB
ejde-629	237	17	2−β	2−β	NUM
ejde-629	237	18	=	=	SYM
ejde-629	237	19	0	0	NUM
ejde-629	237	20	.	.	PUNCT
ejde-629	238	1	(	(	PUNCT
ejde-629	238	2	3.11	3.11	NUM
ejde-629	238	3	)	)	PUNCT
ejde-629	238	4	combining	combine	VERB
ejde-629	238	5	(	(	PUNCT
ejde-629	238	6	3.10	3.10	NUM
ejde-629	238	7	)	)	PUNCT
ejde-629	238	8	with	with	ADP
ejde-629	238	9	(	(	PUNCT
ejde-629	238	10	3.11	3.11	NUM
ejde-629	238	11	)	)	PUNCT
ejde-629	238	12	,	,	PUNCT
ejde-629	238	13	we	we	PRON
ejde-629	238	14	derive	derive	VERB
ejde-629	238	15	(	(	PUNCT
ejde-629	238	16	3.9	3.9	NUM
ejde-629	238	17	)	)	PUNCT
ejde-629	238	18	.	.	PUNCT
ejde-629	239	1	summing	sum	VERB
ejde-629	239	2	up	up	ADP
ejde-629	239	3	,	,	PUNCT
ejde-629	239	4	we	we	PRON
ejde-629	239	5	see	see	VERB
ejde-629	239	6	that	that	SCONJ
ejde-629	239	7	uj	uj	PROPN
ejde-629	239	8	∈	∈	PROPN
ejde-629	239	9	c([0	c([0	PROPN
ejde-629	239	10	,	,	PUNCT
ejde-629	239	11	t	t	X
ejde-629	239	12	]	]	PUNCT
ejde-629	239	13	;	;	PUNCT
ejde-629	239	14	l	l	X
ejde-629	239	15	βn	βn	X
ejde-629	239	16	2−β	2−β	NUM
ejde-629	239	17	(	(	PUNCT
ejde-629	239	18	ω	ω	NOUN
ejde-629	239	19	)	)	PUNCT
ejde-629	239	20	)	)	PUNCT
ejde-629	239	21	for	for	ADP
ejde-629	239	22	any	any	DET
ejde-629	239	23	t	t	NOUN
ejde-629	239	24	>	>	X
ejde-629	239	25	0	0	PROPN
ejde-629	239	26	and	and	CCONJ
ejde-629	239	27	j	j	PROPN
ejde-629	239	28	≥	≥	NOUN
ejde-629	239	29	0	0	NUM
ejde-629	239	30	.	.	PUNCT
ejde-629	240	1	□	□	PUNCT
ejde-629	240	2	proof	proof	NOUN
ejde-629	240	3	of	of	ADP
ejde-629	240	4	theorem	theorem	ADJ
ejde-629	240	5	1.2	1.2	NUM
ejde-629	240	6	.	.	PUNCT
ejde-629	240	7	to	to	PART
ejde-629	240	8	prove	prove	VERB
ejde-629	240	9	the	the	DET
ejde-629	240	10	main	main	ADJ
ejde-629	240	11	result	result	NOUN
ejde-629	240	12	,	,	PUNCT
ejde-629	240	13	we	we	PRON
ejde-629	240	14	only	only	ADV
ejde-629	240	15	need	need	VERB
ejde-629	240	16	to	to	PART
ejde-629	240	17	show	show	VERB
ejde-629	240	18	the	the	DET
ejde-629	240	19	uniform	uniform	ADJ
ejde-629	240	20	convergence	convergence	NOUN
ejde-629	240	21	of	of	ADP
ejde-629	240	22	the	the	DET
ejde-629	240	23	sequence	sequence	NOUN
ejde-629	240	24	{	{	PUNCT
ejde-629	240	25	uj}j≥0	uj}j≥0	NOUN
ejde-629	240	26	under	under	ADP
ejde-629	240	27	the	the	DET
ejde-629	240	28	assumption	assumption	NOUN
ejde-629	240	29	that	that	SCONJ
ejde-629	240	30	r(t	r(t	NOUN
ejde-629	240	31	)	)	PUNCT
ejde-629	240	32	0	0	NUM
ejde-629	240	33	≤	≤	NUM
ejde-629	240	34	ε0	ε0	PROPN
ejde-629	240	35	.	.	PUNCT
ejde-629	241	1	by	by	ADP
ejde-629	241	2	lemma	lemma	PROPN
ejde-629	241	3	2.4	2.4	NUM
ejde-629	241	4	,	,	PUNCT
ejde-629	241	5	we	we	PRON
ejde-629	241	6	define	define	VERB
ejde-629	241	7	the	the	DET
ejde-629	241	8	sequence	sequence	NOUN
ejde-629	241	9	ω0(x	ω0(x	NUM
ejde-629	241	10	,	,	PUNCT
ejde-629	241	11	t	t	PROPN
ejde-629	241	12	)	)	PUNCT
ejde-629	241	13	=	=	SYM
ejde-629	241	14	u0(x	u0(x	PROPN
ejde-629	241	15	,	,	PUNCT
ejde-629	241	16	t	t	PROPN
ejde-629	241	17	)	)	PUNCT
ejde-629	241	18	,	,	PUNCT
ejde-629	241	19	ωj(x	ωj(x	NUM
ejde-629	241	20	,	,	PUNCT
ejde-629	241	21	t	t	PROPN
ejde-629	241	22	)	)	PUNCT
ejde-629	241	23	=	=	SYM
ejde-629	242	1	uj(x	uj(x	NOUN
ejde-629	242	2	,	,	PUNCT
ejde-629	242	3	t)−	t)−	PROPN
ejde-629	242	4	uj−1(x	uj−1(x	PROPN
ejde-629	242	5	,	,	PUNCT
ejde-629	242	6	t	t	PROPN
ejde-629	242	7	)	)	PUNCT
ejde-629	242	8	,	,	PUNCT
ejde-629	242	9	j	j	PROPN
ejde-629	242	10	≥	≥	PROPN
ejde-629	242	11	1	1	NUM
ejde-629	242	12	.	.	PUNCT
ejde-629	242	13	(	(	PUNCT
ejde-629	242	14	3.12	3.12	NUM
ejde-629	242	15	)	)	PUNCT
ejde-629	242	16	obviously	obviously	ADV
ejde-629	242	17	,	,	PUNCT
ejde-629	242	18	ωj	ωj	ADP
ejde-629	242	19	∈	∈	PROPN
ejde-629	242	20	c([0	c([0	NOUN
ejde-629	242	21	,	,	PUNCT
ejde-629	242	22	t	t	X
ejde-629	242	23	]	]	PUNCT
ejde-629	242	24	;	;	PUNCT
ejde-629	242	25	l	l	X
ejde-629	242	26	βn	βn	X
ejde-629	242	27	2−β	2−β	NUM
ejde-629	242	28	(	(	PUNCT
ejde-629	242	29	ω	ω	NOUN
ejde-629	242	30	)	)	PUNCT
ejde-629	242	31	)	)	PUNCT
ejde-629	242	32	for	for	ADP
ejde-629	242	33	any	any	DET
ejde-629	242	34	t	t	NOUN
ejde-629	242	35	>	>	X
ejde-629	242	36	0	0	PROPN
ejde-629	242	37	and	and	CCONJ
ejde-629	242	38	j	j	PROPN
ejde-629	242	39	≥	≥	NUM
ejde-629	242	40	0	0	NUM
ejde-629	242	41	.	.	PUNCT
ejde-629	243	1	in	in	ADP
ejde-629	243	2	addition	addition	NOUN
ejde-629	243	3	,	,	PUNCT
ejde-629	243	4	we	we	PRON
ejde-629	243	5	have	have	VERB
ejde-629	243	6	the	the	DET
ejde-629	243	7	identity	identity	NOUN
ejde-629	243	8	ωj+1(x	ωj+1(x	NUM
ejde-629	243	9	,	,	PUNCT
ejde-629	243	10	t	t	NOUN
ejde-629	243	11	)	)	PUNCT
ejde-629	243	12	=	=	SYM
ejde-629	243	13	uj+1(x	uj+1(x	NOUN
ejde-629	243	14	,	,	PUNCT
ejde-629	243	15	t)−	t)−	PROPN
ejde-629	243	16	uj(x	uj(x	NOUN
ejde-629	243	17	,	,	PUNCT
ejde-629	243	18	t	t	PROPN
ejde-629	243	19	)	)	PUNCT
ejde-629	243	20	=	=	SYM
ejde-629	244	1	∫	∫	PROPN
ejde-629	244	2	t	t	PROPN
ejde-629	244	3	0	0	NUM
ejde-629	244	4	(	(	PUNCT
ejde-629	244	5	t−	t−	PROPN
ejde-629	244	6	s)α−1eα	s)α−1eα	PROPN
ejde-629	244	7	,	,	PUNCT
ejde-629	244	8	α(−(t−	α(−(t−	PUNCT
ejde-629	244	9	s)αa	s)αa	NOUN
ejde-629	244	10	)	)	PUNCT
ejde-629	244	11	(	(	PUNCT
ejde-629	244	12	∇	∇	X
ejde-629	244	13	·	·	PUNCT
ejde-629	244	14	f(∇uj)−∇	f(∇uj)−∇	PROPN
ejde-629	244	15	·	·	PUNCT
ejde-629	244	16	f(∇uj−1	f(∇uj−1	PROPN
ejde-629	244	17	)	)	PUNCT
ejde-629	244	18	)	)	PUNCT
ejde-629	245	1	ds	ds	NOUN
ejde-629	245	2	=	=	SYM
ejde-629	245	3	∫	∫	PROPN
ejde-629	245	4	t	t	PROPN
ejde-629	245	5	0	0	NUM
ejde-629	245	6	(	(	PUNCT
ejde-629	245	7	t−	t−	PROPN
ejde-629	245	8	s)α−1eα	s)α−1eα	PROPN
ejde-629	245	9	,	,	PUNCT
ejde-629	245	10	α(−(t−	α(−(t−	PUNCT
ejde-629	245	11	s)αa	s)αa	NOUN
ejde-629	245	12	)	)	PUNCT
ejde-629	245	13	(	(	PUNCT
ejde-629	245	14	∇2uj	∇2uj	PROPN
ejde-629	245	15	·	·	PUNCT
ejde-629	245	16	f	f	PROPN
ejde-629	245	17	′(∇uj)−∇2uj−1	′(∇uj)−∇2uj−1	NOUN
ejde-629	245	18	·	·	PUNCT
ejde-629	245	19	f	f	X
ejde-629	245	20	′(∇uj−1	′(∇uj−1	NOUN
ejde-629	245	21	)	)	PUNCT
ejde-629	245	22	)	)	PUNCT
ejde-629	246	1	ds	ds	NOUN
ejde-629	246	2	=	=	SYM
ejde-629	246	3	∫	∫	PROPN
ejde-629	246	4	t	t	PROPN
ejde-629	246	5	0	0	NUM
ejde-629	246	6	(	(	PUNCT
ejde-629	246	7	t−	t−	PROPN
ejde-629	246	8	s)α−1eα	s)α−1eα	PROPN
ejde-629	246	9	,	,	PUNCT
ejde-629	246	10	α(−(t−	α(−(t−	NOUN
ejde-629	246	11	s)αa)∇2ωj	s)αa)∇2ωj	NOUN
ejde-629	246	12	·	·	PUNCT
ejde-629	246	13	f	f	PROPN
ejde-629	246	14	′(∇uj	′(∇uj	PROPN
ejde-629	246	15	)	)	PUNCT
ejde-629	246	16	ds	ds	PROPN
ejde-629	246	17	(	(	PUNCT
ejde-629	246	18	3.13	3.13	NUM
ejde-629	246	19	)	)	PUNCT
ejde-629	247	1	+	+	CCONJ
ejde-629	247	2	∫	∫	PROPN
ejde-629	247	3	t	t	PROPN
ejde-629	247	4	0	0	NUM
ejde-629	247	5	(	(	PUNCT
ejde-629	247	6	t−	t−	PROPN
ejde-629	247	7	s)α−1eα	s)α−1eα	PROPN
ejde-629	247	8	,	,	PUNCT
ejde-629	247	9	α(−(t−	α(−(t−	NUM
ejde-629	247	10	s)αa)∇2uj−1	s)αa)∇2uj−1	NOUN
ejde-629	247	11	·	·	PUNCT
ejde-629	247	12	(	(	PUNCT
ejde-629	247	13	f	f	X
ejde-629	247	14	′(∇uj)−	′(∇uj)−	NOUN
ejde-629	247	15	f	f	PROPN
ejde-629	247	16	′(∇uj−1	′(∇uj−1	NOUN
ejde-629	247	17	)	)	PUNCT
ejde-629	247	18	)	)	PUNCT
ejde-629	247	19	ds	ds	PROPN
ejde-629	247	20	.	.	NOUN
ejde-629	248	1	as	as	ADP
ejde-629	248	2	in	in	ADP
ejde-629	248	3	lemma	lemma	PROPN
ejde-629	248	4	3.2	3.2	NUM
ejde-629	248	5	,	,	PUNCT
ejde-629	248	6	to	to	PART
ejde-629	248	7	estimate	estimate	VERB
ejde-629	248	8	ωj	ωj	ADP
ejde-629	248	9	,	,	PUNCT
ejde-629	248	10	we	we	PRON
ejde-629	248	11	to	to	PART
ejde-629	248	12	derive	derive	VERB
ejde-629	248	13	a	a	DET
ejde-629	248	14	priori	priori	ADJ
ejde-629	248	15	estimates	estimate	NOUN
ejde-629	248	16	for	for	ADP
ejde-629	248	17	∇ωj	∇ωj	NOUN
ejde-629	248	18	and	and	CCONJ
ejde-629	248	19	∇2ωj	∇2ωj	PROPN
ejde-629	248	20	.	.	PUNCT
ejde-629	249	1	so	so	ADV
ejde-629	249	2	we	we	PRON
ejde-629	249	3	define	define	VERB
ejde-629	249	4	r̃(t)j	r̃(t)j	NOUN
ejde-629	249	5	=	=	SYM
ejde-629	249	6	max	max	NOUN
ejde-629	249	7	{	{	PUNCT
ejde-629	249	8	sup	sup	NOUN
ejde-629	249	9	0	0	NUM
ejde-629	249	10	<	<	NOUN
ejde-629	249	11	s≤t	s≤t	PROPN
ejde-629	249	12	s	s	NOUN
ejde-629	249	13	α	α	NOUN
ejde-629	249	14	2	2	NUM
ejde-629	249	15	∥∇2ωj(s)∥	∥∇2ωj(s)∥	ADP
ejde-629	249	16	βn	βn	NOUN
ejde-629	249	17	2−β	2−β	NUM
ejde-629	249	18	,	,	PUNCT
ejde-629	249	19	sup	sup	NOUN
ejde-629	249	20	0	0	NUM
ejde-629	249	21	<	<	NOUN
ejde-629	249	22	s≤t	s≤t	PROPN
ejde-629	249	23	s	s	PART
ejde-629	249	24	α	α	PROPN
ejde-629	249	25	2β−	2β−	PROPN
ejde-629	249	26	αγ	αγ	NUM
ejde-629	249	27	4β2	4β2	NUM
ejde-629	249	28	∥∇ωj(s)∥	∥∇ωj(s)∥	NUM
ejde-629	249	29	β2n	β2n	ADJ
ejde-629	249	30	γ	γ	X
ejde-629	249	31	}	}	PUNCT
ejde-629	249	32	(	(	PUNCT
ejde-629	249	33	3.14	3.14	NUM
ejde-629	249	34	)	)	PUNCT
ejde-629	249	35	for	for	ADP
ejde-629	249	36	t	t	PROPN
ejde-629	249	37	>	>	X
ejde-629	249	38	0	0	PROPN
ejde-629	249	39	and	and	CCONJ
ejde-629	249	40	j	j	PROPN
ejde-629	249	41	≥	≥	NUM
ejde-629	249	42	0	0	NUM
ejde-629	249	43	,	,	PUNCT
ejde-629	249	44	where	where	SCONJ
ejde-629	249	45	0	0	PUNCT
ejde-629	249	46	<	<	X
ejde-629	249	47	γ	γ	X
ejde-629	249	48	<	<	X
ejde-629	249	49	min{2β	min{2β	PROPN
ejde-629	249	50	,	,	PUNCT
ejde-629	249	51	β(n+1)−2	β(n+1)−2	ADJ
ejde-629	249	52	}	}	PUNCT
ejde-629	249	53	.	.	PUNCT
ejde-629	250	1	obviously	obviously	ADV
ejde-629	250	2	,	,	PUNCT
ejde-629	250	3	r̃(t)0	r̃(t)0	X
ejde-629	250	4	=	=	SYM
ejde-629	250	5	r(t)0	r(t)0	PROPN
ejde-629	250	6	.	.	PUNCT
ejde-629	251	1	let	let	VERB
ejde-629	251	2	r(t	r(t	NOUN
ejde-629	251	3	)	)	PUNCT
ejde-629	252	1	0	0	NUM
ejde-629	252	2	≤	≤	NUM
ejde-629	252	3	ε0	ε0	PROPN
ejde-629	252	4	.	.	PUNCT
ejde-629	253	1	by	by	ADP
ejde-629	253	2	hölder	hölder	PROPN
ejde-629	253	3	’s	’s	PART
ejde-629	253	4	inequality	inequality	NOUN
ejde-629	253	5	,	,	PUNCT
ejde-629	253	6	we	we	PRON
ejde-629	253	7	obtain	obtain	VERB
ejde-629	253	8	that	that	PRON
ejde-629	253	9	for	for	ADP
ejde-629	253	10	0	0	NUM
ejde-629	253	11	<	<	X
ejde-629	253	12	s	s	PART
ejde-629	253	13	≤	≤	NUM
ejde-629	253	14	t	t	PROPN
ejde-629	253	15	≤	≤	PROPN
ejde-629	253	16	t	t	PROPN
ejde-629	253	17	,	,	PUNCT
ejde-629	253	18	∥∇2ωj(s	∥∇2ωj(s	PROPN
ejde-629	253	19	)	)	PUNCT
ejde-629	253	20	·	·	PUNCT
ejde-629	254	1	f	f	X
ejde-629	254	2	′(∇uj(s))∥	′(∇uj(s))∥	X
ejde-629	254	3	βn	βn	VERB
ejde-629	254	4	2−β+γ	2−β+γ	NUM
ejde-629	254	5	≤	≤	NOUN
ejde-629	254	6	∥∇2ωj(s)∥	∥∇2ωj(s)∥	ADP
ejde-629	254	7	βn	βn	NOUN
ejde-629	254	8	2−β	2−β	NUM
ejde-629	254	9	∥f	∥f	PROPN
ejde-629	254	10	′(∇uj(s))∥	′(∇uj(s))∥	PROPN
ejde-629	254	11	βn	βn	NOUN
ejde-629	254	12	γ	γ	X
ejde-629	254	13	=	=	PROPN
ejde-629	254	14	s−α+αγ	s−α+αγ	PROPN
ejde-629	254	15	4β	4β	NUM
ejde-629	254	16	(	(	PUNCT
ejde-629	254	17	s	s	NOUN
ejde-629	254	18	α	α	PRON
ejde-629	254	19	2	2	NUM
ejde-629	254	20	∥∇2ωj(s)∥	∥∇2ωj(s)∥	ADP
ejde-629	254	21	βn	βn	NOUN
ejde-629	254	22	2−β	2−β	NUM
ejde-629	254	23	)	)	PUNCT
ejde-629	254	24	(	(	PUNCT
ejde-629	254	25	s	s	NOUN
ejde-629	254	26	α	α	PRON
ejde-629	254	27	2	2	NUM
ejde-629	254	28	−αγ	−αγ	NOUN
ejde-629	254	29	4β	4β	NOUN
ejde-629	254	30	∥∇uj(s)∥ββ2n	∥∇uj(s)∥ββ2n	PROPN
ejde-629	254	31	γ	γ	X
ejde-629	254	32	)	)	PUNCT
ejde-629	254	33	≤	≤	PUNCT
ejde-629	255	1	s−α+αγ	s−α+αγ	PROPN
ejde-629	255	2	4β	4β	PROPN
ejde-629	255	3	r̃(t	r̃(t	PROPN
ejde-629	255	4	)	)	PUNCT
ejde-629	255	5	jr(t	jr(t	PUNCT
ejde-629	255	6	)	)	PUNCT
ejde-629	255	7	βj	βj	NOUN
ejde-629	255	8	≤	≤	NUM
ejde-629	255	9	cs−α+αγ	cs−α+αγ	NOUN
ejde-629	255	10	4β	4β	PROPN
ejde-629	255	11	r̃(t	r̃(t	PROPN
ejde-629	255	12	)	)	PUNCT
ejde-629	255	13	jr(t	jr(t	PUNCT
ejde-629	255	14	)	)	PUNCT
ejde-629	255	15	β0	β0	NOUN
ejde-629	255	16	.	.	PUNCT
ejde-629	256	1	(	(	PUNCT
ejde-629	256	2	3.15	3.15	NUM
ejde-629	256	3	)	)	PUNCT
ejde-629	256	4	ejde-2024/58	ejde-2024/58	ADJ
ejde-629	256	5	equations	equation	NOUN
ejde-629	256	6	modeling	model	VERB
ejde-629	256	7	thin	thin	ADJ
ejde-629	256	8	film	film	NOUN
ejde-629	256	9	growth	growth	NOUN
ejde-629	256	10	11	11	NUM
ejde-629	256	11	in	in	ADP
ejde-629	256	12	addition	addition	NOUN
ejde-629	256	13	,	,	PUNCT
ejde-629	256	14	the	the	DET
ejde-629	256	15	growth	growth	NOUN
ejde-629	256	16	condition	condition	NOUN
ejde-629	256	17	on	on	ADP
ejde-629	256	18	f	f	PROPN
ejde-629	256	19	′	′	NOUN
ejde-629	256	20	and	and	CCONJ
ejde-629	256	21	hölder	hölder	PROPN
ejde-629	256	22	’s	’s	PART
ejde-629	256	23	inequality	inequality	NOUN
ejde-629	256	24	yield	yield	NOUN
ejde-629	256	25	,	,	PUNCT
ejde-629	256	26	for	for	ADP
ejde-629	256	27	0	0	NUM
ejde-629	256	28	<	<	X
ejde-629	256	29	s	s	PART
ejde-629	256	30	≤	≤	NUM
ejde-629	256	31	t	t	PROPN
ejde-629	256	32	≤	≤	PROPN
ejde-629	256	33	t	t	NOUN
ejde-629	256	34	,	,	PUNCT
ejde-629	256	35	∥f	∥f	PROPN
ejde-629	256	36	′(∇uj(s))−	′(∇uj(s))−	NUM
ejde-629	256	37	f	f	PROPN
ejde-629	256	38	′(∇uj−1(s))∥	′(∇uj−1(s))∥	NOUN
ejde-629	256	39	βn	βn	VERB
ejde-629	256	40	γ	γ	PROPN
ejde-629	256	41	≤	≤	NOUN
ejde-629	256	42	∥∥∥∇ωj(s	∥∥∥∇ωj(s	PROPN
ejde-629	256	43	)	)	PUNCT
ejde-629	256	44	(	(	PUNCT
ejde-629	256	45	|∇uj(s)|β−1	|∇uj(s)|β−1	X
ejde-629	256	46	+	+	NUM
ejde-629	256	47	|∇uj−1(s)|β−1	|∇uj−1(s)|β−1	ADJ
ejde-629	256	48	)	)	PUNCT
ejde-629	256	49	∥∥∥	∥∥∥	NOUN
ejde-629	256	50	βn	βn	AUX
ejde-629	256	51	γ	γ	X
ejde-629	256	52	≤	≤	NOUN
ejde-629	256	53	∥∇ωj(s)∥	∥∇ωj(s)∥	NUM
ejde-629	256	54	β2n	β2n	PROPN
ejde-629	256	55	γ	γ	X
ejde-629	256	56	∥∥∥|∇uj(s)|β−1	∥∥∥|∇uj(s)|β−1	X
ejde-629	256	57	+	+	NUM
ejde-629	256	58	|∇uj−1(s)|β−1	|∇uj−1(s)|β−1	ADJ
ejde-629	256	59	∥∥∥	∥∥∥	NUM
ejde-629	256	60	β2n	β2n	PUNCT
ejde-629	256	61	γ(β−1	γ(β−1	NOUN
ejde-629	256	62	)	)	PUNCT
ejde-629	256	63	≤	≤	NOUN
ejde-629	256	64	∥∇ωj(s)∥	∥∇ωj(s)∥	NUM
ejde-629	257	1	β2n	β2n	PUNCT
ejde-629	257	2	γ	γ	X
ejde-629	257	3	(	(	PUNCT
ejde-629	257	4	∥∇uj(s)∥β−1	∥∇uj(s)∥β−1	ADP
ejde-629	257	5	β2n	β2n	PART
ejde-629	257	6	γ	γ	X
ejde-629	257	7	+	+	CCONJ
ejde-629	257	8	∥∇uj−1(s)∥β−1	∥∇uj−1(s)∥β−1	ADV
ejde-629	257	9	β2n	β2n	ADJ
ejde-629	257	10	γ	γ	NOUN
ejde-629	257	11	)	)	PUNCT
ejde-629	257	12	≤	≤	NUM
ejde-629	257	13	s−	s−	PROPN
ejde-629	257	14	α	α	NOUN
ejde-629	257	15	2	2	NUM
ejde-629	258	1	+	+	NOUN
ejde-629	258	2	αγ	αγ	PROPN
ejde-629	258	3	4β	4β	PROPN
ejde-629	258	4	r̃(t	r̃(t	PROPN
ejde-629	258	5	)	)	PUNCT
ejde-629	258	6	j	j	PROPN
ejde-629	258	7	(	(	PUNCT
ejde-629	258	8	r(t	r(t	NOUN
ejde-629	258	9	)	)	PUNCT
ejde-629	258	10	β−1	β−1	PUNCT
ejde-629	258	11	j	j	PROPN
ejde-629	259	1	+	+	NOUN
ejde-629	259	2	r(t	r(t	NOUN
ejde-629	259	3	)	)	PUNCT
ejde-629	260	1	β−1	β−1	PUNCT
ejde-629	260	2	j−1	j−1	PROPN
ejde-629	260	3	)	)	PUNCT
ejde-629	260	4	.	.	PUNCT
ejde-629	261	1	then	then	ADV
ejde-629	261	2	for	for	ADP
ejde-629	261	3	r(t	r(t	NOUN
ejde-629	261	4	)	)	PUNCT
ejde-629	261	5	0	0	NUM
ejde-629	261	6	≤	≤	NUM
ejde-629	261	7	ε0	ε0	PROPN
ejde-629	261	8	,	,	PUNCT
ejde-629	261	9	we	we	PRON
ejde-629	261	10	have	have	AUX
ejde-629	261	11	∥∇2uj−1(s	∥∇2uj−1(	VERB
ejde-629	261	12	)	)	PUNCT
ejde-629	261	13	·	·	PUNCT
ejde-629	262	1	(	(	PUNCT
ejde-629	262	2	f	f	X
ejde-629	262	3	′(∇uj(s))−	′(∇uj(s))−	PROPN
ejde-629	262	4	f	f	PROPN
ejde-629	262	5	′(∇uj−1(s	′(∇uj−1(	NOUN
ejde-629	262	6	)	)	PUNCT
ejde-629	262	7	)	)	PUNCT
ejde-629	262	8	)	)	PUNCT
ejde-629	263	1	∥	∥	PUNCT
ejde-629	263	2	βn	βn	VERB
ejde-629	263	3	2−β+γ	2−β+γ	NUM
ejde-629	263	4	≤	≤	NOUN
ejde-629	263	5	∥∇2uj−1(s)∥	∥∇2uj−1(s)∥	ADP
ejde-629	263	6	βn	βn	NOUN
ejde-629	263	7	2−β	2−β	NUM
ejde-629	264	1	∥f	∥f	PROPN
ejde-629	264	2	′(∇uj(s))−	′(∇uj(s))−	ADJ
ejde-629	264	3	f	f	PROPN
ejde-629	264	4	′(∇uj−1(s))∥	′(∇uj−1(s))∥	NOUN
ejde-629	264	5	βn	βn	VERB
ejde-629	264	6	γ	γ	X
ejde-629	264	7	≤	≤	ADJ
ejde-629	264	8	s−α+αγ	s−α+αγ	PROPN
ejde-629	264	9	4β	4β	PROPN
ejde-629	264	10	r̃(t	r̃(t	PROPN
ejde-629	264	11	)	)	PUNCT
ejde-629	264	12	jr(t	jr(t	PUNCT
ejde-629	264	13	)	)	PUNCT
ejde-629	265	1	j−1	j−1	NOUN
ejde-629	265	2	(	(	PUNCT
ejde-629	265	3	r(t	r(t	NOUN
ejde-629	265	4	)	)	PUNCT
ejde-629	265	5	β−1	β−1	PUNCT
ejde-629	265	6	j	j	PROPN
ejde-629	266	1	+	+	NOUN
ejde-629	266	2	r(t	r(t	NOUN
ejde-629	266	3	)	)	PUNCT
ejde-629	266	4	β−1	β−1	PUNCT
ejde-629	267	1	j−1	j−1	X
ejde-629	267	2	)	)	PUNCT
ejde-629	267	3	≤	≤	NUM
ejde-629	268	1	cs−α+αγ	cs−α+αγ	NOUN
ejde-629	268	2	4β	4β	PROPN
ejde-629	268	3	r̃(t	r̃(t	PROPN
ejde-629	268	4	)	)	PUNCT
ejde-629	268	5	jr(t	jr(t	PUNCT
ejde-629	268	6	)	)	PUNCT
ejde-629	268	7	β0	β0	NOUN
ejde-629	268	8	.	.	PUNCT
ejde-629	269	1	(	(	PUNCT
ejde-629	269	2	3.16	3.16	NUM
ejde-629	269	3	)	)	PUNCT
ejde-629	269	4	applying	apply	VERB
ejde-629	269	5	the	the	DET
ejde-629	269	6	differential	differential	ADJ
ejde-629	269	7	operator	operator	NOUN
ejde-629	269	8	∇	∇	X
ejde-629	269	9	to	to	ADP
ejde-629	269	10	(	(	PUNCT
ejde-629	269	11	3.13	3.13	NUM
ejde-629	269	12	)	)	PUNCT
ejde-629	269	13	,	,	PUNCT
ejde-629	269	14	and	and	CCONJ
ejde-629	269	15	combining	combine	VERB
ejde-629	269	16	this	this	PRON
ejde-629	269	17	with	with	ADP
ejde-629	269	18	(	(	PUNCT
ejde-629	269	19	3.15	3.15	NUM
ejde-629	269	20	)	)	PUNCT
ejde-629	269	21	–	–	PUNCT
ejde-629	269	22	(	(	PUNCT
ejde-629	269	23	3.16	3.16	NUM
ejde-629	269	24	)	)	PUNCT
ejde-629	269	25	,	,	PUNCT
ejde-629	269	26	we	we	PRON
ejde-629	269	27	have	have	VERB
ejde-629	269	28	∥∇ωj+1∥	∥∇ωj+1∥	PRON
ejde-629	269	29	β2n	β2n	PUNCT
ejde-629	270	1	γ	γ	PROPN
ejde-629	270	2	≤	≤	X
ejde-629	270	3	∫	∫	PROPN
ejde-629	270	4	t	t	PROPN
ejde-629	270	5	0	0	NUM
ejde-629	270	6	(	(	PUNCT
ejde-629	270	7	t−	t−	PROPN
ejde-629	270	8	s)α−1∥∇eα	s)α−1∥∇eα	PROPN
ejde-629	270	9	,	,	PUNCT
ejde-629	270	10	α(−(t−	α(−(t−	NOUN
ejde-629	270	11	s)αa)∇2ωj	s)αa)∇2ωj	NOUN
ejde-629	270	12	·	·	PUNCT
ejde-629	270	13	f	f	X
ejde-629	271	1	′(∇uj)∥	′(∇uj)∥	PROPN
ejde-629	271	2	β2n	β2n	NOUN
ejde-629	272	1	γ	γ	X
ejde-629	272	2	ds	ds	PROPN
ejde-629	272	3	+	+	CCONJ
ejde-629	272	4	∫	∫	PROPN
ejde-629	272	5	t	t	PROPN
ejde-629	272	6	0	0	NUM
ejde-629	272	7	(	(	PUNCT
ejde-629	272	8	t−	t−	PROPN
ejde-629	272	9	s)α−1∥∇eα	s)α−1∥∇eα	PROPN
ejde-629	272	10	,	,	PUNCT
ejde-629	272	11	α(−(t−	α(−(t−	NUM
ejde-629	272	12	s)αa)∇2uj−1	s)αa)∇2uj−1	NOUN
ejde-629	272	13	·	·	PUNCT
ejde-629	272	14	(	(	PUNCT
ejde-629	272	15	f	f	X
ejde-629	272	16	′(∇uj)−	′(∇uj)−	NOUN
ejde-629	272	17	f	f	PROPN
ejde-629	272	18	′(∇uj−1	′(∇uj−1	NOUN
ejde-629	272	19	)	)	PUNCT
ejde-629	272	20	)	)	PUNCT
ejde-629	273	1	∥	∥	PUNCT
ejde-629	273	2	β2n	β2n	PUNCT
ejde-629	274	1	γ	γ	X
ejde-629	274	2	ds	ds	ADJ
ejde-629	274	3	≤	≤	PROPN
ejde-629	274	4	c	c	PROPN
ejde-629	274	5	∫	∫	PROPN
ejde-629	274	6	t	t	PROPN
ejde-629	274	7	0	0	NUM
ejde-629	274	8	(	(	PUNCT
ejde-629	274	9	t−	t−	PROPN
ejde-629	274	10	s	s	PART
ejde-629	274	11	)	)	PUNCT
ejde-629	274	12	α−1	α−1	PROPN
ejde-629	274	13	+	+	SYM
ejde-629	274	14	αγ	αγ	PROPN
ejde-629	274	15	4β2	4β2	NUM
ejde-629	274	16	−	−	NUM
ejde-629	274	17	α	α	NOUN
ejde-629	274	18	2β−αγ	2β−αγ	NOUN
ejde-629	274	19	4β	4β	NOUN
ejde-629	274	20	∥∇2ωj	∥∇2ωj	NOUN
ejde-629	274	21	·	·	PUNCT
ejde-629	274	22	f	f	X
ejde-629	274	23	′(∇uj)∥	′(∇uj)∥	PROPN
ejde-629	274	24	βn	βn	VERB
ejde-629	274	25	2−β+γ	2−β+γ	NUM
ejde-629	274	26	ds	ds	NOUN
ejde-629	274	27	+	+	CCONJ
ejde-629	274	28	c	c	NOUN
ejde-629	274	29	∫	∫	PROPN
ejde-629	274	30	t	t	PROPN
ejde-629	274	31	0	0	NUM
ejde-629	274	32	(	(	PUNCT
ejde-629	274	33	t−	t−	PROPN
ejde-629	274	34	s	s	PART
ejde-629	274	35	)	)	PUNCT
ejde-629	274	36	α−1	α−1	PROPN
ejde-629	274	37	+	+	SYM
ejde-629	274	38	αγ	αγ	PROPN
ejde-629	274	39	4β2	4β2	NUM
ejde-629	274	40	−	−	NUM
ejde-629	274	41	α	α	NOUN
ejde-629	274	42	2β−αγ	2β−αγ	NUM
ejde-629	274	43	4β	4β	NOUN
ejde-629	274	44	∥∇2uj−1	∥∇2uj−1	NOUN
ejde-629	274	45	·	·	PUNCT
ejde-629	274	46	(	(	PUNCT
ejde-629	274	47	f	f	X
ejde-629	274	48	′(∇uj)−	′(∇uj)−	NOUN
ejde-629	274	49	f	f	PROPN
ejde-629	274	50	′(∇uj−1	′(∇uj−1	NOUN
ejde-629	274	51	)	)	PUNCT
ejde-629	274	52	)	)	PUNCT
ejde-629	275	1	∥	∥	PUNCT
ejde-629	275	2	βn	βn	VERB
ejde-629	275	3	2−β+γ	2−β+γ	NUM
ejde-629	275	4	ds	ds	ADJ
ejde-629	275	5	≤	≤	NUM
ejde-629	275	6	cr̃(t	cr̃(t	NOUN
ejde-629	275	7	)	)	PUNCT
ejde-629	275	8	jr(t	jr(t	PUNCT
ejde-629	275	9	)	)	PUNCT
ejde-629	275	10	β0	β0	NOUN
ejde-629	275	11	∫	∫	PROPN
ejde-629	275	12	t	t	PROPN
ejde-629	275	13	0	0	NUM
ejde-629	275	14	(	(	PUNCT
ejde-629	275	15	t−	t−	PROPN
ejde-629	275	16	s	s	PART
ejde-629	275	17	)	)	PUNCT
ejde-629	275	18	α−1	α−1	PROPN
ejde-629	275	19	+	+	SYM
ejde-629	275	20	αγ	αγ	PROPN
ejde-629	275	21	4β2	4β2	NUM
ejde-629	275	22	−	−	NUM
ejde-629	275	23	α	α	NOUN
ejde-629	275	24	2β−αγ	2β−αγ	NOUN
ejde-629	275	25	4β	4β	NOUN
ejde-629	275	26	s−α+αγ	s−α+αγ	PROPN
ejde-629	275	27	4β	4β	NOUN
ejde-629	275	28	ds	ds	VERB
ejde-629	275	29	≤	≤	NUM
ejde-629	275	30	ct	ct	NUM
ejde-629	275	31	αγ	αγ	PROPN
ejde-629	275	32	4β2	4β2	NUM
ejde-629	275	33	−	−	NOUN
ejde-629	276	1	α	α	NUM
ejde-629	276	2	2β	2β	NUM
ejde-629	276	3	r̃(t	r̃(t	PROPN
ejde-629	276	4	)	)	PUNCT
ejde-629	276	5	jr(t	jr(t	PUNCT
ejde-629	276	6	)	)	PUNCT
ejde-629	277	1	β0	β0	NOUN
ejde-629	277	2	,	,	PUNCT
ejde-629	277	3	j	j	PROPN
ejde-629	277	4	≥	≥	PROPN
ejde-629	277	5	1	1	NUM
ejde-629	277	6	.	.	PUNCT
ejde-629	278	1	(	(	PUNCT
ejde-629	278	2	3.17	3.17	NUM
ejde-629	278	3	)	)	PUNCT
ejde-629	278	4	similarly	similarly	ADV
ejde-629	278	5	,	,	PUNCT
ejde-629	278	6	we	we	PRON
ejde-629	278	7	have	have	VERB
ejde-629	278	8	∥∇2ωj+1∥	∥∇2ωj+1∥	NOUN
ejde-629	278	9	βn	βn	VERB
ejde-629	278	10	2−β	2−β	NUM
ejde-629	278	11	≤	≤	NUM
ejde-629	278	12	∫	∫	PROPN
ejde-629	278	13	t	t	NOUN
ejde-629	278	14	0	0	NUM
ejde-629	278	15	(	(	PUNCT
ejde-629	278	16	t−	t−	PROPN
ejde-629	278	17	s)α−1∥∇2eα	s)α−1∥∇2eα	NOUN
ejde-629	278	18	,	,	PUNCT
ejde-629	278	19	α(−(t−	α(−(t−	PROPN
ejde-629	278	20	s)αa)∇2ωj	s)αa)∇2ωj	NOUN
ejde-629	278	21	·	·	PUNCT
ejde-629	279	1	f	f	PROPN
ejde-629	279	2	′(∇uj)∥	′(∇uj)∥	PROPN
ejde-629	279	3	βn	βn	VERB
ejde-629	279	4	2−β	2−β	NUM
ejde-629	279	5	ds	ds	NOUN
ejde-629	279	6	+	+	CCONJ
ejde-629	279	7	∫	∫	PROPN
ejde-629	279	8	t	t	PROPN
ejde-629	279	9	0	0	NUM
ejde-629	279	10	(	(	PUNCT
ejde-629	279	11	t−	t−	PROPN
ejde-629	279	12	s)α−1∥∇2eα	s)α−1∥∇2eα	NOUN
ejde-629	279	13	,	,	PUNCT
ejde-629	279	14	α(−(t−	α(−(t−	PROPN
ejde-629	279	15	s)αa)∇2uj−1	s)αa)∇2uj−1	NOUN
ejde-629	279	16	·	·	PUNCT
ejde-629	279	17	(	(	PUNCT
ejde-629	279	18	f	f	X
ejde-629	279	19	′(∇uj)−	′(∇uj)−	NOUN
ejde-629	279	20	f	f	PROPN
ejde-629	279	21	′(∇uj−1	′(∇uj−1	NOUN
ejde-629	279	22	)	)	PUNCT
ejde-629	279	23	)	)	PUNCT
ejde-629	279	24	∥	∥	PUNCT
ejde-629	279	25	βn	βn	VERB
ejde-629	279	26	2−β	2−β	NUM
ejde-629	279	27	ds	ds	NOUN
ejde-629	279	28	≤	≤	NUM
ejde-629	279	29	c	c	PROPN
ejde-629	279	30	∫	∫	PROPN
ejde-629	279	31	t	t	PROPN
ejde-629	279	32	0	0	NUM
ejde-629	279	33	(	(	PUNCT
ejde-629	279	34	t−	t−	PROPN
ejde-629	279	35	s	s	X
ejde-629	279	36	)	)	PUNCT
ejde-629	279	37	α	α	DET
ejde-629	279	38	2	2	NUM
ejde-629	279	39	−1−αγ	−1−αγ	NOUN
ejde-629	279	40	4β	4β	NOUN
ejde-629	279	41	∥∇2ωj	∥∇2ωj	PROPN
ejde-629	279	42	·	·	PUNCT
ejde-629	279	43	f	f	X
ejde-629	279	44	′(∇uj)∥	′(∇uj)∥	PROPN
ejde-629	279	45	βn	βn	VERB
ejde-629	279	46	2−β+γ	2−β+γ	NUM
ejde-629	279	47	ds	ds	NOUN
ejde-629	279	48	12	12	NUM
ejde-629	279	49	q.	q.	PROPN
ejde-629	279	50	liu	liu	PROPN
ejde-629	279	51	,	,	PUNCT
ejde-629	279	52	w.	w.	PROPN
ejde-629	279	53	zhu	zhu	PROPN
ejde-629	279	54	,	,	PUNCT
ejde-629	279	55	h.	h.	PROPN
ejde-629	279	56	ye	ye	PROPN
ejde-629	279	57	ejde-2024/58	ejde-2024/58	PROPN
ejde-629	280	1	+	+	CCONJ
ejde-629	280	2	c	c	AUX
ejde-629	280	3	∫	∫	PROPN
ejde-629	280	4	t	t	PROPN
ejde-629	280	5	0	0	NUM
ejde-629	280	6	(	(	PUNCT
ejde-629	280	7	t−	t−	PROPN
ejde-629	280	8	s	s	X
ejde-629	280	9	)	)	PUNCT
ejde-629	280	10	α	α	DET
ejde-629	280	11	2	2	NUM
ejde-629	280	12	−1−αγ	−1−αγ	NOUN
ejde-629	280	13	4β	4β	NUM
ejde-629	280	14	∥∇2uj−1	∥∇2uj−1	NOUN
ejde-629	280	15	·	·	PUNCT
ejde-629	280	16	(	(	PUNCT
ejde-629	280	17	f	f	X
ejde-629	280	18	′(∇uj)−	′(∇uj)−	NOUN
ejde-629	280	19	f	f	PROPN
ejde-629	280	20	′(∇uj−1	′(∇uj−1	NOUN
ejde-629	280	21	)	)	PUNCT
ejde-629	280	22	)	)	PUNCT
ejde-629	280	23	∥	∥	PUNCT
ejde-629	280	24	βn	βn	VERB
ejde-629	280	25	2−β+γ	2−β+γ	NUM
ejde-629	280	26	ds	ds	ADJ
ejde-629	280	27	≤	≤	NUM
ejde-629	280	28	cr̃(t	cr̃(t	NOUN
ejde-629	280	29	)	)	PUNCT
ejde-629	280	30	jr(t	jr(t	PUNCT
ejde-629	280	31	)	)	PUNCT
ejde-629	280	32	β0	β0	NOUN
ejde-629	280	33	∫	∫	PROPN
ejde-629	280	34	t	t	PROPN
ejde-629	280	35	0	0	NUM
ejde-629	280	36	(	(	PUNCT
ejde-629	280	37	t−	t−	PROPN
ejde-629	280	38	s	s	X
ejde-629	280	39	)	)	PUNCT
ejde-629	280	40	α	α	DET
ejde-629	280	41	2	2	NUM
ejde-629	280	42	−1−αγ	−1−αγ	NOUN
ejde-629	280	43	4β	4β	NOUN
ejde-629	280	44	s−α+αγ	s−α+αγ	PROPN
ejde-629	280	45	4β	4β	NOUN
ejde-629	280	46	ds	ds	VERB
ejde-629	280	47	≤	≤	NUM
ejde-629	280	48	ct−	ct−	DET
ejde-629	280	49	α	α	NOUN
ejde-629	280	50	2	2	NUM
ejde-629	280	51	r̃(t	r̃(t	PROPN
ejde-629	280	52	)	)	PUNCT
ejde-629	280	53	jr(t	jr(t	PUNCT
ejde-629	280	54	)	)	PUNCT
ejde-629	280	55	β0	β0	NOUN
ejde-629	280	56	,	,	PUNCT
ejde-629	280	57	j	j	PROPN
ejde-629	280	58	≥	≥	PROPN
ejde-629	280	59	1	1	NUM
ejde-629	280	60	.	.	PUNCT
ejde-629	281	1	(	(	PUNCT
ejde-629	281	2	3.18	3.18	NUM
ejde-629	281	3	)	)	PUNCT
ejde-629	281	4	combining	combine	VERB
ejde-629	281	5	(	(	PUNCT
ejde-629	281	6	3.14	3.14	NUM
ejde-629	281	7	)	)	PUNCT
ejde-629	281	8	,	,	PUNCT
ejde-629	281	9	(	(	PUNCT
ejde-629	281	10	3.17	3.17	NUM
ejde-629	281	11	)	)	PUNCT
ejde-629	281	12	with	with	ADP
ejde-629	281	13	(	(	PUNCT
ejde-629	281	14	3.18	3.18	NUM
ejde-629	281	15	)	)	PUNCT
ejde-629	281	16	,	,	PUNCT
ejde-629	281	17	for	for	ADP
ejde-629	281	18	any	any	DET
ejde-629	281	19	fixed	fix	VERB
ejde-629	281	20	t	t	PROPN
ejde-629	281	21	>	>	X
ejde-629	281	22	0	0	PROPN
ejde-629	281	23	,	,	PUNCT
ejde-629	281	24	we	we	PRON
ejde-629	281	25	have	have	VERB
ejde-629	281	26	r̃(t	r̃(t	NOUN
ejde-629	281	27	)	)	PUNCT
ejde-629	281	28	j+1	j+1	ADJ
ejde-629	281	29	≤	≤	NUM
ejde-629	281	30	cr̃(t	cr̃(t	NOUN
ejde-629	281	31	)	)	PUNCT
ejde-629	281	32	jr(t	jr(t	PUNCT
ejde-629	281	33	)	)	PUNCT
ejde-629	282	1	β0	β0	ADV
ejde-629	282	2	,	,	PUNCT
ejde-629	282	3	j	j	PROPN
ejde-629	282	4	=	=	SYM
ejde-629	282	5	1	1	NUM
ejde-629	282	6	,	,	PUNCT
ejde-629	282	7	2	2	NUM
ejde-629	282	8	,	,	PUNCT
ejde-629	282	9	.	.	PUNCT
ejde-629	282	10	.	.	PUNCT
ejde-629	282	11	.	.	PUNCT
ejde-629	283	1	(	(	PUNCT
ejde-629	283	2	3.19	3.19	NUM
ejde-629	283	3	)	)	PUNCT
ejde-629	283	4	where	where	SCONJ
ejde-629	283	5	c	c	X
ejde-629	283	6	>	>	X
ejde-629	283	7	0	0	NUM
ejde-629	283	8	is	be	AUX
ejde-629	283	9	independent	independent	ADJ
ejde-629	283	10	of	of	ADP
ejde-629	283	11	t	t	PROPN
ejde-629	283	12	.	.	PUNCT
ejde-629	284	1	noting	note	VERB
ejde-629	284	2	that	that	SCONJ
ejde-629	284	3	ω1	ω1	PROPN
ejde-629	284	4	=	=	SYM
ejde-629	284	5	∫	∫	PROPN
ejde-629	284	6	t	t	PROPN
ejde-629	284	7	0	0	NUM
ejde-629	284	8	(	(	PUNCT
ejde-629	284	9	t−	t−	PROPN
ejde-629	284	10	s)α−1eα	s)α−1eα	PROPN
ejde-629	284	11	,	,	PUNCT
ejde-629	284	12	α(−(t−	α(−(t−	NOUN
ejde-629	284	13	s)αa)∇	s)αa)∇	NOUN
ejde-629	284	14	·	·	PUNCT
ejde-629	284	15	f(∇u0	f(∇u0	ADJ
ejde-629	284	16	)	)	PUNCT
ejde-629	284	17	ds	ds	PROPN
ejde-629	284	18	,	,	PUNCT
ejde-629	284	19	following	follow	VERB
ejde-629	284	20	the	the	DET
ejde-629	284	21	same	same	ADJ
ejde-629	284	22	idea	idea	NOUN
ejde-629	284	23	in	in	ADP
ejde-629	284	24	the	the	DET
ejde-629	284	25	proof	proof	NOUN
ejde-629	284	26	(	(	PUNCT
ejde-629	284	27	3.17	3.17	NUM
ejde-629	284	28	)	)	PUNCT
ejde-629	284	29	and	and	CCONJ
ejde-629	284	30	(	(	PUNCT
ejde-629	284	31	3.18	3.18	NUM
ejde-629	284	32	)	)	PUNCT
ejde-629	284	33	,	,	PUNCT
ejde-629	284	34	we	we	PRON
ejde-629	284	35	obtain	obtain	VERB
ejde-629	284	36	r̃(t	r̃(t	PROPN
ejde-629	284	37	)	)	PUNCT
ejde-629	284	38	1	1	NUM
ejde-629	284	39	≤	≤	NUM
ejde-629	284	40	cr̃(t	cr̃(t	NOUN
ejde-629	284	41	)	)	PUNCT
ejde-629	284	42	0r(t	0r(t	NOUN
ejde-629	284	43	)	)	PUNCT
ejde-629	284	44	β0	β0	NOUN
ejde-629	284	45	=	=	SYM
ejde-629	284	46	cr(t	cr(t	NOUN
ejde-629	284	47	)	)	PUNCT
ejde-629	284	48	1+β	1+β	NUM
ejde-629	284	49	0	0	NUM
ejde-629	284	50	.	.	PUNCT
ejde-629	285	1	(	(	PUNCT
ejde-629	285	2	3.20	3.20	NUM
ejde-629	285	3	)	)	PUNCT
ejde-629	285	4	combining	combine	VERB
ejde-629	285	5	(	(	PUNCT
ejde-629	285	6	3.19	3.19	NUM
ejde-629	285	7	)	)	PUNCT
ejde-629	285	8	with	with	ADP
ejde-629	285	9	(	(	PUNCT
ejde-629	285	10	3.20	3.20	NUM
ejde-629	285	11	)	)	PUNCT
ejde-629	285	12	,	,	PUNCT
ejde-629	285	13	we	we	PRON
ejde-629	285	14	finally	finally	ADV
ejde-629	285	15	derive	derive	VERB
ejde-629	285	16	r̃(t	r̃(t	PROPN
ejde-629	285	17	)	)	PUNCT
ejde-629	285	18	j	j	PROPN
ejde-629	285	19	≤	≤	PROPN
ejde-629	285	20	r(t	r(t	NOUN
ejde-629	285	21	)	)	PUNCT
ejde-629	285	22	0	0	NUM
ejde-629	285	23	(	(	PUNCT
ejde-629	285	24	cr(t	cr(t	NUM
ejde-629	285	25	)	)	PUNCT
ejde-629	285	26	β0	β0	NOUN
ejde-629	285	27	)	)	PUNCT
ejde-629	285	28	j	j	PROPN
ejde-629	285	29	,	,	PUNCT
ejde-629	285	30	j	j	PROPN
ejde-629	285	31	=	=	SYM
ejde-629	285	32	0	0	NUM
ejde-629	285	33	,	,	PUNCT
ejde-629	285	34	1	1	NUM
ejde-629	285	35	,	,	PUNCT
ejde-629	285	36	2	2	NUM
ejde-629	285	37	,	,	PUNCT
ejde-629	285	38	.	.	PUNCT
ejde-629	285	39	.	.	PUNCT
ejde-629	286	1	.	.	PUNCT
ejde-629	287	1	provided	provide	VERB
ejde-629	287	2	that	that	DET
ejde-629	287	3	r(t	r(t	NOUN
ejde-629	287	4	)	)	PUNCT
ejde-629	287	5	0	0	NUM
ejde-629	287	6	≤	≤	NUM
ejde-629	287	7	ε0	ε0	PROPN
ejde-629	287	8	.	.	PUNCT
ejde-629	288	1	with	with	ADP
ejde-629	288	2	the	the	DET
ejde-629	288	3	help	help	NOUN
ejde-629	288	4	of	of	ADP
ejde-629	288	5	a	a	DET
ejde-629	288	6	priori	priori	ADJ
ejde-629	288	7	estimates	estimate	NOUN
ejde-629	288	8	above	above	ADV
ejde-629	288	9	,	,	PUNCT
ejde-629	288	10	now	now	ADV
ejde-629	288	11	we	we	PRON
ejde-629	288	12	can	can	AUX
ejde-629	288	13	estimate	estimate	VERB
ejde-629	288	14	ωj	ωj	ADP
ejde-629	288	15	,	,	PUNCT
ejde-629	288	16	∥ωj+1∥	∥ωj+1∥	NUM
ejde-629	288	17	βn	βn	NOUN
ejde-629	288	18	2−β	2−β	PROPN
ejde-629	288	19	≤	≤	NUM
ejde-629	288	20	∫	∫	PROPN
ejde-629	288	21	t	t	NOUN
ejde-629	288	22	0	0	NUM
ejde-629	288	23	(	(	PUNCT
ejde-629	288	24	t−	t−	PROPN
ejde-629	288	25	s)α−1∥eα	s)α−1∥eα	PROPN
ejde-629	288	26	,	,	PUNCT
ejde-629	288	27	α(−(t−	α(−(t−	PROPN
ejde-629	288	28	s)αa)∇2ωj	s)αa)∇2ωj	NOUN
ejde-629	288	29	·	·	PUNCT
ejde-629	289	1	f	f	PROPN
ejde-629	289	2	′(∇uj)∥	′(∇uj)∥	PROPN
ejde-629	289	3	βn	βn	VERB
ejde-629	289	4	2−β	2−β	NUM
ejde-629	289	5	ds	ds	NOUN
ejde-629	289	6	+	+	CCONJ
ejde-629	289	7	∫	∫	PROPN
ejde-629	289	8	t	t	PROPN
ejde-629	289	9	0	0	NUM
ejde-629	289	10	(	(	PUNCT
ejde-629	289	11	t−	t−	PROPN
ejde-629	289	12	s)α−1∥eα	s)α−1∥eα	PROPN
ejde-629	289	13	,	,	PUNCT
ejde-629	289	14	α(−(t−	α(−(t−	NUM
ejde-629	289	15	s)αa)∇2uj−1	s)αa)∇2uj−1	NOUN
ejde-629	289	16	·	·	PUNCT
ejde-629	289	17	(	(	PUNCT
ejde-629	289	18	f	f	X
ejde-629	289	19	′(∇uj)−	′(∇uj)−	NOUN
ejde-629	289	20	f	f	PROPN
ejde-629	289	21	′(∇uj−1	′(∇uj−1	NOUN
ejde-629	289	22	)	)	PUNCT
ejde-629	289	23	)	)	PUNCT
ejde-629	289	24	∥	∥	PUNCT
ejde-629	289	25	βn	βn	VERB
ejde-629	289	26	2−β	2−β	NUM
ejde-629	289	27	ds	ds	NOUN
ejde-629	289	28	≤	≤	NUM
ejde-629	289	29	c	c	PROPN
ejde-629	289	30	∫	∫	PROPN
ejde-629	289	31	t	t	PROPN
ejde-629	289	32	0	0	NUM
ejde-629	290	1	(	(	PUNCT
ejde-629	290	2	t−	t−	PROPN
ejde-629	290	3	s)α−1−αγ	s)α−1−αγ	NOUN
ejde-629	290	4	4β	4β	NOUN
ejde-629	290	5	∥∇2ωj	∥∇2ωj	NOUN
ejde-629	290	6	·	·	PUNCT
ejde-629	290	7	f	f	X
ejde-629	290	8	′(∇uj)∥	′(∇uj)∥	PROPN
ejde-629	290	9	βn	βn	VERB
ejde-629	290	10	2−β+γ	2−β+γ	NUM
ejde-629	290	11	ds	ds	NOUN
ejde-629	290	12	+	+	CCONJ
ejde-629	290	13	c	c	NOUN
ejde-629	290	14	∫	∫	PROPN
ejde-629	290	15	t	t	PROPN
ejde-629	290	16	0	0	NUM
ejde-629	290	17	(	(	PUNCT
ejde-629	290	18	t−	t−	PROPN
ejde-629	290	19	s)α−1−αγ	s)α−1−αγ	PROPN
ejde-629	290	20	4β	4β	NUM
ejde-629	290	21	∥∇2uj−1	∥∇2uj−1	NOUN
ejde-629	290	22	·	·	PUNCT
ejde-629	290	23	(	(	PUNCT
ejde-629	290	24	f	f	X
ejde-629	290	25	′(∇uj)−	′(∇uj)−	NOUN
ejde-629	290	26	f	f	PROPN
ejde-629	290	27	′(∇uj−1	′(∇uj−1	NOUN
ejde-629	290	28	)	)	PUNCT
ejde-629	290	29	)	)	PUNCT
ejde-629	290	30	∥	∥	PUNCT
ejde-629	290	31	βn	βn	VERB
ejde-629	290	32	2−β+γ	2−β+γ	NUM
ejde-629	290	33	ds	ds	ADJ
ejde-629	290	34	≤	≤	NUM
ejde-629	290	35	cr̃(t	cr̃(t	NOUN
ejde-629	290	36	)	)	PUNCT
ejde-629	290	37	jr(t	jr(t	PUNCT
ejde-629	290	38	)	)	PUNCT
ejde-629	290	39	β0	β0	NOUN
ejde-629	290	40	∫	∫	PROPN
ejde-629	290	41	t	t	PROPN
ejde-629	290	42	0	0	NUM
ejde-629	290	43	(	(	PUNCT
ejde-629	290	44	t−	t−	PROPN
ejde-629	290	45	s)α−1−αγ	s)α−1−αγ	NOUN
ejde-629	290	46	4β	4β	NOUN
ejde-629	290	47	s−α+αγ	s−α+αγ	PROPN
ejde-629	290	48	4β	4β	NOUN
ejde-629	290	49	ds	ds	VERB
ejde-629	290	50	≤	≤	NUM
ejde-629	290	51	r(t	r(t	NOUN
ejde-629	290	52	)	)	PUNCT
ejde-629	290	53	0	0	NUM
ejde-629	290	54	(	(	PUNCT
ejde-629	290	55	cr(t	cr(t	NUM
ejde-629	290	56	)	)	PUNCT
ejde-629	290	57	β0	β0	NOUN
ejde-629	290	58	)	)	PUNCT
ejde-629	290	59	j+1	j+1	PROPN
ejde-629	290	60	,	,	PUNCT
ejde-629	290	61	j	j	PROPN
ejde-629	290	62	≥	≥	PROPN
ejde-629	290	63	1	1	NUM
ejde-629	290	64	.	.	PUNCT
ejde-629	290	65	(	(	PUNCT
ejde-629	290	66	3.21	3.21	NUM
ejde-629	290	67	)	)	PUNCT
ejde-629	290	68	similarly	similarly	ADV
ejde-629	290	69	,	,	PUNCT
ejde-629	290	70	we	we	PRON
ejde-629	290	71	obtain	obtain	VERB
ejde-629	290	72	that	that	SCONJ
ejde-629	290	73	∥ω1∥	∥ω1∥	PROPN
ejde-629	290	74	βn	βn	AUX
ejde-629	290	75	2−β	2−β	NOUN
ejde-629	290	76	≤	≤	NOUN
ejde-629	290	77	cr(t	cr(t	NOUN
ejde-629	290	78	)	)	PUNCT
ejde-629	291	1	1+β	1+β	NUM
ejde-629	291	2	0	0	NUM
ejde-629	291	3	.	.	PUNCT
ejde-629	292	1	therefore	therefore	ADV
ejde-629	292	2	,	,	PUNCT
ejde-629	292	3	mj	mj	X
ejde-629	292	4	:	:	PUNCT
ejde-629	292	5	=	=	SYM
ejde-629	292	6	sup	sup	NOUN
ejde-629	292	7	0≤t≤t	0≤t≤t	NUM
ejde-629	292	8	∥ωj(t)∥	∥ωj(t)∥	PROPN
ejde-629	292	9	βn	βn	VERB
ejde-629	292	10	2−β	2−β	NUM
ejde-629	292	11	≤	≤	ADJ
ejde-629	292	12	r(t	r(t	NOUN
ejde-629	292	13	)	)	PUNCT
ejde-629	292	14	0	0	NUM
ejde-629	292	15	(	(	PUNCT
ejde-629	292	16	cr(t	cr(t	NUM
ejde-629	292	17	)	)	PUNCT
ejde-629	292	18	β0	β0	NOUN
ejde-629	292	19	)	)	PUNCT
ejde-629	292	20	j	j	PROPN
ejde-629	292	21	,	,	PUNCT
ejde-629	292	22	j	j	PROPN
ejde-629	292	23	≥	≥	NUM
ejde-629	292	24	0	0	NUM
ejde-629	292	25	and	and	CCONJ
ejde-629	292	26	the	the	DET
ejde-629	292	27	sequence	sequence	NOUN
ejde-629	292	28	{	{	PUNCT
ejde-629	292	29	mj}j≥0	mj}j≥0	NOUN
ejde-629	292	30	is	be	AUX
ejde-629	292	31	summable	summable	ADJ
ejde-629	292	32	provided	provide	VERB
ejde-629	292	33	that	that	SCONJ
ejde-629	292	34	r(t	r(t	NOUN
ejde-629	292	35	)	)	PUNCT
ejde-629	292	36	0	0	PUNCT
ejde-629	293	1	<	<	X
ejde-629	293	2	min{ε0	min{ε0	NOUN
ejde-629	293	3	,	,	PUNCT
ejde-629	293	4	c−	c−	X
ejde-629	293	5	1	1	NUM
ejde-629	293	6	β	β	NOUN
ejde-629	293	7	}	}	PUNCT
ejde-629	293	8	.	.	PUNCT
ejde-629	294	1	(	(	PUNCT
ejde-629	294	2	3.22	3.22	NUM
ejde-629	294	3	)	)	PUNCT
ejde-629	294	4	ejde-2024/58	ejde-2024/58	ADJ
ejde-629	294	5	equations	equation	NOUN
ejde-629	294	6	modeling	model	VERB
ejde-629	294	7	thin	thin	ADJ
ejde-629	294	8	film	film	NOUN
ejde-629	294	9	growth	growth	NOUN
ejde-629	294	10	13	13	NUM
ejde-629	294	11	since	since	SCONJ
ejde-629	294	12	limt→0	limt→0	NOUN
ejde-629	294	13	+	+	SYM
ejde-629	294	14	r(t	r(t	NOUN
ejde-629	294	15	)	)	PUNCT
ejde-629	294	16	0	0	PUNCT
ejde-629	295	1	=	=	SYM
ejde-629	295	2	0	0	NUM
ejde-629	295	3	,	,	PUNCT
ejde-629	295	4	we	we	PRON
ejde-629	295	5	can	can	AUX
ejde-629	295	6	choose	choose	VERB
ejde-629	295	7	t	t	PROPN
ejde-629	295	8	>	>	X
ejde-629	295	9	0	0	PUNCT
ejde-629	296	1	small	small	ADJ
ejde-629	296	2	enough	enough	ADV
ejde-629	296	3	such	such	ADJ
ejde-629	296	4	that	that	SCONJ
ejde-629	296	5	(	(	PUNCT
ejde-629	296	6	3.22	3.22	NUM
ejde-629	296	7	)	)	PUNCT
ejde-629	296	8	holds	hold	VERB
ejde-629	296	9	.	.	PUNCT
ejde-629	297	1	then	then	ADV
ejde-629	297	2	lemma	lemma	PROPN
ejde-629	297	3	2.4	2.4	NUM
ejde-629	297	4	implies	imply	VERB
ejde-629	297	5	that	that	SCONJ
ejde-629	297	6	{	{	PUNCT
ejde-629	297	7	uj}j≥0	uj}j≥0	NOUN
ejde-629	297	8	is	be	AUX
ejde-629	297	9	a	a	DET
ejde-629	297	10	cauchy	cauchy	ADJ
ejde-629	297	11	sequence	sequence	NOUN
ejde-629	297	12	in	in	ADP
ejde-629	297	13	c([0	c([0	PROPN
ejde-629	297	14	,	,	PUNCT
ejde-629	297	15	t	t	X
ejde-629	297	16	]	]	PUNCT
ejde-629	297	17	;	;	PUNCT
ejde-629	297	18	l	l	X
ejde-629	297	19	βn	βn	X
ejde-629	297	20	2−β	2−β	NUM
ejde-629	297	21	(	(	PUNCT
ejde-629	297	22	ω	ω	NOUN
ejde-629	297	23	)	)	PUNCT
ejde-629	297	24	)	)	PUNCT
ejde-629	297	25	,	,	PUNCT
ejde-629	297	26	and	and	CCONJ
ejde-629	297	27	converges	converge	VERB
ejde-629	297	28	to	to	ADP
ejde-629	297	29	a	a	DET
ejde-629	297	30	unique	unique	ADJ
ejde-629	297	31	solution	solution	NOUN
ejde-629	297	32	u	u	PROPN
ejde-629	297	33	∈	∈	PROPN
ejde-629	297	34	c([0	c([0	NOUN
ejde-629	297	35	,	,	PUNCT
ejde-629	297	36	t	t	X
ejde-629	297	37	]	]	PUNCT
ejde-629	297	38	;	;	PUNCT
ejde-629	297	39	l	l	X
ejde-629	297	40	βn	βn	X
ejde-629	297	41	2−β	2−β	NUM
ejde-629	297	42	(	(	PUNCT
ejde-629	297	43	ω	ω	NOUN
ejde-629	297	44	)	)	PUNCT
ejde-629	297	45	)	)	PUNCT
ejde-629	297	46	of	of	ADP
ejde-629	297	47	the	the	DET
ejde-629	297	48	integral	integral	ADJ
ejde-629	297	49	equation	equation	NOUN
ejde-629	297	50	(	(	PUNCT
ejde-629	297	51	1.5	1.5	NUM
ejde-629	297	52	)	)	PUNCT
ejde-629	297	53	.	.	PUNCT
ejde-629	298	1	moreover	moreover	ADV
ejde-629	298	2	,	,	PUNCT
ejde-629	298	3	recalling	recall	VERB
ejde-629	298	4	that	that	SCONJ
ejde-629	298	5	u0(x	u0(x	NOUN
ejde-629	298	6	,	,	PUNCT
ejde-629	298	7	t	t	PROPN
ejde-629	298	8	)	)	PUNCT
ejde-629	298	9	=	=	SYM
ejde-629	298	10	eα(−tαa)φ	eα(−tαa)φ	NOUN
ejde-629	298	11	,	,	PUNCT
ejde-629	298	12	and	and	CCONJ
ejde-629	298	13	combining	combine	VERB
ejde-629	298	14	this	this	PRON
ejde-629	298	15	with	with	ADP
ejde-629	298	16	proposition	proposition	NOUN
ejde-629	298	17	2.5	2.5	NUM
ejde-629	298	18	,	,	PUNCT
ejde-629	298	19	we	we	PRON
ejde-629	298	20	obtain	obtain	VERB
ejde-629	298	21	r(t	r(t	NOUN
ejde-629	298	22	)	)	PUNCT
ejde-629	298	23	0	0	X
ejde-629	299	1	≤	≤	NUM
ejde-629	299	2	max	max	NOUN
ejde-629	299	3	{	{	PUNCT
ejde-629	299	4	sup	sup	PROPN
ejde-629	299	5	0≤t≤t	0≤t≤t	NUM
ejde-629	299	6	t	t	NOUN
ejde-629	299	7	α	α	PROPN
ejde-629	299	8	2β−	2β−	PROPN
ejde-629	299	9	αγ	αγ	SYM
ejde-629	299	10	4β2	4β2	NUM
ejde-629	299	11	∥∇u0(t)∥	∥∇u0(t)∥	NOUN
ejde-629	299	12	β2n	β2n	ADV
ejde-629	299	13	γ	γ	NOUN
ejde-629	299	14	,	,	PUNCT
ejde-629	299	15	sup	sup	NOUN
ejde-629	299	16	0≤t≤t	0≤t≤t	NUM
ejde-629	299	17	t	t	NOUN
ejde-629	299	18	α	α	NOUN
ejde-629	299	19	2	2	NUM
ejde-629	299	20	∥∇2u0(t)∥	∥∇2u0(t)∥	PROPN
ejde-629	299	21	βn	βn	VERB
ejde-629	299	22	2−β	2−β	NUM
ejde-629	299	23	}	}	PUNCT
ejde-629	299	24	≤	≤	NOUN
ejde-629	299	25	c∥φ∥	c∥φ∥	PROPN
ejde-629	299	26	βn	βn	PUNCT
ejde-629	299	27	2−β	2−β	NUM
ejde-629	299	28	.	.	PUNCT
ejde-629	300	1	so	so	ADV
ejde-629	300	2	if	if	SCONJ
ejde-629	300	3	∥φ∥	∥φ∥	VERB
ejde-629	300	4	βn	βn	X
ejde-629	300	5	2−β	2−β	NOUN
ejde-629	300	6	is	be	AUX
ejde-629	300	7	sufficiently	sufficiently	ADV
ejde-629	300	8	small	small	ADJ
ejde-629	300	9	,	,	PUNCT
ejde-629	300	10	the	the	DET
ejde-629	300	11	solution	solution	NOUN
ejde-629	300	12	u	u	NOUN
ejde-629	300	13	can	can	AUX
ejde-629	300	14	be	be	AUX
ejde-629	300	15	extended	extend	VERB
ejde-629	300	16	to	to	PART
ejde-629	300	17	be	be	AUX
ejde-629	300	18	global	global	ADJ
ejde-629	300	19	.	.	PUNCT
ejde-629	301	1	the	the	DET
ejde-629	301	2	proof	proof	NOUN
ejde-629	301	3	of	of	ADP
ejde-629	301	4	theorem	theorem	ADJ
ejde-629	301	5	1.2	1.2	NUM
ejde-629	301	6	is	be	AUX
ejde-629	301	7	complete	complete	ADJ
ejde-629	301	8	.	.	PUNCT
ejde-629	302	1	□	□	PUNCT
ejde-629	302	2	acknowledgements	acknowledgement	NOUN
ejde-629	302	3	.	.	PUNCT
ejde-629	303	1	this	this	DET
ejde-629	303	2	work	work	NOUN
ejde-629	303	3	is	be	AUX
ejde-629	303	4	supported	support	VERB
ejde-629	303	5	by	by	ADP
ejde-629	303	6	the	the	DET
ejde-629	303	7	nsfc	nsfc	NOUN
ejde-629	303	8	(	(	PUNCT
ejde-629	303	9	12271186	12271186	NUM
ejde-629	303	10	,	,	PUNCT
ejde-629	303	11	12271178	12271178	NUM
ejde-629	303	12	)	)	PUNCT
ejde-629	303	13	,	,	PUNCT
ejde-629	303	14	by	by	ADP
ejde-629	303	15	the	the	DET
ejde-629	303	16	guangdong	guangdong	PROPN
ejde-629	303	17	basic	basic	ADJ
ejde-629	303	18	and	and	CCONJ
ejde-629	303	19	applied	apply	VERB
ejde-629	303	20	basic	basic	ADJ
ejde-629	303	21	research	research	NOUN
ejde-629	303	22	foundation	foundation	NOUN
ejde-629	303	23	(	(	PUNCT
ejde-629	303	24	2022b1515120009	2022b1515120009	NUM
ejde-629	303	25	,	,	PUNCT
ejde-629	303	26	2022a1515010348	2022a1515010348	NOUN
ejde-629	303	27	)	)	PUNCT
ejde-629	303	28	,	,	PUNCT
ejde-629	303	29	by	by	ADP
ejde-629	303	30	the	the	DET
ejde-629	303	31	science	science	NOUN
ejde-629	303	32	and	and	CCONJ
ejde-629	303	33	technology	technology	NOUN
ejde-629	303	34	program	program	NOUN
ejde-629	303	35	of	of	ADP
ejde-629	303	36	shenzhen	shenzhen	PROPN
ejde-629	303	37	,	,	PUNCT
ejde-629	303	38	china	china	PROPN
ejde-629	303	39	(	(	PUNCT
ejde-629	303	40	20231121110406001	20231121110406001	NUM
ejde-629	303	41	,	,	PUNCT
ejde-629	303	42	20231120205244001	20231120205244001	NUM
ejde-629	303	43	)	)	PUNCT
ejde-629	303	44	,	,	PUNCT
ejde-629	303	45	and	and	CCONJ
ejde-629	303	46	by	by	ADP
ejde-629	303	47	the	the	DET
ejde-629	303	48	china	china	PROPN
ejde-629	303	49	scholarship	scholarship	PROPN
ejde-629	303	50	council	council	PROPN
ejde-629	303	51	(	(	PUNCT
ejde-629	303	52	202308440378	202308440378	NUM
ejde-629	303	53	)	)	PUNCT
ejde-629	303	54	.	.	PUNCT
ejde-629	304	1	references	reference	NOUN
ejde-629	304	2	[	[	X
ejde-629	304	3	1	1	NUM
ejde-629	304	4	]	]	PUNCT
ejde-629	304	5	h.	h.	PROPN
ejde-629	304	6	amann	amann	PROPN
ejde-629	304	7	;	;	PUNCT
ejde-629	304	8	dynamic	dynamic	ADJ
ejde-629	304	9	theory	theory	NOUN
ejde-629	304	10	of	of	ADP
ejde-629	304	11	quasilinear	quasilinear	PROPN
ejde-629	304	12	parabolic	parabolic	PROPN
ejde-629	304	13	equations	equations	PROPN
ejde-629	304	14	ii	ii	PROPN
ejde-629	304	15	.	.	PUNCT
ejde-629	304	16	reaction	reaction	NOUN
ejde-629	304	17	-	-	PUNCT
ejde-629	304	18	diffusion	diffusion	NOUN
ejde-629	304	19	systems	system	NOUN
ejde-629	304	20	,	,	PUNCT
ejde-629	304	21	differential	differential	ADJ
ejde-629	304	22	integral	integral	ADJ
ejde-629	304	23	equations	equation	NOUN
ejde-629	304	24	,	,	PUNCT
ejde-629	304	25	4	4	NUM
ejde-629	304	26	(	(	PUNCT
ejde-629	304	27	1990	1990	NUM
ejde-629	304	28	)	)	PUNCT
ejde-629	304	29	,	,	PUNCT
ejde-629	304	30	13–75	13–75	NUM
ejde-629	304	31	.	.	PUNCT
ejde-629	305	1	[	[	X
ejde-629	305	2	2	2	X
ejde-629	305	3	]	]	PUNCT
ejde-629	305	4	h.	h.	PROPN
ejde-629	305	5	amann	amann	PROPN
ejde-629	305	6	;	;	PUNCT
ejde-629	305	7	nonhomogeneous	nonhomogeneous	ADJ
ejde-629	305	8	linear	linear	NOUN
ejde-629	305	9	and	and	CCONJ
ejde-629	305	10	quasilinear	quasilinear	NOUN
ejde-629	305	11	elliptic	elliptic	ADJ
ejde-629	305	12	and	and	CCONJ
ejde-629	305	13	parabolic	parabolic	ADJ
ejde-629	305	14	boundary	boundary	ADJ
ejde-629	305	15	value	value	NOUN
ejde-629	305	16	problem	problem	NOUN
ejde-629	305	17	,	,	PUNCT
ejde-629	305	18	in	in	ADP
ejde-629	305	19	:	:	PUNCT
ejde-629	305	20	h.	h.	PROPN
ejde-629	305	21	t.	t.	PROPN
ejde-629	305	22	h.	h.	PROPN
ejde-629	305	23	j.	j.	PROPN
ejde-629	305	24	schmeisser	schmeisser	PROPN
ejde-629	305	25	(	(	PUNCT
ejde-629	305	26	ed	ed	NOUN
ejde-629	305	27	.	.	PUNCT
ejde-629	305	28	)	)	PUNCT
ejde-629	305	29	,	,	PUNCT
ejde-629	305	30	function	function	NOUN
ejde-629	305	31	spaces	space	NOUN
ejde-629	305	32	,	,	PUNCT
ejde-629	305	33	differential	differential	ADJ
ejde-629	305	34	operators	operator	NOUN
ejde-629	305	35	and	and	CCONJ
ejde-629	305	36	nonlinear	nonlinear	ADJ
ejde-629	305	37	analysis	analysis	NOUN
ejde-629	305	38	,	,	PUNCT
ejde-629	305	39	teubner	teubner	NOUN
ejde-629	305	40	,	,	PUNCT
ejde-629	305	41	stuttgart	stuttgart	PROPN
ejde-629	305	42	,	,	PUNCT
ejde-629	305	43	leipzig	leipzig	PROPN
ejde-629	305	44	,	,	PUNCT
ejde-629	305	45	(	(	PUNCT
ejde-629	305	46	1993	1993	NUM
ejde-629	305	47	)	)	PUNCT
ejde-629	305	48	,	,	PUNCT
ejde-629	305	49	9–126	9–126	X
ejde-629	305	50	.	.	PUNCT
ejde-629	306	1	[	[	X
ejde-629	306	2	3	3	X
ejde-629	306	3	]	]	X
ejde-629	306	4	p.	p.	NOUN
ejde-629	306	5	m.	m.	PROPN
ejde-629	306	6	carvalho	carvalho	PROPN
ejde-629	306	7	-	-	PUNCT
ejde-629	306	8	neto	neto	VERB
ejde-629	306	9	;	;	PUNCT
ejde-629	306	10	fractional	fractional	ADJ
ejde-629	306	11	differential	differential	ADJ
ejde-629	306	12	equations	equation	NOUN
ejde-629	306	13	:	:	PUNCT
ejde-629	306	14	a	a	DET
ejde-629	306	15	novel	novel	ADJ
ejde-629	306	16	study	study	NOUN
ejde-629	306	17	of	of	ADP
ejde-629	306	18	local	local	ADJ
ejde-629	306	19	and	and	CCONJ
ejde-629	306	20	global	global	ADJ
ejde-629	306	21	solutions	solution	NOUN
ejde-629	306	22	in	in	ADP
ejde-629	306	23	banach	banach	NOUN
ejde-629	306	24	spaces	space	NOUN
ejde-629	306	25	,	,	PUNCT
ejde-629	306	26	phd	phd	NOUN
ejde-629	306	27	thesis	thesis	NOUN
ejde-629	306	28	,	,	PUNCT
ejde-629	306	29	universidade	universidade	PROPN
ejde-629	306	30	de	de	PROPN
ejde-629	306	31	sao	sao	PROPN
ejde-629	306	32	paulo	paulo	PROPN
ejde-629	306	33	,	,	PUNCT
ejde-629	306	34	sao	sao	PROPN
ejde-629	306	35	carlos	carlos	PROPN
ejde-629	306	36	,	,	PUNCT
ejde-629	306	37	2013	2013	NUM
ejde-629	306	38	.	.	PUNCT
ejde-629	307	1	[	[	X
ejde-629	307	2	4	4	X
ejde-629	307	3	]	]	PUNCT
ejde-629	307	4	l.	l.	PROPN
ejde-629	307	5	z.	z.	PROPN
ejde-629	307	6	chen	chen	PROPN
ejde-629	307	7	,	,	PUNCT
ejde-629	307	8	j.	j.	PROPN
ejde-629	307	9	zhang	zhang	PROPN
ejde-629	307	10	,	,	PUNCT
ejde-629	307	11	j.	j.	PROPN
ejde-629	307	12	zhao	zhao	PROPN
ejde-629	307	13	,	,	PUNCT
ejde-629	307	14	w.	w.	PROPN
ejde-629	307	15	x.	x.	PROPN
ejde-629	307	16	cao	cao	PROPN
ejde-629	307	17	,	,	PUNCT
ejde-629	307	18	h.	h.	PROPN
ejde-629	307	19	wang	wang	PROPN
ejde-629	307	20	,	,	PUNCT
ejde-629	307	21	j.	j.	PROPN
ejde-629	307	22	w.	w.	PROPN
ejde-629	307	23	zhang	zhang	PROPN
ejde-629	307	24	;	;	PUNCT
ejde-629	307	25	an	an	DET
ejde-629	307	26	accurate	accurate	ADJ
ejde-629	307	27	and	and	CCONJ
ejde-629	307	28	efficient	efficient	ADJ
ejde-629	307	29	algorithm	algorithm	NOUN
ejde-629	307	30	for	for	ADP
ejde-629	307	31	the	the	DET
ejde-629	307	32	time	time	NOUN
ejde-629	307	33	-	-	PUNCT
ejde-629	307	34	fractional	fractional	ADJ
ejde-629	307	35	molecular	molecular	ADJ
ejde-629	307	36	beam	beam	NOUN
ejde-629	307	37	epitaxy	epitaxy	PROPN
ejde-629	307	38	model	model	NOUN
ejde-629	307	39	with	with	ADP
ejde-629	307	40	slope	slope	NOUN
ejde-629	307	41	selection	selection	NOUN
ejde-629	307	42	,	,	PUNCT
ejde-629	307	43	comput	comput	NOUN
ejde-629	307	44	.	.	PUNCT
ejde-629	308	1	phys	phy	NOUN
ejde-629	308	2	.	.	PUNCT
ejde-629	309	1	commun	commun	PROPN
ejde-629	309	2	.	.	PROPN
ejde-629	309	3	,	,	PUNCT
ejde-629	309	4	245	245	NUM
ejde-629	309	5	(	(	PUNCT
ejde-629	309	6	2019	2019	NUM
ejde-629	309	7	)	)	PUNCT
ejde-629	309	8	,	,	PUNCT
ejde-629	309	9	106842	106842	NUM
ejde-629	309	10	.	.	PUNCT
ejde-629	310	1	[	[	X
ejde-629	310	2	5	5	X
ejde-629	310	3	]	]	X
ejde-629	310	4	y.	y.	PROPN
ejde-629	310	5	feng	feng	PROPN
ejde-629	310	6	,	,	PUNCT
ejde-629	310	7	b.	b.	PROPN
ejde-629	310	8	y.	y.	PROPN
ejde-629	310	9	hu	hu	PROPN
ejde-629	310	10	,	,	PUNCT
ejde-629	310	11	x.	x.	PROPN
ejde-629	310	12	q.	q.	PROPN
ejde-629	310	13	x.	x.	PROPN
ejde-629	310	14	;	;	PUNCT
ejde-629	310	15	suppression	suppression	NOUN
ejde-629	310	16	of	of	ADP
ejde-629	310	17	epitaxial	epitaxial	ADJ
ejde-629	310	18	thin	thin	ADJ
ejde-629	310	19	film	film	NOUN
ejde-629	310	20	growth	growth	NOUN
ejde-629	310	21	by	by	ADP
ejde-629	310	22	mixing	mix	VERB
ejde-629	310	23	,	,	PUNCT
ejde-629	310	24	j.	j.	PROPN
ejde-629	310	25	differential	differential	PROPN
ejde-629	310	26	equations	equations	PROPN
ejde-629	310	27	,	,	PUNCT
ejde-629	310	28	317	317	NUM
ejde-629	310	29	(	(	PUNCT
ejde-629	310	30	2022	2022	NUM
ejde-629	310	31	)	)	PUNCT
ejde-629	310	32	,	,	PUNCT
ejde-629	310	33	561	561	NUM
ejde-629	310	34	-	-	SYM
ejde-629	310	35	602	602	NUM
ejde-629	310	36	.	.	PUNCT
ejde-629	311	1	[	[	X
ejde-629	311	2	6	6	NUM
ejde-629	311	3	]	]	PUNCT
ejde-629	311	4	k.	k.	PROPN
ejde-629	311	5	ishige	ishige	PROPN
ejde-629	311	6	,	,	PUNCT
ejde-629	311	7	n.	n.	PROPN
ejde-629	311	8	miyake	miyake	PROPN
ejde-629	311	9	,	,	PUNCT
ejde-629	311	10	s.	s.	PROPN
ejde-629	311	11	okabe	okabe	PROPN
ejde-629	311	12	;	;	PUNCT
ejde-629	311	13	blowup	blowup	VERB
ejde-629	311	14	for	for	ADP
ejde-629	311	15	a	a	DET
ejde-629	311	16	fourth	fourth	ADJ
ejde-629	311	17	-	-	PUNCT
ejde-629	311	18	order	order	NOUN
ejde-629	311	19	parabolic	parabolic	ADJ
ejde-629	311	20	equation	equation	NOUN
ejde-629	311	21	with	with	ADP
ejde-629	311	22	gradient	gradient	ADJ
ejde-629	311	23	nonlinearity	nonlinearity	NOUN
ejde-629	311	24	,	,	PUNCT
ejde-629	311	25	siam	siam	PROPN
ejde-629	311	26	j.	j.	PROPN
ejde-629	311	27	math	math	PROPN
ejde-629	311	28	.	.	PUNCT
ejde-629	312	1	anal	anal	PROPN
ejde-629	312	2	.	.	PROPN
ejde-629	312	3	,	,	PUNCT
ejde-629	312	4	52	52	NUM
ejde-629	312	5	(	(	PUNCT
ejde-629	312	6	2020	2020	NUM
ejde-629	312	7	)	)	PUNCT
ejde-629	312	8	,	,	PUNCT
ejde-629	313	1	no	no	INTJ
ejde-629	313	2	.	.	NOUN
ejde-629	313	3	1	1	NUM
ejde-629	313	4	,	,	PUNCT
ejde-629	313	5	927–953	927–953	NUM
ejde-629	313	6	.	.	PUNCT
ejde-629	314	1	[	[	X
ejde-629	314	2	7	7	X
ejde-629	314	3	]	]	X
ejde-629	314	4	h.	h.	PROPN
ejde-629	314	5	jeffreys	jeffreys	PROPN
ejde-629	314	6	,	,	PUNCT
ejde-629	314	7	b.	b.	PROPN
ejde-629	314	8	jeffreys	jeffreys	PROPN
ejde-629	314	9	;	;	PUNCT
ejde-629	314	10	methods	method	NOUN
ejde-629	314	11	of	of	ADP
ejde-629	314	12	mathematical	mathematical	ADJ
ejde-629	314	13	physics	physics	NOUN
ejde-629	314	14	(	(	PUNCT
ejde-629	314	15	3rd	3rd	NOUN
ejde-629	314	16	edition	edition	NOUN
ejde-629	314	17	)	)	PUNCT
ejde-629	314	18	,	,	PUNCT
ejde-629	314	19	cambridge	cambridge	PROPN
ejde-629	314	20	university	university	PROPN
ejde-629	314	21	press	press	NOUN
ejde-629	314	22	,	,	PUNCT
ejde-629	314	23	2000	2000	NUM
ejde-629	314	24	.	.	PUNCT
ejde-629	315	1	[	[	X
ejde-629	315	2	8	8	X
ejde-629	315	3	]	]	PUNCT
ejde-629	315	4	j.	j.	PROPN
ejde-629	315	5	kemppainen	kemppainen	PROPN
ejde-629	315	6	,	,	PUNCT
ejde-629	315	7	j.	j.	PROPN
ejde-629	315	8	siljander	siljander	PROPN
ejde-629	315	9	,	,	PUNCT
ejde-629	315	10	r.	r.	PROPN
ejde-629	315	11	zacher	zacher	PROPN
ejde-629	315	12	;	;	PUNCT
ejde-629	315	13	representation	representation	NOUN
ejde-629	315	14	of	of	ADP
ejde-629	315	15	solutions	solution	NOUN
ejde-629	315	16	and	and	CCONJ
ejde-629	315	17	large	large	ADJ
ejde-629	315	18	-	-	PUNCT
ejde-629	315	19	time	time	NOUN
ejde-629	315	20	behavior	behavior	NOUN
ejde-629	315	21	for	for	ADP
ejde-629	315	22	fully	fully	ADV
ejde-629	315	23	nonlocal	nonlocal	ADJ
ejde-629	315	24	diffusion	diffusion	NOUN
ejde-629	315	25	equations	equation	NOUN
ejde-629	315	26	,	,	PUNCT
ejde-629	315	27	j.	j.	PROPN
ejde-629	315	28	differential	differential	PROPN
ejde-629	315	29	equations	equation	NOUN
ejde-629	315	30	,	,	PUNCT
ejde-629	315	31	263	263	NUM
ejde-629	315	32	(	(	PUNCT
ejde-629	315	33	2017	2017	NUM
ejde-629	315	34	)	)	PUNCT
ejde-629	315	35	,	,	PUNCT
ejde-629	315	36	149–201	149–201	NUM
ejde-629	315	37	.	.	PUNCT
ejde-629	316	1	[	[	X
ejde-629	316	2	9	9	NUM
ejde-629	316	3	]	]	X
ejde-629	316	4	b.	b.	PROPN
ejde-629	316	5	b.	b.	PROPN
ejde-629	316	6	king	king	PROPN
ejde-629	316	7	,	,	PUNCT
ejde-629	316	8	m.	m.	NOUN
ejde-629	316	9	winkler	winkler	NOUN
ejde-629	316	10	;	;	PUNCT
ejde-629	316	11	a	a	DET
ejde-629	316	12	fourth	fourth	ADJ
ejde-629	316	13	-	-	PUNCT
ejde-629	316	14	order	order	NOUN
ejde-629	316	15	parabolic	parabolic	ADJ
ejde-629	316	16	equation	equation	NOUN
ejde-629	316	17	modeling	model	VERB
ejde-629	316	18	epitaxial	epitaxial	ADJ
ejde-629	316	19	thin	thin	ADJ
ejde-629	316	20	film	film	NOUN
ejde-629	316	21	growth	growth	NOUN
ejde-629	316	22	,	,	PUNCT
ejde-629	316	23	j.	j.	PROPN
ejde-629	316	24	math	math	PROPN
ejde-629	316	25	.	.	PUNCT
ejde-629	317	1	anal.appl	anal.appl	PROPN
ejde-629	317	2	.	.	PROPN
ejde-629	317	3	,	,	PUNCT
ejde-629	317	4	286	286	NUM
ejde-629	317	5	(	(	PUNCT
ejde-629	317	6	2003	2003	NUM
ejde-629	317	7	)	)	PUNCT
ejde-629	317	8	,	,	PUNCT
ejde-629	317	9	459–490	459–490	NUM
ejde-629	317	10	.	.	PUNCT
ejde-629	318	1	[	[	X
ejde-629	318	2	10	10	NUM
ejde-629	318	3	]	]	X
ejde-629	318	4	l.	l.	PROPN
ejde-629	318	5	li	li	PROPN
ejde-629	318	6	,	,	PUNCT
ejde-629	318	7	j.	j.	PROPN
ejde-629	318	8	g.	g.	PROPN
ejde-629	318	9	liu	liu	PROPN
ejde-629	318	10	;	;	PUNCT
ejde-629	318	11	a	a	DET
ejde-629	318	12	generalized	generalized	ADJ
ejde-629	318	13	definition	definition	NOUN
ejde-629	318	14	of	of	ADP
ejde-629	318	15	caputo	caputo	PROPN
ejde-629	318	16	derivatives	derivative	NOUN
ejde-629	318	17	and	and	CCONJ
ejde-629	318	18	its	its	PRON
ejde-629	318	19	application	application	NOUN
ejde-629	318	20	to	to	ADP
ejde-629	318	21	fractional	fractional	ADJ
ejde-629	318	22	odes	ode	NOUN
ejde-629	318	23	,	,	PUNCT
ejde-629	318	24	siam	siam	PROPN
ejde-629	318	25	j.	j.	PROPN
ejde-629	318	26	math	math	PROPN
ejde-629	318	27	.	.	PUNCT
ejde-629	319	1	anal	anal	PROPN
ejde-629	319	2	.	.	PROPN
ejde-629	319	3	,	,	PUNCT
ejde-629	319	4	50	50	NUM
ejde-629	319	5	(	(	PUNCT
ejde-629	319	6	2018	2018	NUM
ejde-629	319	7	)	)	PUNCT
ejde-629	319	8	,	,	PUNCT
ejde-629	319	9	2867–2900	2867–2900	NUM
ejde-629	319	10	.	.	PUNCT
ejde-629	320	1	[	[	X
ejde-629	320	2	11	11	NUM
ejde-629	320	3	]	]	PUNCT
ejde-629	320	4	a.	a.	NOUN
ejde-629	320	5	lunardi	lunardi	NOUN
ejde-629	320	6	;	;	PUNCT
ejde-629	320	7	analytic	analytic	ADJ
ejde-629	320	8	semigroups	semigroup	NOUN
ejde-629	320	9	and	and	CCONJ
ejde-629	320	10	optimal	optimal	ADJ
ejde-629	320	11	regularity	regularity	NOUN
ejde-629	320	12	in	in	ADP
ejde-629	320	13	parabolic	parabolic	ADJ
ejde-629	320	14	problems	problem	NOUN
ejde-629	320	15	,	,	PUNCT
ejde-629	320	16	springerverlag	springerverlag	NOUN
ejde-629	320	17	,	,	PUNCT
ejde-629	320	18	1995	1995	NUM
ejde-629	320	19	.	.	PUNCT
ejde-629	321	1	[	[	X
ejde-629	321	2	12	12	NUM
ejde-629	321	3	]	]	PUNCT
ejde-629	321	4	f.	f.	PROPN
ejde-629	321	5	mainardi	mainardi	PROPN
ejde-629	321	6	;	;	PUNCT
ejde-629	321	7	on	on	ADP
ejde-629	321	8	the	the	DET
ejde-629	321	9	initial	initial	ADJ
ejde-629	321	10	value	value	NOUN
ejde-629	321	11	problem	problem	NOUN
ejde-629	321	12	for	for	ADP
ejde-629	321	13	the	the	DET
ejde-629	321	14	fractional	fractional	ADJ
ejde-629	321	15	diffusion	diffusion	NOUN
ejde-629	321	16	-	-	PUNCT
ejde-629	321	17	wave	wave	NOUN
ejde-629	321	18	equation	equation	NOUN
ejde-629	321	19	,	,	PUNCT
ejde-629	321	20	ser	ser	NOUN
ejde-629	321	21	.	.	PUNCT
ejde-629	322	1	adv	adv	PROPN
ejde-629	322	2	.	.	PUNCT
ejde-629	322	3	math	math	PROPN
ejde-629	322	4	.	.	PUNCT
ejde-629	323	1	appl	appl	PROPN
ejde-629	323	2	.	.	PUNCT
ejde-629	324	1	sci	sci	PROPN
ejde-629	324	2	.	.	PROPN
ejde-629	324	3	,	,	PUNCT
ejde-629	324	4	23	23	NUM
ejde-629	324	5	(	(	PUNCT
ejde-629	324	6	1994	1994	NUM
ejde-629	324	7	)	)	PUNCT
ejde-629	324	8	,	,	PUNCT
ejde-629	324	9	246–251	246–251	NUM
ejde-629	324	10	.	.	PUNCT
ejde-629	325	1	[	[	X
ejde-629	325	2	13	13	NUM
ejde-629	325	3	]	]	PUNCT
ejde-629	325	4	c.	c.	PROPN
ejde-629	325	5	miao	miao	PROPN
ejde-629	325	6	;	;	PUNCT
ejde-629	325	7	weak	weak	ADJ
ejde-629	325	8	solution	solution	NOUN
ejde-629	325	9	of	of	ADP
ejde-629	325	10	class	class	NOUN
ejde-629	325	11	of	of	ADP
ejde-629	325	12	nonlinear	nonlinear	ADJ
ejde-629	325	13	heat	heat	NOUN
ejde-629	325	14	equation	equation	NOUN
ejde-629	325	15	systems	system	NOUN
ejde-629	325	16	and	and	CCONJ
ejde-629	325	17	application	application	NOUN
ejde-629	325	18	to	to	ADP
ejde-629	325	19	the	the	DET
ejde-629	325	20	navier	navier	NOUN
ejde-629	325	21	-	-	PUNCT
ejde-629	325	22	stokes	stoke	NOUN
ejde-629	325	23	system	system	NOUN
ejde-629	325	24	,	,	PUNCT
ejde-629	325	25	j.	j.	PROPN
ejde-629	325	26	differential	differential	PROPN
ejde-629	325	27	equations	equation	NOUN
ejde-629	325	28	,	,	PUNCT
ejde-629	325	29	61	61	NUM
ejde-629	325	30	(	(	PUNCT
ejde-629	325	31	1986	1986	NUM
ejde-629	325	32	)	)	PUNCT
ejde-629	325	33	,	,	PUNCT
ejde-629	325	34	141–151	141–151	NUM
ejde-629	325	35	.	.	PUNCT
ejde-629	326	1	[	[	X
ejde-629	326	2	14	14	NUM
ejde-629	326	3	]	]	X
ejde-629	326	4	udo	udo	PROPN
ejde-629	326	5	w.	w.	PROPN
ejde-629	326	6	pohl	pohl	PROPN
ejde-629	326	7	;	;	PUNCT
ejde-629	326	8	epitaxy	epitaxy	NOUN
ejde-629	326	9	of	of	ADP
ejde-629	326	10	semiconductors	semiconductor	NOUN
ejde-629	326	11	:	:	PUNCT
ejde-629	326	12	introduction	introduction	NOUN
ejde-629	326	13	to	to	ADP
ejde-629	326	14	physical	physical	ADJ
ejde-629	326	15	principles	principle	NOUN
ejde-629	326	16	.	.	PUNCT
ejde-629	327	1	springerverlag	springerverlag	PROPN
ejde-629	327	2	berlin	berlin	PROPN
ejde-629	327	3	heidelberg	heidelberg	PROPN
ejde-629	327	4	,	,	PUNCT
ejde-629	327	5	2013	2013	NUM
ejde-629	327	6	.	.	PUNCT
ejde-629	328	1	[	[	X
ejde-629	328	2	15	15	NUM
ejde-629	328	3	]	]	PUNCT
ejde-629	328	4	a.	a.	NOUN
ejde-629	328	5	n.	n.	PROPN
ejde-629	328	6	sandjo	sandjo	PROPN
ejde-629	328	7	;	;	PUNCT
ejde-629	328	8	solutions	solution	NOUN
ejde-629	328	9	for	for	ADP
ejde-629	328	10	fourth	fourth	ADJ
ejde-629	328	11	-	-	PUNCT
ejde-629	328	12	order	order	NOUN
ejde-629	328	13	parabolic	parabolic	ADJ
ejde-629	328	14	equation	equation	NOUN
ejde-629	328	15	modeling	model	VERB
ejde-629	328	16	epitaxial	epitaxial	ADJ
ejde-629	328	17	thin	thin	ADJ
ejde-629	328	18	film	film	NOUN
ejde-629	328	19	growth	growth	NOUN
ejde-629	328	20	,	,	PUNCT
ejde-629	328	21	dissertation	dissertation	NOUN
ejde-629	328	22	,	,	PUNCT
ejde-629	328	23	rwth	rwth	PROPN
ejde-629	328	24	aachen	aachen	PROPN
ejde-629	328	25	university	university	PROPN
ejde-629	328	26	,	,	PUNCT
ejde-629	328	27	2011	2011	NUM
ejde-629	328	28	.	.	PUNCT
ejde-629	329	1	14	14	NUM
ejde-629	329	2	q.	q.	PROPN
ejde-629	329	3	liu	liu	PROPN
ejde-629	329	4	,	,	PUNCT
ejde-629	329	5	w.	w.	PROPN
ejde-629	329	6	zhu	zhu	PROPN
ejde-629	329	7	,	,	PUNCT
ejde-629	329	8	h.	h.	PROPN
ejde-629	329	9	ye	ye	PROPN
ejde-629	329	10	ejde-2024/58	ejde-2024/58	PROPN
ejde-629	330	1	[	[	X
ejde-629	330	2	16	16	NUM
ejde-629	330	3	]	]	PUNCT
ejde-629	330	4	a.	a.	NOUN
ejde-629	330	5	n.	n.	PROPN
ejde-629	330	6	sandjo	sandjo	PROPN
ejde-629	330	7	,	,	PUNCT
ejde-629	330	8	s.	s.	PROPN
ejde-629	330	9	moutari	moutari	PROPN
ejde-629	330	10	,	,	PUNCT
ejde-629	330	11	y.	y.	PROPN
ejde-629	330	12	gningue	gningue	PROPN
ejde-629	330	13	;	;	PUNCT
ejde-629	330	14	solutions	solution	NOUN
ejde-629	330	15	of	of	ADP
ejde-629	330	16	fourth	fourth	ADJ
ejde-629	330	17	-	-	PUNCT
ejde-629	330	18	order	order	NOUN
ejde-629	330	19	parabolic	parabolic	ADJ
ejde-629	330	20	equation	equation	NOUN
ejde-629	330	21	modeling	model	VERB
ejde-629	330	22	thin	thin	ADJ
ejde-629	330	23	film	film	NOUN
ejde-629	330	24	growth	growth	NOUN
ejde-629	330	25	,	,	PUNCT
ejde-629	330	26	j.	j.	PROPN
ejde-629	330	27	differential	differential	PROPN
ejde-629	330	28	equations	equations	PROPN
ejde-629	330	29	,	,	PUNCT
ejde-629	330	30	259	259	NUM
ejde-629	330	31	(	(	PUNCT
ejde-629	330	32	2015	2015	NUM
ejde-629	330	33	)	)	PUNCT
ejde-629	330	34	,	,	PUNCT
ejde-629	330	35	7260–7283	7260–7283	NUM
ejde-629	330	36	.	.	PUNCT
ejde-629	331	1	[	[	X
ejde-629	331	2	17	17	NUM
ejde-629	331	3	]	]	X
ejde-629	331	4	r.	r.	PROPN
ejde-629	331	5	l.	l.	PROPN
ejde-629	331	6	schwoebel	schwoebel	PROPN
ejde-629	331	7	,	,	PUNCT
ejde-629	331	8	e.	e.	PROPN
ejde-629	331	9	j.	j.	PROPN
ejde-629	331	10	shipsey	shipsey	PROPN
ejde-629	331	11	step	step	NOUN
ejde-629	331	12	;	;	PUNCT
ejde-629	331	13	motion	motion	NOUN
ejde-629	331	14	on	on	ADP
ejde-629	331	15	crystal	crystal	NOUN
ejde-629	331	16	surfaces	surface	NOUN
ejde-629	331	17	,	,	PUNCT
ejde-629	331	18	j.	j.	PROPN
ejde-629	331	19	appl	appl	PROPN
ejde-629	331	20	.	.	PUNCT
ejde-629	332	1	phys	phy	NOUN
ejde-629	332	2	.	.	PUNCT
ejde-629	332	3	,	,	PUNCT
ejde-629	332	4	37	37	NUM
ejde-629	332	5	(	(	PUNCT
ejde-629	332	6	1966	1966	NUM
ejde-629	332	7	)	)	PUNCT
ejde-629	332	8	,	,	PUNCT
ejde-629	332	9	3682–3686	3682–3686	NUM
ejde-629	332	10	.	.	PUNCT
ejde-629	333	1	[	[	X
ejde-629	333	2	18	18	NUM
ejde-629	333	3	]	]	PUNCT
ejde-629	333	4	t.	t.	PROPN
ejde-629	333	5	tang	tang	PROPN
ejde-629	333	6	,	,	PUNCT
ejde-629	333	7	h.	h.	PROPN
ejde-629	333	8	yu	yu	PROPN
ejde-629	333	9	,	,	PUNCT
ejde-629	333	10	t.	t.	PROPN
ejde-629	333	11	zhou	zhou	PROPN
ejde-629	333	12	;	;	PUNCT
ejde-629	333	13	on	on	ADP
ejde-629	333	14	energy	energy	NOUN
ejde-629	333	15	dissipation	dissipation	NOUN
ejde-629	333	16	theory	theory	NOUN
ejde-629	333	17	and	and	CCONJ
ejde-629	333	18	numerical	numerical	ADJ
ejde-629	333	19	stability	stability	NOUN
ejde-629	333	20	for	for	ADP
ejde-629	333	21	timefractional	timefractional	ADJ
ejde-629	333	22	phase	phase	NOUN
ejde-629	333	23	-	-	PUNCT
ejde-629	333	24	field	field	NOUN
ejde-629	333	25	equations	equation	NOUN
ejde-629	333	26	,	,	PUNCT
ejde-629	333	27	siam	siam	PROPN
ejde-629	333	28	j.	j.	PROPN
ejde-629	333	29	sci	sci	PROPN
ejde-629	333	30	.	.	PUNCT
ejde-629	334	1	comput	comput	PROPN
ejde-629	334	2	.	.	PUNCT
ejde-629	334	3	,	,	PUNCT
ejde-629	334	4	41(6)(2019	41(6)(2019	NUM
ejde-629	334	5	)	)	PUNCT
ejde-629	334	6	,	,	PUNCT
ejde-629	334	7	3757–3778	3757–3778	NUM
ejde-629	334	8	.	.	PUNCT
ejde-629	335	1	[	[	X
ejde-629	335	2	19	19	NUM
ejde-629	335	3	]	]	X
ejde-629	335	4	r.	r.	PROPN
ejde-629	335	5	n.	n.	PROPN
ejde-629	335	6	wang	wang	PROPN
ejde-629	335	7	,	,	PUNCT
ejde-629	335	8	d.	d.	PROPN
ejde-629	335	9	h.	h.	PROPN
ejde-629	335	10	chen	chen	PROPN
ejde-629	335	11	,	,	PUNCT
ejde-629	335	12	t.	t.	PROPN
ejde-629	335	13	j.	j.	PROPN
ejde-629	335	14	xiao	xiao	PROPN
ejde-629	335	15	;	;	PUNCT
ejde-629	335	16	abstract	abstract	ADJ
ejde-629	335	17	fractional	fractional	ADJ
ejde-629	335	18	cauchy	cauchy	NOUN
ejde-629	335	19	problems	problem	NOUN
ejde-629	335	20	with	with	ADP
ejde-629	335	21	almost	almost	ADV
ejde-629	335	22	sectorial	sectorial	ADJ
ejde-629	335	23	operators	operator	NOUN
ejde-629	335	24	,	,	PUNCT
ejde-629	335	25	j.	j.	PROPN
ejde-629	335	26	differential	differential	PROPN
ejde-629	335	27	equations	equation	NOUN
ejde-629	335	28	,	,	PUNCT
ejde-629	335	29	252	252	NUM
ejde-629	335	30	(	(	PUNCT
ejde-629	335	31	2012	2012	NUM
ejde-629	335	32	)	)	PUNCT
ejde-629	335	33	,	,	PUNCT
ejde-629	335	34	202–235	202–235	NUM
ejde-629	335	35	.	.	PUNCT
ejde-629	336	1	[	[	X
ejde-629	336	2	20	20	NUM
ejde-629	336	3	]	]	PUNCT
ejde-629	336	4	j.	j.	PROPN
ejde-629	336	5	d.	d.	PROPN
ejde-629	336	6	wang	wang	PROPN
ejde-629	336	7	,	,	PUNCT
ejde-629	336	8	y.	y.	PROPN
ejde-629	336	9	yang	yang	PROPN
ejde-629	336	10	,	,	PUNCT
ejde-629	336	11	b.	b.	PROPN
ejde-629	336	12	q.	q.	PROPN
ejde-629	336	13	ji	ji	PROPN
ejde-629	336	14	;	;	PUNCT
ejde-629	336	15	two	two	NUM
ejde-629	336	16	energy	energy	NOUN
ejde-629	336	17	stable	stable	ADJ
ejde-629	336	18	variable	variable	ADJ
ejde-629	336	19	-	-	PUNCT
ejde-629	336	20	step	step	NOUN
ejde-629	336	21	l1	l1	PROPN
ejde-629	336	22	schemes	scheme	NOUN
ejde-629	336	23	for	for	ADP
ejde-629	336	24	the	the	DET
ejde-629	336	25	timefractional	timefractional	ADJ
ejde-629	336	26	mbe	mbe	PROPN
ejde-629	336	27	model	model	NOUN
ejde-629	336	28	without	without	ADP
ejde-629	336	29	slope	slope	NOUN
ejde-629	336	30	selection	selection	NOUN
ejde-629	336	31	,	,	PUNCT
ejde-629	336	32	j.	j.	PROPN
ejde-629	336	33	comput	comput	PROPN
ejde-629	336	34	.	.	PUNCT
ejde-629	337	1	appl	appl	PROPN
ejde-629	337	2	.	.	PROPN
ejde-629	337	3	math	math	PROPN
ejde-629	337	4	.	.	PUNCT
ejde-629	338	1	,	,	PUNCT
ejde-629	338	2	419	419	NUM
ejde-629	338	3	(	(	PUNCT
ejde-629	338	4	2023	2023	NUM
ejde-629	338	5	)	)	PUNCT
ejde-629	338	6	,	,	PUNCT
ejde-629	338	7	1–15	1–15	NUM
ejde-629	338	8	.	.	PUNCT
ejde-629	339	1	[	[	X
ejde-629	339	2	21	21	NUM
ejde-629	339	3	]	]	X
ejde-629	339	4	f.	f.	PROPN
ejde-629	339	5	b.	b.	PROPN
ejde-629	339	6	weisler	weisler	PROPN
ejde-629	339	7	;	;	PUNCT
ejde-629	339	8	semilinear	semilinear	PROPN
ejde-629	339	9	evolution	evolution	NOUN
ejde-629	339	10	equations	equation	NOUN
ejde-629	339	11	in	in	ADP
ejde-629	339	12	banach	banach	NOUN
ejde-629	339	13	spaces	space	NOUN
ejde-629	339	14	,	,	PUNCT
ejde-629	339	15	j.	j.	PROPN
ejde-629	339	16	funct	funct	PROPN
ejde-629	339	17	.	.	PUNCT
ejde-629	340	1	anal	anal	PROPN
ejde-629	340	2	.	.	PROPN
ejde-629	340	3	,	,	PUNCT
ejde-629	340	4	32	32	NUM
ejde-629	340	5	(	(	PUNCT
ejde-629	340	6	1979	1979	NUM
ejde-629	340	7	)	)	PUNCT
ejde-629	340	8	,	,	PUNCT
ejde-629	340	9	277–296	277–296	NUM
ejde-629	340	10	.	.	PUNCT
ejde-629	341	1	[	[	X
ejde-629	341	2	22	22	NUM
ejde-629	341	3	]	]	X
ejde-629	341	4	h.	h.	PROPN
ejde-629	341	5	l.	l.	PROPN
ejde-629	341	6	ye	ye	PROPN
ejde-629	341	7	,	,	PUNCT
ejde-629	341	8	q.	q.	PROPN
ejde-629	341	9	liu	liu	PROPN
ejde-629	341	10	,	,	PUNCT
ejde-629	341	11	z.	z.	PROPN
ejde-629	341	12	m.	m.	PROPN
ejde-629	341	13	chen	chen	PROPN
ejde-629	341	14	;	;	PUNCT
ejde-629	341	15	global	global	ADJ
ejde-629	341	16	existence	existence	NOUN
ejde-629	341	17	of	of	ADP
ejde-629	341	18	solutions	solution	NOUN
ejde-629	341	19	of	of	ADP
ejde-629	341	20	the	the	DET
ejde-629	341	21	time	time	NOUN
ejde-629	341	22	fractional	fractional	ADJ
ejde-629	341	23	cahnhilliard	cahnhilliard	NOUN
ejde-629	341	24	equation	equation	NOUN
ejde-629	341	25	in	in	ADP
ejde-629	341	26	r3	r3	PROPN
ejde-629	341	27	,	,	PUNCT
ejde-629	341	28	j.	j.	PROPN
ejde-629	341	29	evol	evol	PROPN
ejde-629	341	30	.	.	PUNCT
ejde-629	342	1	equ	equ	PROPN
ejde-629	342	2	.	.	PROPN
ejde-629	342	3	,	,	PUNCT
ejde-629	342	4	21	21	NUM
ejde-629	342	5	(	(	PUNCT
ejde-629	342	6	2021	2021	NUM
ejde-629	342	7	)	)	PUNCT
ejde-629	342	8	,	,	PUNCT
ejde-629	342	9	no.2	no.2	PROPN
ejde-629	342	10	,	,	PUNCT
ejde-629	342	11	2377–2411	2377–2411	NUM
ejde-629	342	12	.	.	PUNCT
ejde-629	343	1	[	[	X
ejde-629	343	2	23	23	NUM
ejde-629	343	3	]	]	PUNCT
ejde-629	343	4	a.	a.	NOUN
ejde-629	343	5	zangwill	zangwill	NOUN
ejde-629	343	6	;	;	PUNCT
ejde-629	343	7	some	some	DET
ejde-629	343	8	causes	cause	NOUN
ejde-629	343	9	and	and	CCONJ
ejde-629	343	10	a	a	DET
ejde-629	343	11	consequence	consequence	NOUN
ejde-629	343	12	of	of	ADP
ejde-629	343	13	epitaxial	epitaxial	ADJ
ejde-629	343	14	roughening	roughening	NOUN
ejde-629	343	15	,	,	PUNCT
ejde-629	343	16	j.	j.	PROPN
ejde-629	343	17	cryst	cryst	PROPN
ejde-629	343	18	.	.	PUNCT
ejde-629	344	1	growth	growth	NOUN
ejde-629	344	2	,	,	PUNCT
ejde-629	344	3	163	163	NUM
ejde-629	344	4	(	(	PUNCT
ejde-629	344	5	1996	1996	NUM
ejde-629	344	6	)	)	PUNCT
ejde-629	344	7	,	,	PUNCT
ejde-629	344	8	8–21	8–21	NOUN
ejde-629	344	9	.	.	PUNCT
ejde-629	345	1	qiang	qiang	PROPN
ejde-629	345	2	liu	liu	PROPN
ejde-629	345	3	school	school	PROPN
ejde-629	345	4	of	of	ADP
ejde-629	345	5	mathematical	mathematical	ADJ
ejde-629	345	6	sciences	sciences	PROPN
ejde-629	345	7	,	,	PUNCT
ejde-629	345	8	shenzhen	shenzhen	PROPN
ejde-629	345	9	university	university	PROPN
ejde-629	345	10	,	,	PUNCT
ejde-629	345	11	shenzhen	shenzhen	PROPN
ejde-629	345	12	,	,	PUNCT
ejde-629	345	13	518060	518060	NUM
ejde-629	345	14	,	,	PUNCT
ejde-629	345	15	china	china	PROPN
ejde-629	345	16	email	email	NOUN
ejde-629	345	17	address	address	NOUN
ejde-629	345	18	:	:	PUNCT
ejde-629	345	19	matliu@szu.edu.cn	matliu@szu.edu.cn	PROPN
ejde-629	345	20	wanyu	wanyu	PROPN
ejde-629	345	21	zhu	zhu	PROPN
ejde-629	345	22	school	school	PROPN
ejde-629	345	23	of	of	ADP
ejde-629	345	24	mathematical	mathematical	ADJ
ejde-629	345	25	sciences	sciences	PROPN
ejde-629	345	26	,	,	PUNCT
ejde-629	345	27	shenzhen	shenzhen	PROPN
ejde-629	345	28	university	university	PROPN
ejde-629	345	29	,	,	PUNCT
ejde-629	345	30	shenzhen	shenzhen	PROPN
ejde-629	345	31	,	,	PUNCT
ejde-629	345	32	518060	518060	NUM
ejde-629	345	33	,	,	PUNCT
ejde-629	345	34	china	china	PROPN
ejde-629	345	35	email	email	NOUN
ejde-629	345	36	address	address	NOUN
ejde-629	345	37	:	:	PUNCT
ejde-629	345	38	2200201025@email.szu.edu.cn	2200201025@email.szu.edu.cn	NUM
ejde-629	345	39	hailong	hailong	NOUN
ejde-629	345	40	ye	ye	NOUN
ejde-629	345	41	(	(	PUNCT
ejde-629	345	42	corresponding	corresponding	ADJ
ejde-629	345	43	author	author	NOUN
ejde-629	345	44	)	)	PUNCT
ejde-629	345	45	school	school	NOUN
ejde-629	345	46	of	of	ADP
ejde-629	345	47	mathematical	mathematical	ADJ
ejde-629	345	48	sciences	sciences	PROPN
ejde-629	345	49	,	,	PUNCT
ejde-629	345	50	shenzhen	shenzhen	PROPN
ejde-629	345	51	university	university	PROPN
ejde-629	345	52	,	,	PUNCT
ejde-629	345	53	shenzhen	shenzhen	PROPN
ejde-629	345	54	,	,	PUNCT
ejde-629	345	55	518060	518060	NUM
ejde-629	345	56	,	,	PUNCT
ejde-629	345	57	china	china	PROPN
ejde-629	345	58	email	email	NOUN
ejde-629	345	59	address	address	NOUN
ejde-629	345	60	:	:	PUNCT
ejde-629	345	61	yhl@szu.edu.cn	yhl@szu.edu.cn	PROPN
ejde-629	345	62	1	1	NUM
ejde-629	345	63	.	.	PUNCT
ejde-629	345	64	introduction	introduction	NOUN
ejde-629	345	65	and	and	CCONJ
ejde-629	345	66	main	main	ADJ
ejde-629	345	67	result	result	NOUN
ejde-629	345	68	2	2	NUM
ejde-629	345	69	.	.	X
ejde-629	346	1	a	a	DET
ejde-629	346	2	priori	priori	ADJ
ejde-629	346	3	estimates	estimate	NOUN
ejde-629	346	4	3	3	X
ejde-629	346	5	.	.	PUNCT
ejde-629	346	6	proof	proof	NOUN
ejde-629	346	7	of	of	ADP
ejde-629	346	8	theorem	theorem	ADJ
ejde-629	346	9	1.2	1.2	NUM
ejde-629	346	10	acknowledgements	acknowledgement	NOUN
ejde-629	346	11	references	reference	NOUN