id	sid	tid	token	lemma	pos
ejpam-93	1	1	european	european	PROPN
ejpam-93	1	2	journal	journal	PROPN
ejpam-93	1	3	of	of	ADP
ejpam-93	1	4	pure	pure	ADJ
ejpam-93	1	5	and	and	CCONJ
ejpam-93	1	6	applied	apply	VERB
ejpam-93	1	7	mathematics	mathematic	NOUN
ejpam-93	1	8	vol	vol	NOUN
ejpam-93	1	9	.	.	PROPN
ejpam-93	2	1	1	1	NUM
ejpam-93	2	2	,	,	PUNCT
ejpam-93	2	3	no	no	INTJ
ejpam-93	2	4	.	.	NOUN
ejpam-93	2	5	3	3	NUM
ejpam-93	2	6	,	,	PUNCT
ejpam-93	2	7	2008	2008	NUM
ejpam-93	2	8	,	,	PUNCT
ejpam-93	2	9	(	(	PUNCT
ejpam-93	2	10	33	33	NUM
ejpam-93	2	11	-	-	SYM
ejpam-93	2	12	39	39	NUM
ejpam-93	2	13	)	)	PUNCT
ejpam-93	2	14	issn	issn	PROPN
ejpam-93	2	15	1307	1307	NUM
ejpam-93	2	16	-	-	SYM
ejpam-93	2	17	5543	5543	NUM
ejpam-93	2	18	–	–	PUNCT
ejpam-93	2	19	www.ejpam.com	www.ejpam.com	X
ejpam-93	2	20	blow	blow	NOUN
ejpam-93	2	21	-	-	PUNCT
ejpam-93	2	22	up	up	NOUN
ejpam-93	2	23	for	for	ADP
ejpam-93	2	24	nonlinear	nonlinear	ADJ
ejpam-93	2	25	heat	heat	NOUN
ejpam-93	2	26	equations	equation	NOUN
ejpam-93	2	27	with	with	ADP
ejpam-93	2	28	absorptions	absorption	NOUN
ejpam-93	2	29	hailiang	hailiang	PROPN
ejpam-93	2	30	zhang1,∗	zhang1,∗	PROPN
ejpam-93	2	31	,	,	PUNCT
ejpam-93	2	32	xiulan	xiulan	PROPN
ejpam-93	2	33	guo2	guo2	PROPN
ejpam-93	2	34	1	1	NUM
ejpam-93	2	35	department	department	NOUN
ejpam-93	2	36	of	of	ADP
ejpam-93	2	37	mathematics	mathematics	PROPN
ejpam-93	2	38	,	,	PUNCT
ejpam-93	2	39	zhejiang	zhejiang	PROPN
ejpam-93	2	40	ocean	ocean	PROPN
ejpam-93	2	41	university	university	PROPN
ejpam-93	2	42	,	,	PUNCT
ejpam-93	2	43	zhoushan	zhoushan	PROPN
ejpam-93	2	44	316004	316004	NUM
ejpam-93	2	45	,	,	PUNCT
ejpam-93	2	46	china	china	PROPN
ejpam-93	2	47	2	2	NUM
ejpam-93	2	48	college	college	NOUN
ejpam-93	2	49	of	of	ADP
ejpam-93	2	50	science	science	PROPN
ejpam-93	2	51	,	,	PUNCT
ejpam-93	2	52	henan	henan	PROPN
ejpam-93	2	53	university	university	PROPN
ejpam-93	2	54	of	of	ADP
ejpam-93	2	55	technology	technology	PROPN
ejpam-93	2	56	,	,	PUNCT
ejpam-93	2	57	zhengzhou	zhengzhou	PROPN
ejpam-93	2	58	450001	450001	NUM
ejpam-93	2	59	,	,	PUNCT
ejpam-93	2	60	china	china	PROPN
ejpam-93	2	61	abstract	abstract	PROPN
ejpam-93	2	62	.	.	PUNCT
ejpam-93	3	1	this	this	DET
ejpam-93	3	2	paper	paper	NOUN
ejpam-93	3	3	deals	deal	NOUN
ejpam-93	3	4	with	with	ADP
ejpam-93	3	5	the	the	DET
ejpam-93	3	6	blow	blow	NOUN
ejpam-93	3	7	-	-	PUNCT
ejpam-93	3	8	up	up	NOUN
ejpam-93	3	9	of	of	ADP
ejpam-93	3	10	positive	positive	ADJ
ejpam-93	3	11	solution	solution	NOUN
ejpam-93	3	12	of	of	ADP
ejpam-93	3	13	the	the	DET
ejpam-93	3	14	nonlinear	nonlinear	ADJ
ejpam-93	3	15	heat	heat	NOUN
ejpam-93	3	16	equation	equation	NOUN
ejpam-93	3	17	ut	ut	PROPN
ejpam-93	4	1	=	=	PROPN
ejpam-93	4	2	∇(a(u)∇u)−	∇(a(u)∇u)−	PROPN
ejpam-93	4	3	f	f	PROPN
ejpam-93	4	4	(	(	PUNCT
ejpam-93	4	5	u	u	NOUN
ejpam-93	4	6	)	)	PUNCT
ejpam-93	4	7	subject	subject	ADJ
ejpam-93	4	8	to	to	ADP
ejpam-93	4	9	nonlinear	nonlinear	ADJ
ejpam-93	4	10	boundary	boundary	ADJ
ejpam-93	4	11	condition	condition	NOUN
ejpam-93	4	12	∂	∂	NUM
ejpam-93	4	13	u	u	NOUN
ejpam-93	4	14	∂	∂	NOUN
ejpam-93	4	15	n	n	PROPN
ejpam-93	4	16	=	=	SYM
ejpam-93	4	17	b(u	b(u	PROPN
ejpam-93	4	18	)	)	PUNCT
ejpam-93	4	19	.	.	PUNCT
ejpam-93	5	1	under	under	ADP
ejpam-93	5	2	suitable	suitable	ADJ
ejpam-93	5	3	assumptions	assumption	NOUN
ejpam-93	5	4	on	on	ADP
ejpam-93	5	5	nonlinear	nonlinear	ADJ
ejpam-93	5	6	functions	function	NOUN
ejpam-93	5	7	a	a	DET
ejpam-93	5	8	,	,	PUNCT
ejpam-93	5	9	f	f	PROPN
ejpam-93	5	10	,	,	PUNCT
ejpam-93	5	11	b	b	PROPN
ejpam-93	5	12	and	and	CCONJ
ejpam-93	5	13	initial	initial	ADJ
ejpam-93	5	14	data	datum	NOUN
ejpam-93	5	15	u0(x	u0(x	NUM
ejpam-93	5	16	)	)	PUNCT
ejpam-93	5	17	,	,	PUNCT
ejpam-93	5	18	we	we	PRON
ejpam-93	5	19	obtain	obtain	VERB
ejpam-93	5	20	the	the	DET
ejpam-93	5	21	blow	blow	NOUN
ejpam-93	5	22	-	-	PUNCT
ejpam-93	5	23	up	up	ADP
ejpam-93	5	24	rate	rate	NOUN
ejpam-93	5	25	and	and	CCONJ
ejpam-93	5	26	the	the	DET
ejpam-93	5	27	blow	blow	NOUN
ejpam-93	5	28	-	-	PUNCT
ejpam-93	5	29	up	up	ADP
ejpam-93	5	30	set	set	NOUN
ejpam-93	5	31	of	of	ADP
ejpam-93	5	32	the	the	DET
ejpam-93	5	33	solutions	solution	NOUN
ejpam-93	5	34	of	of	ADP
ejpam-93	5	35	the	the	DET
ejpam-93	5	36	problem	problem	NOUN
ejpam-93	5	37	by	by	ADP
ejpam-93	5	38	the	the	DET
ejpam-93	5	39	nirenberg	nirenberg	PROPN
ejpam-93	5	40	maximum	maximum	PROPN
ejpam-93	5	41	principle	principle	NOUN
ejpam-93	5	42	.	.	PUNCT
ejpam-93	6	1	ams	am	NOUN
ejpam-93	6	2	subject	subject	ADJ
ejpam-93	6	3	classifications	classification	NOUN
ejpam-93	6	4	:	:	PUNCT
ejpam-93	6	5	3333	3333	NUM
ejpam-93	6	6	key	key	ADJ
ejpam-93	6	7	words	word	NOUN
ejpam-93	6	8	:	:	PUNCT
ejpam-93	6	9	nonlinear	nonlinear	ADJ
ejpam-93	6	10	heat	heat	NOUN
ejpam-93	6	11	equation	equation	NOUN
ejpam-93	6	12	,	,	PUNCT
ejpam-93	6	13	nonlinear	nonlinear	ADJ
ejpam-93	6	14	boundary	boundary	ADJ
ejpam-93	6	15	condition	condition	NOUN
ejpam-93	6	16	,	,	PUNCT
ejpam-93	6	17	blow	blow	NOUN
ejpam-93	6	18	-	-	PUNCT
ejpam-93	6	19	up	up	NOUN
ejpam-93	6	20	,	,	PUNCT
ejpam-93	6	21	absorption	absorption	NOUN
ejpam-93	6	22	,	,	PUNCT
ejpam-93	6	23	maximum	maximum	ADJ
ejpam-93	6	24	principle	principle	NOUN
ejpam-93	6	25	.	.	PUNCT
ejpam-93	7	1	1	1	X
ejpam-93	7	2	.	.	X
ejpam-93	7	3	introduction	introduction	NOUN
ejpam-93	7	4	in	in	ADP
ejpam-93	7	5	the	the	DET
ejpam-93	7	6	last	last	ADJ
ejpam-93	7	7	few	few	ADJ
ejpam-93	7	8	decades	decade	NOUN
ejpam-93	7	9	,	,	PUNCT
ejpam-93	7	10	blow	blow	NOUN
ejpam-93	7	11	-	-	PUNCT
ejpam-93	7	12	up	up	ADP
ejpam-93	7	13	phenomena	phenomenon	NOUN
ejpam-93	7	14	for	for	ADP
ejpam-93	7	15	the	the	DET
ejpam-93	7	16	nonlinear	nonlinear	ADJ
ejpam-93	7	17	parabolic	parabolic	ADJ
ejpam-93	7	18	equations	equation	NOUN
ejpam-93	7	19	with	with	ADP
ejpam-93	7	20	heat	heat	NOUN
ejpam-93	7	21	sources	source	NOUN
ejpam-93	7	22	have	have	AUX
ejpam-93	7	23	been	be	AUX
ejpam-93	7	24	studied	study	VERB
ejpam-93	7	25	by	by	ADP
ejpam-93	7	26	many	many	ADJ
ejpam-93	7	27	authors	author	NOUN
ejpam-93	7	28	,	,	PUNCT
ejpam-93	7	29	and	and	CCONJ
ejpam-93	7	30	the	the	DET
ejpam-93	7	31	reader	reader	NOUN
ejpam-93	7	32	is	be	AUX
ejpam-93	7	33	referred	refer	VERB
ejpam-93	7	34	to	to	ADP
ejpam-93	7	35	[	[	PUNCT
ejpam-93	7	36	3	3	NUM
ejpam-93	7	37	-	-	SYM
ejpam-93	7	38	5	5	NUM
ejpam-93	7	39	,	,	PUNCT
ejpam-93	7	40	9	9	NUM
ejpam-93	7	41	,	,	PUNCT
ejpam-93	7	42	11	11	NUM
ejpam-93	7	43	,	,	PUNCT
ejpam-93	7	44	14	14	NUM
ejpam-93	7	45	]	]	PUNCT
ejpam-93	7	46	and	and	CCONJ
ejpam-93	7	47	the	the	DET
ejpam-93	7	48	references	reference	NOUN
ejpam-93	7	49	therein	therein	ADV
ejpam-93	7	50	.	.	PUNCT
ejpam-93	8	1	for	for	ADP
ejpam-93	8	2	the	the	DET
ejpam-93	8	3	parabolic	parabolic	ADJ
ejpam-93	8	4	equations	equation	NOUN
ejpam-93	8	5	with	with	ADP
ejpam-93	8	6	no	no	DET
ejpam-93	8	7	sources	source	NOUN
ejpam-93	8	8	,	,	PUNCT
ejpam-93	8	9	some	some	DET
ejpam-93	8	10	necessary	necessary	ADJ
ejpam-93	8	11	conditions	condition	NOUN
ejpam-93	8	12	for	for	ADP
ejpam-93	8	13	the	the	DET
ejpam-93	8	14	global	global	ADJ
ejpam-93	8	15	existence	existence	NOUN
ejpam-93	8	16	and	and	CCONJ
ejpam-93	8	17	blow	blow	NOUN
ejpam-93	8	18	-	-	PUNCT
ejpam-93	8	19	up	up	NOUN
ejpam-93	8	20	of	of	ADP
ejpam-93	8	21	the	the	DET
ejpam-93	8	22	solutions	solution	NOUN
ejpam-93	8	23	are	be	AUX
ejpam-93	8	24	given	give	VERB
ejpam-93	8	25	in	in	ADP
ejpam-93	8	26	[	[	X
ejpam-93	8	27	6	6	NUM
ejpam-93	8	28	,	,	PUNCT
ejpam-93	8	29	8	8	NUM
ejpam-93	8	30	,	,	PUNCT
ejpam-93	8	31	12	12	NUM
ejpam-93	8	32	-	-	SYM
ejpam-93	8	33	13	13	NUM
ejpam-93	8	34	]	]	PUNCT
ejpam-93	8	35	.	.	PUNCT
ejpam-93	9	1	here	here	ADV
ejpam-93	9	2	we	we	PRON
ejpam-93	9	3	are	be	AUX
ejpam-93	9	4	interested	interested	ADJ
ejpam-93	9	5	in	in	ADP
ejpam-93	9	6	the	the	DET
ejpam-93	9	7	blow	blow	NOUN
ejpam-93	9	8	-	-	PUNCT
ejpam-93	9	9	up	up	ADP
ejpam-93	9	10	phenomena	phenomenon	NOUN
ejpam-93	9	11	of	of	ADP
ejpam-93	9	12	the	the	DET
ejpam-93	9	13	solutions	solution	NOUN
ejpam-93	9	14	of	of	ADP
ejpam-93	9	15	the	the	DET
ejpam-93	9	16	parabolic	parabolic	ADJ
ejpam-93	9	17	problems	problem	NOUN
ejpam-93	9	18	with	with	ADP
ejpam-93	9	19	absorptions	absorption	NOUN
ejpam-93	9	20	at	at	ADP
ejpam-93	9	21	interior	interior	NOUN
ejpam-93	9	22	of	of	ADP
ejpam-93	9	23	the	the	DET
ejpam-93	9	24	domains	domain	NOUN
ejpam-93	9	25	.	.	PUNCT
ejpam-93	10	1	in	in	ADP
ejpam-93	10	2	this	this	DET
ejpam-93	10	3	paper	paper	NOUN
ejpam-93	10	4	,	,	PUNCT
ejpam-93	10	5	we	we	PRON
ejpam-93	10	6	investigate	investigate	VERB
ejpam-93	10	7	the	the	DET
ejpam-93	10	8	following	follow	VERB
ejpam-93	10	9	initial	initial	ADJ
ejpam-93	10	10	-	-	PUNCT
ejpam-93	10	11	boundary	boundary	NOUN
ejpam-93	10	12	value	value	NOUN
ejpam-93	10	13	problem	problem	NOUN
ejpam-93	10	14	:	:	PUNCT
ejpam-93	10	15	ut	ut	PROPN
ejpam-93	10	16	=	=	PROPN
ejpam-93	10	17	div(a(u)∇u)−	div(a(u)∇u)−	PROPN
ejpam-93	10	18	f	f	PROPN
ejpam-93	10	19	(	(	PUNCT
ejpam-93	10	20	u	u	NOUN
ejpam-93	10	21	)	)	PUNCT
ejpam-93	10	22	in	in	ADP
ejpam-93	10	23	ω×	ω×	PROPN
ejpam-93	10	24	(	(	PUNCT
ejpam-93	10	25	0	0	NUM
ejpam-93	10	26	,	,	PUNCT
ejpam-93	10	27	t	t	NOUN
ejpam-93	10	28	)	)	PUNCT
ejpam-93	10	29	(	(	PUNCT
ejpam-93	10	30	1	1	NUM
ejpam-93	10	31	)	)	PUNCT
ejpam-93	10	32	∂	∂	NUM
ejpam-93	10	33	u	u	NOUN
ejpam-93	10	34	∂	∂	NOUN
ejpam-93	10	35	n	n	PROPN
ejpam-93	10	36	=	=	SYM
ejpam-93	10	37	b(u	b(u	PROPN
ejpam-93	10	38	)	)	PUNCT
ejpam-93	10	39	on	on	ADP
ejpam-93	10	40	∂ω×	∂ω×	PROPN
ejpam-93	10	41	(	(	PUNCT
ejpam-93	10	42	0	0	NUM
ejpam-93	10	43	,	,	PUNCT
ejpam-93	10	44	t	t	NOUN
ejpam-93	10	45	)	)	PUNCT
ejpam-93	10	46	(	(	PUNCT
ejpam-93	10	47	2	2	X
ejpam-93	10	48	)	)	PUNCT
ejpam-93	10	49	u(x	u(x	NOUN
ejpam-93	10	50	,	,	PUNCT
ejpam-93	10	51	0	0	NUM
ejpam-93	10	52	)	)	PUNCT
ejpam-93	10	53	=	=	SYM
ejpam-93	10	54	u0(x	u0(x	NOUN
ejpam-93	10	55	)	)	PUNCT
ejpam-93	10	56	>	>	X
ejpam-93	10	57	0	0	PUNCT
ejpam-93	11	1	in	in	ADP
ejpam-93	11	2	ω	ω	PROPN
ejpam-93	11	3	(	(	PUNCT
ejpam-93	11	4	3	3	NUM
ejpam-93	11	5	)	)	PUNCT
ejpam-93	11	6	where	where	SCONJ
ejpam-93	11	7	ω	ω	PROPN
ejpam-93	11	8	is	be	AUX
ejpam-93	11	9	a	a	DET
ejpam-93	11	10	bounded	bounded	ADJ
ejpam-93	11	11	domain	domain	NOUN
ejpam-93	11	12	in	in	ADP
ejpam-93	11	13	rn	rn	PROPN
ejpam-93	11	14	with	with	ADP
ejpam-93	11	15	c2	c2	PROPN
ejpam-93	11	16	boundary	boundary	NOUN
ejpam-93	11	17	,	,	PUNCT
ejpam-93	11	18	∂	∂	NUM
ejpam-93	11	19	u	u	NOUN
ejpam-93	11	20	∂	∂	NOUN
ejpam-93	11	21	n	n	NOUN
ejpam-93	11	22	denotes	denote	VERB
ejpam-93	11	23	the	the	DET
ejpam-93	11	24	outward	outward	ADJ
ejpam-93	11	25	normal	normal	ADJ
ejpam-93	11	26	derivative	derivative	NOUN
ejpam-93	11	27	;	;	PUNCT
ejpam-93	11	28	u0(x	u0(x	X
ejpam-93	11	29	)	)	PUNCT
ejpam-93	11	30	∈	∈	PROPN
ejpam-93	11	31	c(ω	c(ω	PROPN
ejpam-93	11	32	)	)	PUNCT
ejpam-93	11	33	∩	∩	NOUN
ejpam-93	11	34	c2(ω	c2(ω	CCONJ
ejpam-93	11	35	)	)	PUNCT
ejpam-93	11	36	is	be	AUX
ejpam-93	11	37	a	a	DET
ejpam-93	11	38	positive	positive	ADJ
ejpam-93	11	39	function	function	NOUN
ejpam-93	11	40	,	,	PUNCT
ejpam-93	11	41	satisfying	satisfy	VERB
ejpam-93	11	42	compatibility	compatibility	NOUN
ejpam-93	11	43	condition	condition	NOUN
ejpam-93	11	44	;	;	PUNCT
ejpam-93	11	45	a	a	DET
ejpam-93	11	46	(	(	PUNCT
ejpam-93	11	47	·	·	PUNCT
ejpam-93	11	48	)	)	PUNCT
ejpam-93	11	49	,	,	PUNCT
ejpam-93	11	50	f	f	PROPN
ejpam-93	11	51	(	(	PUNCT
ejpam-93	11	52	·	·	PUNCT
ejpam-93	11	53	)	)	PUNCT
ejpam-93	11	54	,	,	PUNCT
ejpam-93	11	55	b	b	X
ejpam-93	11	56	(	(	PUNCT
ejpam-93	11	57	·	·	PUNCT
ejpam-93	11	58	)	)	PUNCT
ejpam-93	11	59	are	be	AUX
ejpam-93	11	60	smooth	smooth	ADJ
ejpam-93	11	61	positive	positive	ADJ
ejpam-93	11	62	functions	function	NOUN
ejpam-93	11	63	.	.	PUNCT
ejpam-93	12	1	problem	problem	NOUN
ejpam-93	12	2	(	(	PUNCT
ejpam-93	12	3	1)-(3	1)-(3	NOUN
ejpam-93	12	4	)	)	PUNCT
ejpam-93	12	5	has	have	AUX
ejpam-93	12	6	been	be	AUX
ejpam-93	12	7	formulated	formulate	VERB
ejpam-93	12	8	from	from	ADP
ejpam-93	12	9	physical	physical	ADJ
ejpam-93	12	10	models	model	NOUN
ejpam-93	12	11	arising	arise	VERB
ejpam-93	12	12	in	in	ADP
ejpam-93	12	13	various	various	ADJ
ejpam-93	12	14	fields	field	NOUN
ejpam-93	12	15	of	of	ADP
ejpam-93	12	16	applied	applied	ADJ
ejpam-93	12	17	sciences	science	NOUN
ejpam-93	12	18	.	.	PUNCT
ejpam-93	13	1	for	for	ADP
ejpam-93	13	2	example	example	NOUN
ejpam-93	13	3	it	it	PRON
ejpam-93	13	4	can	can	AUX
ejpam-93	13	5	be	be	AUX
ejpam-93	13	6	interpreted	interpret	VERB
ejpam-93	13	7	as	as	ADP
ejpam-93	13	8	a	a	DET
ejpam-93	13	9	heat	heat	NOUN
ejpam-93	13	10	conduction	conduction	NOUN
ejpam-93	13	11	problem	problem	NOUN
ejpam-93	13	12	with	with	ADP
ejpam-93	13	13	nonlinear	nonlinear	ADJ
ejpam-93	13	14	∗corresponding	∗corresponde	VERB
ejpam-93	13	15	author	author	NOUN
ejpam-93	13	16	.	.	PUNCT
ejpam-93	14	1	email	email	NOUN
ejpam-93	14	2	addresses	address	NOUN
ejpam-93	14	3	:	:	PUNCT
ejpam-93	14	4	hlzhang@zjou.edu.cn	hlzhang@zjou.edu.cn	PROPN
ejpam-93	14	5	(	(	PUNCT
ejpam-93	14	6	h.	h.	PROPN
ejpam-93	14	7	zhang	zhang	PROPN
ejpam-93	14	8	)	)	PUNCT
ejpam-93	14	9	guoxiulanlm@yahoo.cn	guoxiulanlm@yahoo.cn	PROPN
ejpam-93	14	10	(	(	PUNCT
ejpam-93	14	11	x.	x.	NOUN
ejpam-93	14	12	guo	guo	PROPN
ejpam-93	14	13	)	)	PUNCT
ejpam-93	14	14	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-93	15	1	33	33	NUM
ejpam-93	15	2	c	c	X
ejpam-93	15	3	©	©	PROPN
ejpam-93	15	4	2008	2008	NUM
ejpam-93	15	5	ejpam	ejpam	VERB
ejpam-93	15	6	all	all	DET
ejpam-93	15	7	rights	right	NOUN
ejpam-93	15	8	reserved	reserve	VERB
ejpam-93	15	9	.	.	PUNCT
ejpam-93	16	1	h.	h.	PROPN
ejpam-93	16	2	zhang	zhang	PROPN
ejpam-93	16	3	,	,	PUNCT
ejpam-93	16	4	x.	x.	PROPN
ejpam-93	16	5	guo	guo	PROPN
ejpam-93	16	6	/	/	SYM
ejpam-93	16	7	eur	eur	PROPN
ejpam-93	16	8	.	.	PUNCT
ejpam-93	17	1	j.	j.	PROPN
ejpam-93	17	2	pure	pure	PROPN
ejpam-93	17	3	appl	appl	PROPN
ejpam-93	17	4	.	.	PROPN
ejpam-93	17	5	math	math	PROPN
ejpam-93	17	6	,	,	PUNCT
ejpam-93	17	7	1	1	NUM
ejpam-93	17	8	(	(	PUNCT
ejpam-93	17	9	2008	2008	NUM
ejpam-93	17	10	)	)	PUNCT
ejpam-93	17	11	,	,	PUNCT
ejpam-93	17	12	(	(	PUNCT
ejpam-93	17	13	33	33	NUM
ejpam-93	17	14	-	-	SYM
ejpam-93	17	15	39	39	NUM
ejpam-93	17	16	)	)	PUNCT
ejpam-93	17	17	34	34	NUM
ejpam-93	17	18	diffusivity	diffusivity	NOUN
ejpam-93	17	19	,	,	PUNCT
ejpam-93	17	20	absorption	absorption	NOUN
ejpam-93	17	21	at	at	ADP
ejpam-93	17	22	interior	interior	NOUN
ejpam-93	17	23	of	of	ADP
ejpam-93	17	24	the	the	DET
ejpam-93	17	25	domain	domain	NOUN
ejpam-93	17	26	and	and	CCONJ
ejpam-93	17	27	a	a	DET
ejpam-93	17	28	nonlinear	nonlinear	ADJ
ejpam-93	17	29	radiation	radiation	NOUN
ejpam-93	17	30	law	law	NOUN
ejpam-93	17	31	on	on	ADP
ejpam-93	17	32	the	the	DET
ejpam-93	17	33	boundary	boundary	NOUN
ejpam-93	17	34	of	of	ADP
ejpam-93	17	35	the	the	DET
ejpam-93	17	36	material	material	NOUN
ejpam-93	17	37	body	body	NOUN
ejpam-93	17	38	.	.	PUNCT
ejpam-93	18	1	the	the	DET
ejpam-93	18	2	local	local	ADJ
ejpam-93	18	3	existence	existence	NOUN
ejpam-93	18	4	and	and	CCONJ
ejpam-93	18	5	uniqueness	uniqueness	NOUN
ejpam-93	18	6	of	of	ADP
ejpam-93	18	7	positive	positive	ADJ
ejpam-93	18	8	classical	classical	ADJ
ejpam-93	18	9	solution	solution	NOUN
ejpam-93	18	10	of	of	ADP
ejpam-93	18	11	the	the	DET
ejpam-93	18	12	problem	problem	NOUN
ejpam-93	18	13	(	(	PUNCT
ejpam-93	18	14	1)-(3	1)-(3	NOUN
ejpam-93	18	15	)	)	PUNCT
ejpam-93	18	16	were	be	AUX
ejpam-93	18	17	established	establish	VERB
ejpam-93	18	18	by	by	ADP
ejpam-93	18	19	amann	amann	NOUN
ejpam-93	19	1	[	[	X
ejpam-93	19	2	1	1	NUM
ejpam-93	19	3	]	]	PUNCT
ejpam-93	19	4	,	,	PUNCT
ejpam-93	19	5	finite	finite	ADJ
ejpam-93	19	6	extinction	extinction	NOUN
ejpam-93	19	7	time	time	NOUN
ejpam-93	19	8	is	be	AUX
ejpam-93	19	9	studied	study	VERB
ejpam-93	19	10	by	by	ADP
ejpam-93	19	11	leung	leung	PROPN
ejpam-93	19	12	and	and	CCONJ
ejpam-93	19	13	zhang	zhang	PROPN
ejpam-93	20	1	[	[	X
ejpam-93	20	2	7	7	NUM
ejpam-93	20	3	]	]	PUNCT
ejpam-93	20	4	.	.	PUNCT
ejpam-93	21	1	here	here	ADV
ejpam-93	21	2	we	we	PRON
ejpam-93	21	3	are	be	AUX
ejpam-93	21	4	interested	interested	ADJ
ejpam-93	21	5	in	in	ADP
ejpam-93	21	6	the	the	DET
ejpam-93	21	7	blow	blow	NOUN
ejpam-93	21	8	-	-	PUNCT
ejpam-93	21	9	up	up	ADP
ejpam-93	21	10	phenomenon	phenomenon	NOUN
ejpam-93	21	11	of	of	ADP
ejpam-93	21	12	the	the	DET
ejpam-93	21	13	solution	solution	NOUN
ejpam-93	21	14	of	of	ADP
ejpam-93	21	15	the	the	DET
ejpam-93	21	16	problem	problem	NOUN
ejpam-93	21	17	(	(	PUNCT
ejpam-93	21	18	1)-(3).we	1)-(3).we	NOUN
ejpam-93	21	19	say	say	VERB
ejpam-93	21	20	that	that	SCONJ
ejpam-93	21	21	the	the	DET
ejpam-93	21	22	solution	solution	NOUN
ejpam-93	21	23	u	u	NOUN
ejpam-93	21	24	blows	blow	VERB
ejpam-93	21	25	up	up	ADP
ejpam-93	21	26	if	if	SCONJ
ejpam-93	21	27	there	there	PRON
ejpam-93	21	28	exists	exist	VERB
ejpam-93	21	29	a	a	DET
ejpam-93	21	30	0	0	NUM
ejpam-93	21	31	<	<	X
ejpam-93	21	32	t	t	X
ejpam-93	21	33	<	<	X
ejpam-93	21	34	+	+	NOUN
ejpam-93	21	35	∞	∞	NUM
ejpam-93	21	36	such	such	ADJ
ejpam-93	21	37	that	that	SCONJ
ejpam-93	21	38	lim	lim	PROPN
ejpam-93	21	39	t→t	t→t	NUM
ejpam-93	21	40	‖	‖	PROPN
ejpam-93	21	41	u	u	NOUN
ejpam-93	21	42	‖l∞(ω)=+∞.	‖l∞(ω)=+∞.	X
ejpam-93	21	43	in	in	ADP
ejpam-93	21	44	this	this	DET
ejpam-93	21	45	paper	paper	NOUN
ejpam-93	21	46	,	,	PUNCT
ejpam-93	21	47	we	we	PRON
ejpam-93	21	48	study	study	VERB
ejpam-93	21	49	the	the	DET
ejpam-93	21	50	blow	blow	NOUN
ejpam-93	21	51	-	-	PUNCT
ejpam-93	21	52	up	up	ADP
ejpam-93	21	53	rate	rate	NOUN
ejpam-93	21	54	and	and	CCONJ
ejpam-93	21	55	blow	blow	NOUN
ejpam-93	21	56	-	-	PUNCT
ejpam-93	21	57	up	up	NOUN
ejpam-93	21	58	set	set	VERB
ejpam-93	21	59	by	by	ADP
ejpam-93	21	60	the	the	DET
ejpam-93	21	61	maximum	maximum	ADJ
ejpam-93	21	62	principles	principle	NOUN
ejpam-93	21	63	.	.	PUNCT
ejpam-93	22	1	our	our	PRON
ejpam-93	22	2	results	result	NOUN
ejpam-93	22	3	generalize	generalize	VERB
ejpam-93	22	4	and	and	CCONJ
ejpam-93	22	5	deepen	deepen	VERB
ejpam-93	22	6	ones	one	NOUN
ejpam-93	22	7	from	from	ADP
ejpam-93	22	8	corresponding	correspond	VERB
ejpam-93	22	9	work	work	NOUN
ejpam-93	22	10	in	in	ADP
ejpam-93	22	11	[	[	PUNCT
ejpam-93	22	12	2	2	NUM
ejpam-93	22	13	-	-	SYM
ejpam-93	22	14	6	6	NUM
ejpam-93	22	15	,	,	PUNCT
ejpam-93	22	16	8	8	NUM
ejpam-93	22	17	-	-	SYM
ejpam-93	22	18	12	12	NUM
ejpam-93	22	19	]	]	PUNCT
ejpam-93	22	20	.	.	PUNCT
ejpam-93	23	1	2	2	X
ejpam-93	23	2	.	.	X
ejpam-93	23	3	blow	blow	NOUN
ejpam-93	23	4	-	-	PUNCT
ejpam-93	23	5	up	up	ADP
ejpam-93	23	6	rate	rate	NOUN
ejpam-93	23	7	and	and	CCONJ
ejpam-93	23	8	blow	blow	NOUN
ejpam-93	23	9	-	-	PUNCT
ejpam-93	23	10	up	up	ADP
ejpam-93	23	11	set	set	NOUN
ejpam-93	23	12	theorem	theorem	NOUN
ejpam-93	23	13	1	1	X
ejpam-93	23	14	.	.	PUNCT
ejpam-93	24	1	let	let	VERB
ejpam-93	24	2	u(x	u(x	PROPN
ejpam-93	24	3	,	,	PUNCT
ejpam-93	24	4	t	t	PROPN
ejpam-93	24	5	)	)	PUNCT
ejpam-93	24	6	be	be	AUX
ejpam-93	24	7	a	a	DET
ejpam-93	24	8	solution	solution	NOUN
ejpam-93	24	9	of	of	ADP
ejpam-93	24	10	the	the	DET
ejpam-93	24	11	problem	problem	NOUN
ejpam-93	24	12	(	(	PUNCT
ejpam-93	24	13	1)-(3	1)-(3	NUM
ejpam-93	24	14	)	)	PUNCT
ejpam-93	24	15	.	.	PUNCT
ejpam-93	25	1	assume	assume	VERB
ejpam-93	25	2	that	that	SCONJ
ejpam-93	25	3	:	:	PUNCT
ejpam-93	25	4	(	(	PUNCT
ejpam-93	25	5	1	1	X
ejpam-93	25	6	)	)	PUNCT
ejpam-93	25	7	∫	∫	PROPN
ejpam-93	26	1	+	+	PROPN
ejpam-93	26	2	∞	∞	PROPN
ejpam-93	26	3	0	0	NUM
ejpam-93	26	4	a(s	a(s	ADJ
ejpam-93	26	5	)	)	PUNCT
ejpam-93	26	6	b(s)ds	b(s)ds	PART
ejpam-93	27	1	<	<	X
ejpam-93	27	2	+	+	NOUN
ejpam-93	27	3	∞	∞	PROPN
ejpam-93	27	4	and	and	CCONJ
ejpam-93	27	5	a′(s	a′(s	PROPN
ejpam-93	27	6	)	)	PUNCT
ejpam-93	27	7	,	,	PUNCT
ejpam-93	27	8	(	(	PUNCT
ejpam-93	27	9	b′(s	b′(s	X
ejpam-93	27	10	)	)	PUNCT
ejpam-93	27	11	a(s	a(s	PROPN
ejpam-93	27	12	)	)	PUNCT
ejpam-93	27	13	)	)	PUNCT
ejpam-93	28	1	′	′	NOUN
ejpam-93	28	2	,	,	PUNCT
ejpam-93	28	3	(	(	PUNCT
ejpam-93	28	4	b(s	b(s	PROPN
ejpam-93	28	5	)	)	PUNCT
ejpam-93	28	6	f	f	PROPN
ejpam-93	28	7	(	(	PUNCT
ejpam-93	28	8	s	s	NOUN
ejpam-93	28	9	)	)	PUNCT
ejpam-93	28	10	)	)	PUNCT
ejpam-93	29	1	′	′	NUM
ejpam-93	29	2	≥	≥	NOUN
ejpam-93	29	3	0	0	NUM
ejpam-93	30	1	for	for	ADP
ejpam-93	30	2	s	s	PROPN
ejpam-93	30	3	>	>	X
ejpam-93	30	4	0	0	NUM
ejpam-93	30	5	,	,	PUNCT
ejpam-93	30	6	(	(	PUNCT
ejpam-93	30	7	2	2	X
ejpam-93	30	8	)	)	PUNCT
ejpam-93	30	9	div(a(u0)∇u0)≥	div(a(u0)∇u0)≥	VERB
ejpam-93	30	10	f	f	X
ejpam-93	30	11	(	(	PUNCT
ejpam-93	30	12	u0	u0	PROPN
ejpam-93	30	13	)	)	PUNCT
ejpam-93	30	14	.	.	PUNCT
ejpam-93	31	1	then	then	ADV
ejpam-93	31	2	u(x	u(x	PROPN
ejpam-93	31	3	,	,	PUNCT
ejpam-93	31	4	t	t	PROPN
ejpam-93	31	5	)	)	PUNCT
ejpam-93	31	6	must	must	AUX
ejpam-93	31	7	blow	blow	VERB
ejpam-93	31	8	up	up	ADP
ejpam-93	31	9	in	in	ADP
ejpam-93	31	10	finite	finite	ADJ
ejpam-93	31	11	time	time	NOUN
ejpam-93	31	12	t	t	PROPN
ejpam-93	31	13	and	and	CCONJ
ejpam-93	31	14	there	there	PRON
ejpam-93	31	15	exists	exist	VERB
ejpam-93	31	16	a	a	DET
ejpam-93	31	17	constant	constant	ADJ
ejpam-93	31	18	δ	δ	NOUN
ejpam-93	31	19	>	>	X
ejpam-93	31	20	0	0	NUM
ejpam-93	32	1	such	such	ADJ
ejpam-93	32	2	that	that	DET
ejpam-93	32	3	sup	sup	PROPN
ejpam-93	32	4	x∈ω	x∈ω	NOUN
ejpam-93	32	5	u(x	u(x	PROPN
ejpam-93	32	6	,	,	PUNCT
ejpam-93	32	7	t)≤	t)≤	PRON
ejpam-93	32	8	h(δ(t	h(δ(t	PROPN
ejpam-93	32	9	−	−	PROPN
ejpam-93	32	10	t	t	PROPN
ejpam-93	32	11	)	)	PUNCT
ejpam-93	32	12	)	)	PUNCT
ejpam-93	33	1	for	for	ADP
ejpam-93	33	2	0	0	NUM
ejpam-93	33	3	<	<	X
ejpam-93	33	4	t	t	X
ejpam-93	33	5	<	<	X
ejpam-93	33	6	t	t	PROPN
ejpam-93	33	7	,	,	PUNCT
ejpam-93	33	8	where	where	SCONJ
ejpam-93	33	9	h	h	NOUN
ejpam-93	33	10	=	=	SYM
ejpam-93	33	11	g−1	g−1	PROPN
ejpam-93	33	12	and	and	CCONJ
ejpam-93	33	13	g(s	g(	NOUN
ejpam-93	33	14	)	)	PUNCT
ejpam-93	33	15	=	=	SYM
ejpam-93	33	16	∫	∫	PROPN
ejpam-93	34	1	+	+	NUM
ejpam-93	34	2	∞	∞	PROPN
ejpam-93	34	3	s	s	PART
ejpam-93	34	4	a(µ	a(µ	ADJ
ejpam-93	34	5	)	)	PUNCT
ejpam-93	34	6	b(µ)dµ.	b(µ)dµ.	NOUN
ejpam-93	34	7	proof	proof	NOUN
ejpam-93	34	8	.	.	PUNCT
ejpam-93	35	1	we	we	PRON
ejpam-93	35	2	will	will	AUX
ejpam-93	35	3	use	use	VERB
ejpam-93	35	4	the	the	DET
ejpam-93	35	5	ideas	idea	NOUN
ejpam-93	35	6	of	of	ADP
ejpam-93	35	7	[	[	X
ejpam-93	35	8	4	4	NUM
ejpam-93	35	9	]	]	PUNCT
ejpam-93	35	10	or	or	CCONJ
ejpam-93	35	11	[	[	X
ejpam-93	35	12	14	14	NUM
ejpam-93	35	13	]	]	PUNCT
ejpam-93	35	14	.	.	PUNCT
ejpam-93	36	1	step	step	NOUN
ejpam-93	36	2	1	1	NUM
ejpam-93	36	3	:	:	PUNCT
ejpam-93	36	4	growth	growth	NOUN
ejpam-93	36	5	estimate	estimate	NOUN
ejpam-93	36	6	.	.	PUNCT
ejpam-93	37	1	introduce	introduce	VERB
ejpam-93	37	2	an	an	DET
ejpam-93	37	3	auxiliary	auxiliary	ADJ
ejpam-93	37	4	function	function	NOUN
ejpam-93	37	5	j(x	j(x	PROPN
ejpam-93	37	6	,	,	PUNCT
ejpam-93	37	7	t	t	PROPN
ejpam-93	37	8	)	)	PUNCT
ejpam-93	37	9	=	=	PRON
ejpam-93	37	10	a(u)ut	a(u)ut	DET
ejpam-93	37	11	−δb(u	−δb(u	PROPN
ejpam-93	37	12	)	)	PUNCT
ejpam-93	37	13	(	(	PUNCT
ejpam-93	37	14	δ	δ	X
ejpam-93	37	15	>	>	X
ejpam-93	37	16	0	0	NUM
ejpam-93	37	17	)	)	PUNCT
ejpam-93	37	18	(	(	PUNCT
ejpam-93	37	19	4	4	X
ejpam-93	37	20	)	)	PUNCT
ejpam-93	37	21	then	then	ADV
ejpam-93	37	22	we	we	PRON
ejpam-93	37	23	have	have	VERB
ejpam-93	37	24	∇j	∇j	PROPN
ejpam-93	37	25	=	=	PUNCT
ejpam-93	37	26	a	a	PRON
ejpam-93	37	27	′	′	NUM
ejpam-93	38	1	ut∇u+	ut∇u+	ADJ
ejpam-93	38	2	a∇ut	a∇ut	INTJ
ejpam-93	38	3	−δb	−δb	INTJ
ejpam-93	38	4	′	′	NUM
ejpam-93	38	5	∇u	∇u	ADJ
ejpam-93	38	6	4j	4j	NOUN
ejpam-93	38	7	=	=	SYM
ejpam-93	38	8	a4ut	a4ut	X
ejpam-93	38	9	+	+	NUM
ejpam-93	38	10	2a	2a	NUM
ejpam-93	39	1	′	′	NUM
ejpam-93	39	2	∇u∇ut	∇u∇ut	NOUN
ejpam-93	39	3	+	+	CCONJ
ejpam-93	39	4	a	a	DET
ejpam-93	39	5	′′	′′	PROPN
ejpam-93	39	6	ut	ut	PROPN
ejpam-93	39	7	|	|	ADV
ejpam-93	39	8	∇u	∇u	PROPN
ejpam-93	39	9	|2	|2	NUM
ejpam-93	40	1	+	+	NOUN
ejpam-93	40	2	a	a	DET
ejpam-93	40	3	′	′	NUM
ejpam-93	40	4	ut4u−δb	ut4u−δb	ADV
ejpam-93	41	1	′′	′′	PROPN
ejpam-93	41	2	|	|	ADV
ejpam-93	41	3	∇u	∇u	PROPN
ejpam-93	41	4	|2	|2	NUM
ejpam-93	41	5	−δb	−δb	NOUN
ejpam-93	41	6	′	′	NUM
ejpam-93	41	7	4u	4u	NOUN
ejpam-93	41	8	and	and	CCONJ
ejpam-93	41	9	jt	jt	PROPN
ejpam-93	41	10	=	=	PROPN
ejpam-93	42	1	a	a	DET
ejpam-93	42	2	′	′	NUM
ejpam-93	42	3	u2	u2	PROPN
ejpam-93	42	4	t	t	PROPN
ejpam-93	42	5	+	+	CCONJ
ejpam-93	42	6	a24ut	a24ut	PROPN
ejpam-93	42	7	+	+	CCONJ
ejpam-93	42	8	2aa	2aa	PROPN
ejpam-93	42	9	′	′	NUM
ejpam-93	43	1	∇u∇ut	∇u∇ut	NOUN
ejpam-93	44	1	+	+	CCONJ
ejpam-93	44	2	aa	aa	PROPN
ejpam-93	44	3	′′	′′	PROPN
ejpam-93	44	4	ut	ut	PROPN
ejpam-93	44	5	|	|	ADV
ejpam-93	44	6	∇u	∇u	PROPN
ejpam-93	44	7	|2	|2	NUM
ejpam-93	44	8	+	+	ADJ
ejpam-93	44	9	aa	aa	ADJ
ejpam-93	44	10	′	′	ADJ
ejpam-93	44	11	ut4u−	ut4u−	NOUN
ejpam-93	44	12	(	(	PUNCT
ejpam-93	44	13	a	a	DET
ejpam-93	44	14	f	f	X
ejpam-93	44	15	′+δb′)ut	′+δb′)ut	PUNCT
ejpam-93	44	16	.	.	PUNCT
ejpam-93	45	1	hence	hence	ADV
ejpam-93	45	2	,	,	PUNCT
ejpam-93	45	3	jt	jt	PROPN
ejpam-93	45	4	−	−	PROPN
ejpam-93	46	1	a4j	a4j	NOUN
ejpam-93	47	1	+	+	NUM
ejpam-93	47	2	f	f	NOUN
ejpam-93	47	3	′	′	NUM
ejpam-93	47	4	j	j	PROPN
ejpam-93	47	5	=	=	PUNCT
ejpam-93	47	6	a	a	DET
ejpam-93	47	7	′	′	NUM
ejpam-93	47	8	u2	u2	PROPN
ejpam-93	47	9	t	t	PROPN
ejpam-93	47	10	+	+	PROPN
ejpam-93	47	11	δ(ab	δ(ab	PROPN
ejpam-93	47	12	′′	′′	PROPN
ejpam-93	47	13	−	−	PROPN
ejpam-93	48	1	a	a	DET
ejpam-93	48	2	′	′	NUM
ejpam-93	48	3	b	b	NOUN
ejpam-93	48	4	′	′	NUM
ejpam-93	48	5	)	)	PUNCT
ejpam-93	49	1	|	|	ADV
ejpam-93	49	2	∇u	∇u	VERB
ejpam-93	49	3	|2	|2	NUM
ejpam-93	50	1	+	+	ADJ
ejpam-93	50	2	δ(b′	δ(b′	ADJ
ejpam-93	50	3	f	f	PROPN
ejpam-93	50	4	−	−	PROPN
ejpam-93	50	5	b	b	PROPN
ejpam-93	50	6	f	f	PROPN
ejpam-93	50	7	′	′	NUM
ejpam-93	50	8	)	)	PUNCT
ejpam-93	50	9	.	.	PUNCT
ejpam-93	51	1	(	(	PUNCT
ejpam-93	51	2	5	5	X
ejpam-93	51	3	)	)	PUNCT
ejpam-93	51	4	under	under	ADP
ejpam-93	51	5	the	the	DET
ejpam-93	51	6	assumptions	assumption	NOUN
ejpam-93	51	7	of	of	ADP
ejpam-93	51	8	theorem	theorem	NOUN
ejpam-93	51	9	1	1	NUM
ejpam-93	51	10	,	,	PUNCT
ejpam-93	51	11	we	we	PRON
ejpam-93	51	12	obtain	obtain	VERB
ejpam-93	51	13	jt	jt	PROPN
ejpam-93	51	14	−	−	PROPN
ejpam-93	52	1	a4j	a4j	NOUN
ejpam-93	52	2	+	+	NUM
ejpam-93	52	3	f	f	NOUN
ejpam-93	52	4	′j	′j	ADJ
ejpam-93	52	5	≥	≥	NOUN
ejpam-93	52	6	0	0	NUM
ejpam-93	52	7	.	.	PUNCT
ejpam-93	53	1	(	(	PUNCT
ejpam-93	53	2	6	6	NUM
ejpam-93	53	3	)	)	PUNCT
ejpam-93	53	4	since	since	SCONJ
ejpam-93	53	5	u0(x	u0(x	NUM
ejpam-93	53	6	)	)	PUNCT
ejpam-93	53	7	>	>	X
ejpam-93	53	8	0	0	PUNCT
ejpam-93	54	1	and	and	CCONJ
ejpam-93	54	2	div(a(u0)∇u0)≥	div(a(u0)∇u0)≥	VERB
ejpam-93	54	3	f	f	X
ejpam-93	54	4	(	(	PUNCT
ejpam-93	54	5	u0	u0	PROPN
ejpam-93	54	6	)	)	PUNCT
ejpam-93	54	7	,	,	PUNCT
ejpam-93	54	8	by	by	ADP
ejpam-93	54	9	the	the	DET
ejpam-93	54	10	nirenberg	nirenberg	PROPN
ejpam-93	54	11	maximum	maximum	PROPN
ejpam-93	54	12	principle	principle	NOUN
ejpam-93	54	13	,	,	PUNCT
ejpam-93	54	14	u≥	u≥	NOUN
ejpam-93	54	15	0	0	NUM
ejpam-93	54	16	and	and	CCONJ
ejpam-93	54	17	ut	ut	PROPN
ejpam-93	54	18	≥	≥	X
ejpam-93	54	19	c	c	PROPN
ejpam-93	54	20	in	in	ADP
ejpam-93	54	21	ω×	ω×	PROPN
ejpam-93	54	22	(	(	PUNCT
ejpam-93	54	23	ε0	ε0	PROPN
ejpam-93	54	24	,	,	PUNCT
ejpam-93	54	25	t	t	PROPN
ejpam-93	54	26	)	)	PUNCT
ejpam-93	54	27	,	,	PUNCT
ejpam-93	54	28	where	where	SCONJ
ejpam-93	54	29	c	c	X
ejpam-93	54	30	,	,	PUNCT
ejpam-93	54	31	ε0	ε0	PROPN
ejpam-93	54	32	are	be	AUX
ejpam-93	54	33	some	some	DET
ejpam-93	54	34	positive	positive	ADJ
ejpam-93	54	35	constants	constant	NOUN
ejpam-93	54	36	.	.	PUNCT
ejpam-93	55	1	it	it	PRON
ejpam-93	55	2	following	follow	VERB
ejpam-93	55	3	that	that	SCONJ
ejpam-93	55	4	j(x	j(x	PROPN
ejpam-93	55	5	,	,	PUNCT
ejpam-93	55	6	ε0	ε0	PROPN
ejpam-93	55	7	)	)	PUNCT
ejpam-93	55	8	=	=	SYM
ejpam-93	55	9	a(u(x	a(u(x	NOUN
ejpam-93	55	10	,	,	PUNCT
ejpam-93	55	11	ε0))ut(x	ε0))ut(x	NOUN
ejpam-93	55	12	,	,	PUNCT
ejpam-93	55	13	ε0)−δb(u(x	ε0)−δb(u(x	PROPN
ejpam-93	55	14	,	,	PUNCT
ejpam-93	55	15	ε0))≥	ε0))≥	NOUN
ejpam-93	55	16	0	0	PUNCT
ejpam-93	56	1	(	(	PUNCT
ejpam-93	56	2	7	7	X
ejpam-93	56	3	)	)	PUNCT
ejpam-93	56	4	h.	h.	PROPN
ejpam-93	56	5	zhang	zhang	PROPN
ejpam-93	56	6	,	,	PUNCT
ejpam-93	56	7	x.	x.	PROPN
ejpam-93	56	8	guo	guo	PROPN
ejpam-93	56	9	/	/	SYM
ejpam-93	56	10	eur	eur	PROPN
ejpam-93	56	11	.	.	PUNCT
ejpam-93	57	1	j.	j.	PROPN
ejpam-93	57	2	pure	pure	PROPN
ejpam-93	57	3	appl	appl	PROPN
ejpam-93	57	4	.	.	PROPN
ejpam-93	57	5	math	math	PROPN
ejpam-93	57	6	,	,	PUNCT
ejpam-93	57	7	1	1	NUM
ejpam-93	57	8	(	(	PUNCT
ejpam-93	57	9	2008	2008	NUM
ejpam-93	57	10	)	)	PUNCT
ejpam-93	57	11	,	,	PUNCT
ejpam-93	57	12	(	(	PUNCT
ejpam-93	57	13	33	33	NUM
ejpam-93	57	14	-	-	SYM
ejpam-93	57	15	39	39	NUM
ejpam-93	57	16	)	)	PUNCT
ejpam-93	57	17	35	35	NUM
ejpam-93	57	18	provided	provide	VERB
ejpam-93	57	19	δ	δ	PROPN
ejpam-93	57	20	is	be	AUX
ejpam-93	57	21	small	small	ADJ
ejpam-93	57	22	enough	enough	ADV
ejpam-93	57	23	.	.	PUNCT
ejpam-93	58	1	note	note	VERB
ejpam-93	58	2	that	that	SCONJ
ejpam-93	58	3	∂	∂	NUM
ejpam-93	58	4	u	u	NOUN
ejpam-93	58	5	∂	∂	NOUN
ejpam-93	58	6	n	n	PROPN
ejpam-93	58	7	=	=	SYM
ejpam-93	58	8	b(u	b(u	PROPN
ejpam-93	58	9	)	)	PUNCT
ejpam-93	58	10	on	on	ADP
ejpam-93	58	11	∂ω×	∂ω×	PROPN
ejpam-93	58	12	(	(	PUNCT
ejpam-93	58	13	0	0	NUM
ejpam-93	58	14	,	,	PUNCT
ejpam-93	58	15	t	t	PROPN
ejpam-93	58	16	)	)	PUNCT
ejpam-93	58	17	,	,	PUNCT
ejpam-93	58	18	we	we	PRON
ejpam-93	58	19	have	have	VERB
ejpam-93	58	20	∂	∂	NUM
ejpam-93	58	21	ut	ut	PROPN
ejpam-93	58	22	∂	∂	PROPN
ejpam-93	58	23	n	n	NOUN
ejpam-93	58	24	=	=	PUNCT
ejpam-93	58	25	b′(u)ut	b′(u)ut	PROPN
ejpam-93	58	26	on	on	ADP
ejpam-93	58	27	∂ω×	∂ω×	PROPN
ejpam-93	58	28	(	(	PUNCT
ejpam-93	58	29	0	0	NUM
ejpam-93	58	30	,	,	PUNCT
ejpam-93	58	31	t	t	NOUN
ejpam-93	58	32	)	)	PUNCT
ejpam-93	58	33	.	.	PUNCT
ejpam-93	59	1	thus	thus	ADV
ejpam-93	59	2	∂	∂	NUM
ejpam-93	59	3	j	j	PROPN
ejpam-93	59	4	∂	∂	PROPN
ejpam-93	59	5	n	n	NOUN
ejpam-93	59	6	=	=	SYM
ejpam-93	59	7	a	a	DET
ejpam-93	59	8	∂	∂	NUM
ejpam-93	59	9	ut	ut	PROPN
ejpam-93	59	10	∂	∂	PROPN
ejpam-93	59	11	n	n	PROPN
ejpam-93	59	12	+	+	CCONJ
ejpam-93	59	13	(	(	PUNCT
ejpam-93	59	14	a′ut	a′ut	PROPN
ejpam-93	59	15	−δb′	−δb′	PROPN
ejpam-93	59	16	)	)	PUNCT
ejpam-93	59	17	∂	∂	NUM
ejpam-93	59	18	u	u	NOUN
ejpam-93	59	19	∂	∂	NOUN
ejpam-93	59	20	n	n	NOUN
ejpam-93	59	21	=	=	PRON
ejpam-93	59	22	(	(	PUNCT
ejpam-93	59	23	ab)′ut	ab)′ut	PROPN
ejpam-93	59	24	−δbb′.	−δbb′.	NOUN
ejpam-93	59	25	(	(	PUNCT
ejpam-93	59	26	8)	8)	NUM
ejpam-93	59	27	using	use	VERB
ejpam-93	59	28	(	(	PUNCT
ejpam-93	59	29	4	4	NUM
ejpam-93	59	30	)	)	PUNCT
ejpam-93	59	31	and	and	CCONJ
ejpam-93	59	32	(	(	PUNCT
ejpam-93	59	33	8)	8)	NUM
ejpam-93	59	34	we	we	PRON
ejpam-93	59	35	have	have	VERB
ejpam-93	59	36	∂	∂	NUM
ejpam-93	59	37	j	j	PROPN
ejpam-93	59	38	∂	∂	NUM
ejpam-93	59	39	n	n	ADV
ejpam-93	59	40	−	−	PROPN
ejpam-93	59	41	(	(	PUNCT
ejpam-93	59	42	ab)′	ab)′	PUNCT
ejpam-93	59	43	a	a	DET
ejpam-93	59	44	j	j	X
ejpam-93	59	45	=	=	PUNCT
ejpam-93	59	46	δa′b2	δa′b2	PROPN
ejpam-93	59	47	a	a	DET
ejpam-93	59	48	≥	≥	NOUN
ejpam-93	59	49	0	0	NUM
ejpam-93	59	50	on	on	ADP
ejpam-93	59	51	∂ω×	∂ω×	PROPN
ejpam-93	59	52	(	(	PUNCT
ejpam-93	59	53	ε0	ε0	PROPN
ejpam-93	59	54	,	,	PUNCT
ejpam-93	59	55	t	t	PROPN
ejpam-93	59	56	)	)	PUNCT
ejpam-93	59	57	.	.	PUNCT
ejpam-93	60	1	(	(	PUNCT
ejpam-93	60	2	9	9	NUM
ejpam-93	60	3	)	)	PUNCT
ejpam-93	60	4	thus	thus	ADV
ejpam-93	60	5	,	,	PUNCT
ejpam-93	60	6	by	by	ADP
ejpam-93	60	7	the	the	DET
ejpam-93	60	8	maximum	maximum	ADJ
ejpam-93	60	9	principle	principle	NOUN
ejpam-93	60	10	for	for	ADP
ejpam-93	60	11	parabolic	parabolic	NOUN
ejpam-93	60	12	problems	problem	NOUN
ejpam-93	60	13	,	,	PUNCT
ejpam-93	60	14	j(x	j(x	PROPN
ejpam-93	60	15	,	,	PUNCT
ejpam-93	60	16	t)≥	t)≥	PROPN
ejpam-93	60	17	j(x	j(x	PROPN
ejpam-93	60	18	,	,	PUNCT
ejpam-93	60	19	ε0)≥	ε0)≥	CCONJ
ejpam-93	60	20	0	0	NUM
ejpam-93	60	21	in	in	ADP
ejpam-93	60	22	ω×	ω×	PROPN
ejpam-93	60	23	(	(	PUNCT
ejpam-93	60	24	ε0	ε0	PROPN
ejpam-93	60	25	,	,	PUNCT
ejpam-93	60	26	t	t	PROPN
ejpam-93	60	27	)	)	PUNCT
ejpam-93	60	28	,	,	PUNCT
ejpam-93	60	29	i.e.	i.e.	X
ejpam-93	60	30	,	,	PUNCT
ejpam-93	60	31	ut	ut	PROPN
ejpam-93	60	32	≥	≥	PROPN
ejpam-93	60	33	δ	δ	PROPN
ejpam-93	60	34	b(u	b(u	PROPN
ejpam-93	60	35	)	)	PUNCT
ejpam-93	60	36	a(u	a(u	PROPN
ejpam-93	60	37	)	)	PUNCT
ejpam-93	60	38	in	in	ADP
ejpam-93	60	39	ω×	ω×	PROPN
ejpam-93	60	40	(	(	PUNCT
ejpam-93	60	41	ε0	ε0	PROPN
ejpam-93	60	42	,	,	PUNCT
ejpam-93	60	43	t	t	PROPN
ejpam-93	60	44	)	)	PUNCT
ejpam-93	60	45	.	.	PUNCT
ejpam-93	61	1	(	(	PUNCT
ejpam-93	61	2	10	10	NUM
ejpam-93	61	3	)	)	PUNCT
ejpam-93	61	4	step	step	NOUN
ejpam-93	61	5	2	2	NUM
ejpam-93	61	6	:	:	PUNCT
ejpam-93	61	7	blow	blow	VERB
ejpam-93	61	8	-	-	PUNCT
ejpam-93	61	9	up	up	ADP
ejpam-93	61	10	rate	rate	NOUN
ejpam-93	61	11	.	.	PUNCT
ejpam-93	62	1	set	set	VERB
ejpam-93	62	2	g(s	g(s	NOUN
ejpam-93	62	3	)	)	PUNCT
ejpam-93	62	4	=	=	SYM
ejpam-93	63	1	∫	∫	PROPN
ejpam-93	63	2	∞	∞	PROPN
ejpam-93	63	3	s	s	PROPN
ejpam-93	63	4	a(s	a(s	PROPN
ejpam-93	63	5	)	)	PUNCT
ejpam-93	63	6	b(s	b(	NOUN
ejpam-93	63	7	)	)	PUNCT
ejpam-93	64	1	ds	ds	NOUN
ejpam-93	64	2	then	then	ADV
ejpam-93	64	3	−(g(u))t	−(g(u))t	ADV
ejpam-93	64	4	=	=	SYM
ejpam-93	64	5	a(u	a(u	X
ejpam-93	64	6	)	)	PUNCT
ejpam-93	64	7	b(u	b(u	PROPN
ejpam-93	64	8	)	)	PUNCT
ejpam-93	64	9	ut	ut	PROPN
ejpam-93	64	10	.	.	PUNCT
ejpam-93	65	1	by	by	ADP
ejpam-93	65	2	the	the	DET
ejpam-93	65	3	growth	growth	NOUN
ejpam-93	65	4	estimate	estimate	NOUN
ejpam-93	65	5	(	(	PUNCT
ejpam-93	65	6	10	10	NUM
ejpam-93	65	7	)	)	PUNCT
ejpam-93	65	8	we	we	PRON
ejpam-93	65	9	have	have	VERB
ejpam-93	65	10	−(g(u))t	−(g(u))t	PROPN
ejpam-93	65	11	≥	≥	NOUN
ejpam-93	65	12	δ	δ	PROPN
ejpam-93	65	13	in	in	ADP
ejpam-93	65	14	ω×	ω×	PROPN
ejpam-93	65	15	(	(	PUNCT
ejpam-93	65	16	ε0	ε0	PROPN
ejpam-93	65	17	,	,	PUNCT
ejpam-93	65	18	t	t	PROPN
ejpam-93	65	19	)	)	PUNCT
ejpam-93	65	20	.	.	PUNCT
ejpam-93	66	1	by	by	ADP
ejpam-93	66	2	integration	integration	NOUN
ejpam-93	66	3	from	from	ADP
ejpam-93	66	4	t	t	PROPN
ejpam-93	66	5	to	to	ADP
ejpam-93	66	6	t	t	PROPN
ejpam-93	66	7	g(u(x	g(u(x	NOUN
ejpam-93	66	8	,	,	PUNCT
ejpam-93	66	9	t))−	t))−	NOUN
ejpam-93	66	10	g(u(x	g(u(x	NOUN
ejpam-93	66	11	,	,	PUNCT
ejpam-93	66	12	t	t	NOUN
ejpam-93	66	13	)	)	PUNCT
ejpam-93	66	14	)	)	PUNCT
ejpam-93	66	15	≥	≥	PRON
ejpam-93	66	16	δ(t	δ(t	PROPN
ejpam-93	66	17	−	−	PROPN
ejpam-93	66	18	t	t	PROPN
ejpam-93	66	19	)	)	PUNCT
ejpam-93	66	20	ε0	ε0	PROPN
ejpam-93	66	21	<	<	X
ejpam-93	66	22	t	t	X
ejpam-93	66	23	<	<	X
ejpam-93	66	24	t	t	X
ejpam-93	66	25	therefore	therefore	ADV
ejpam-93	66	26	also	also	ADV
ejpam-93	66	27	g(u(x	g(u(x	VERB
ejpam-93	66	28	,	,	PUNCT
ejpam-93	66	29	t))≥	t))≥	PUNCT
ejpam-93	66	30	δ(t	δ(t	PROPN
ejpam-93	66	31	−	−	PROPN
ejpam-93	66	32	t	t	PROPN
ejpam-93	66	33	)	)	PUNCT
ejpam-93	66	34	.	.	PUNCT
ejpam-93	67	1	(	(	PUNCT
ejpam-93	67	2	11	11	NUM
ejpam-93	67	3	)	)	PUNCT
ejpam-93	67	4	since	since	SCONJ
ejpam-93	67	5	∫	∫	PROPN
ejpam-93	68	1	+	+	PROPN
ejpam-93	68	2	∞	∞	PROPN
ejpam-93	68	3	0	0	NUM
ejpam-93	68	4	a(s	a(s	ADJ
ejpam-93	68	5	)	)	PUNCT
ejpam-93	68	6	b(s)ds	b(s)ds	PART
ejpam-93	69	1	<	<	X
ejpam-93	69	2	+	+	NOUN
ejpam-93	69	3	∞	∞	PROPN
ejpam-93	69	4	,	,	PUNCT
ejpam-93	69	5	by	by	ADP
ejpam-93	69	6	(	(	PUNCT
ejpam-93	69	7	11	11	NUM
ejpam-93	69	8	)	)	PUNCT
ejpam-93	69	9	,	,	PUNCT
ejpam-93	69	10	u(x	u(x	PROPN
ejpam-93	69	11	,	,	PUNCT
ejpam-93	69	12	t	t	PROPN
ejpam-93	69	13	)	)	PUNCT
ejpam-93	69	14	must	must	AUX
ejpam-93	69	15	blow	blow	VERB
ejpam-93	69	16	up	up	ADP
ejpam-93	69	17	in	in	ADP
ejpam-93	69	18	finite	finite	ADJ
ejpam-93	69	19	time	time	NOUN
ejpam-93	69	20	t	t	PROPN
ejpam-93	69	21	and	and	CCONJ
ejpam-93	69	22	sup	sup	PROPN
ejpam-93	69	23	x∈ω	x∈ω	NOUN
ejpam-93	69	24	u(x	u(x	PROPN
ejpam-93	69	25	,	,	PUNCT
ejpam-93	69	26	t)≤	t)≤	DET
ejpam-93	69	27	g−1	g−1	X
ejpam-93	69	28	(	(	PUNCT
ejpam-93	69	29	δ(t	δ(t	PROPN
ejpam-93	69	30	−	−	PROPN
ejpam-93	69	31	t	t	PROPN
ejpam-93	69	32	)	)	PUNCT
ejpam-93	69	33	)	)	PUNCT
ejpam-93	69	34	for	for	ADP
ejpam-93	69	35	0	0	NUM
ejpam-93	69	36	<	<	X
ejpam-93	69	37	t	t	X
ejpam-93	69	38	<	<	X
ejpam-93	69	39	t.	t.	X
ejpam-93	69	40	the	the	DET
ejpam-93	69	41	proof	proof	NOUN
ejpam-93	69	42	of	of	ADP
ejpam-93	69	43	theorem	theorem	ADJ
ejpam-93	69	44	1	1	NUM
ejpam-93	69	45	is	be	AUX
ejpam-93	69	46	completed	complete	VERB
ejpam-93	69	47	.	.	PUNCT
ejpam-93	70	1	with	with	ADP
ejpam-93	70	2	analogy	analogy	NOUN
ejpam-93	70	3	to	to	AUX
ejpam-93	70	4	theorem	theorem	VERB
ejpam-93	70	5	1	1	NUM
ejpam-93	70	6	,	,	PUNCT
ejpam-93	70	7	one	one	PRON
ejpam-93	70	8	can	can	AUX
ejpam-93	70	9	also	also	ADV
ejpam-93	70	10	obtain	obtain	VERB
ejpam-93	70	11	bounds	bound	NOUN
ejpam-93	70	12	for	for	ADP
ejpam-93	70	13	the	the	DET
ejpam-93	70	14	global	global	ADJ
ejpam-93	70	15	solutions	solution	NOUN
ejpam-93	70	16	.	.	PUNCT
ejpam-93	71	1	h.	h.	PROPN
ejpam-93	71	2	zhang	zhang	PROPN
ejpam-93	71	3	,	,	PUNCT
ejpam-93	71	4	x.	x.	PROPN
ejpam-93	71	5	guo	guo	PROPN
ejpam-93	71	6	/	/	SYM
ejpam-93	71	7	eur	eur	PROPN
ejpam-93	71	8	.	.	PUNCT
ejpam-93	72	1	j.	j.	PROPN
ejpam-93	72	2	pure	pure	PROPN
ejpam-93	72	3	appl	appl	PROPN
ejpam-93	72	4	.	.	PROPN
ejpam-93	72	5	math	math	PROPN
ejpam-93	72	6	,	,	PUNCT
ejpam-93	72	7	1	1	NUM
ejpam-93	72	8	(	(	PUNCT
ejpam-93	72	9	2008	2008	NUM
ejpam-93	72	10	)	)	PUNCT
ejpam-93	72	11	,	,	PUNCT
ejpam-93	72	12	(	(	PUNCT
ejpam-93	72	13	33	33	NUM
ejpam-93	72	14	-	-	SYM
ejpam-93	72	15	39	39	NUM
ejpam-93	72	16	)	)	PUNCT
ejpam-93	72	17	36	36	NUM
ejpam-93	72	18	corollary	corollary	NOUN
ejpam-93	72	19	1	1	NUM
ejpam-93	72	20	.	.	PUNCT
ejpam-93	73	1	let	let	VERB
ejpam-93	73	2	u(x	u(x	PROPN
ejpam-93	73	3	,	,	PUNCT
ejpam-93	73	4	t	t	PROPN
ejpam-93	73	5	)	)	PUNCT
ejpam-93	73	6	be	be	AUX
ejpam-93	73	7	a	a	DET
ejpam-93	73	8	solution	solution	NOUN
ejpam-93	73	9	of	of	ADP
ejpam-93	73	10	the	the	DET
ejpam-93	73	11	problem	problem	NOUN
ejpam-93	73	12	(	(	PUNCT
ejpam-93	73	13	1)-(3	1)-(3	NUM
ejpam-93	73	14	)	)	PUNCT
ejpam-93	73	15	.	.	PUNCT
ejpam-93	74	1	if	if	SCONJ
ejpam-93	74	2	∫	∫	PROPN
ejpam-93	75	1	+	+	PROPN
ejpam-93	75	2	∞	∞	PROPN
ejpam-93	75	3	0	0	NUM
ejpam-93	75	4	a(s	a(s	ADJ
ejpam-93	75	5	)	)	PUNCT
ejpam-93	75	6	b(s)ds	b(s)d	NOUN
ejpam-93	75	7	=	=	PUNCT
ejpam-93	76	1	+	+	NUM
ejpam-93	76	2	∞	∞	PROPN
ejpam-93	76	3	,	,	PUNCT
ejpam-93	76	4	a′(s	a′(s	PROPN
ejpam-93	76	5	)	)	PUNCT
ejpam-93	76	6	≤	≤	NOUN
ejpam-93	76	7	0	0	NUM
ejpam-93	76	8	,	,	PUNCT
ejpam-93	76	9	and	and	CCONJ
ejpam-93	76	10	(	(	PUNCT
ejpam-93	76	11	b′(s	b′(s	PROPN
ejpam-93	76	12	)	)	PUNCT
ejpam-93	76	13	a(s	a(s	PROPN
ejpam-93	76	14	)	)	PUNCT
ejpam-93	76	15	)	)	PUNCT
ejpam-93	77	1	′	′	NUM
ejpam-93	77	2	≤	≤	NUM
ejpam-93	77	3	0	0	PUNCT
ejpam-93	78	1	for	for	ADP
ejpam-93	78	2	s	s	PROPN
ejpam-93	78	3	>	>	X
ejpam-93	78	4	0	0	PROPN
ejpam-93	78	5	,	,	PUNCT
ejpam-93	78	6	then	then	ADV
ejpam-93	78	7	u(x	u(x	PROPN
ejpam-93	78	8	,	,	PUNCT
ejpam-93	78	9	t	t	PROPN
ejpam-93	78	10	)	)	PUNCT
ejpam-93	78	11	exists	exist	VERB
ejpam-93	78	12	globally	globally	ADV
ejpam-93	78	13	and	and	CCONJ
ejpam-93	78	14	sup	sup	NUM
ejpam-93	78	15	x∈ω	x∈ω	X
ejpam-93	78	16	u(x	u(x	PROPN
ejpam-93	78	17	,	,	PUNCT
ejpam-93	78	18	t)≤	t)≤	PRON
ejpam-93	78	19	g−1((t	g−1((t	PROPN
ejpam-93	78	20	+	+	X
ejpam-93	78	21	g(m	g(m	PROPN
ejpam-93	78	22	)	)	PUNCT
ejpam-93	78	23	)	)	PUNCT
ejpam-93	78	24	)	)	PUNCT
ejpam-93	78	25	for	for	ADP
ejpam-93	78	26	t	t	PROPN
ejpam-93	78	27	>	>	X
ejpam-93	78	28	0	0	PROPN
ejpam-93	78	29	,	,	PUNCT
ejpam-93	78	30	where	where	SCONJ
ejpam-93	78	31	m	m	PROPN
ejpam-93	78	32	=	=	VERB
ejpam-93	78	33	max	max	PROPN
ejpam-93	78	34	ω	ω	X
ejpam-93	78	35	u0	u0	PROPN
ejpam-93	78	36	.	.	PUNCT
ejpam-93	79	1	proof	proof	NOUN
ejpam-93	79	2	.	.	PUNCT
ejpam-93	80	1	let	let	VERB
ejpam-93	80	2	w(x	w(x	PRON
ejpam-93	80	3	,	,	PUNCT
ejpam-93	80	4	t	t	PROPN
ejpam-93	80	5	)	)	PUNCT
ejpam-93	80	6	be	be	AUX
ejpam-93	80	7	a	a	DET
ejpam-93	80	8	smooth	smooth	ADJ
ejpam-93	80	9	positive	positive	ADJ
ejpam-93	80	10	solution	solution	NOUN
ejpam-93	80	11	of	of	ADP
ejpam-93	80	12	the	the	DET
ejpam-93	80	13	following	following	ADJ
ejpam-93	80	14	problem	problem	NOUN
ejpam-93	80	15	:	:	PUNCT
ejpam-93	80	16	wt	wt	PROPN
ejpam-93	80	17	=	=	PUNCT
ejpam-93	80	18	div(a(w)∇w	div(a(w)∇w	X
ejpam-93	80	19	)	)	PUNCT
ejpam-93	80	20	in	in	ADP
ejpam-93	80	21	ω×	ω×	PROPN
ejpam-93	80	22	(	(	PUNCT
ejpam-93	80	23	0	0	NUM
ejpam-93	80	24	,	,	PUNCT
ejpam-93	80	25	t	t	NOUN
ejpam-93	80	26	)	)	PUNCT
ejpam-93	80	27	,	,	PUNCT
ejpam-93	80	28	(	(	PUNCT
ejpam-93	80	29	12	12	NUM
ejpam-93	80	30	)	)	PUNCT
ejpam-93	80	31	∂	∂	NUM
ejpam-93	80	32	w	w	NOUN
ejpam-93	80	33	∂	∂	NUM
ejpam-93	80	34	n	n	NOUN
ejpam-93	80	35	=	=	SYM
ejpam-93	80	36	b(w	b(w	PROPN
ejpam-93	80	37	)	)	PUNCT
ejpam-93	80	38	on	on	ADP
ejpam-93	80	39	∂ω×	∂ω×	PROPN
ejpam-93	80	40	(	(	PUNCT
ejpam-93	80	41	0	0	NUM
ejpam-93	80	42	,	,	PUNCT
ejpam-93	80	43	t	t	NOUN
ejpam-93	80	44	)	)	PUNCT
ejpam-93	80	45	,	,	PUNCT
ejpam-93	80	46	(	(	PUNCT
ejpam-93	80	47	13	13	NUM
ejpam-93	80	48	)	)	PUNCT
ejpam-93	80	49	u(x	u(x	NOUN
ejpam-93	80	50	,	,	PUNCT
ejpam-93	80	51	0	0	NUM
ejpam-93	80	52	)	)	PUNCT
ejpam-93	80	53	=	=	NOUN
ejpam-93	81	1	m	m	PUNCT
ejpam-93	81	2	=	=	VERB
ejpam-93	81	3	max	max	PROPN
ejpam-93	81	4	ω	ω	X
ejpam-93	81	5	u0	u0	PROPN
ejpam-93	81	6	in	in	ADP
ejpam-93	81	7	ω	ω	PROPN
ejpam-93	81	8	.	.	PUNCT
ejpam-93	82	1	(	(	PUNCT
ejpam-93	82	2	14	14	NUM
ejpam-93	82	3	)	)	PUNCT
ejpam-93	82	4	with	with	ADP
ejpam-93	82	5	analogy	analogy	NOUN
ejpam-93	82	6	to	to	ADP
ejpam-93	82	7	the	the	DET
ejpam-93	82	8	proof	proof	NOUN
ejpam-93	82	9	of	of	ADP
ejpam-93	82	10	theorem	theorem	NOUN
ejpam-93	82	11	1	1	NUM
ejpam-93	82	12	,	,	PUNCT
ejpam-93	82	13	by	by	ADP
ejpam-93	82	14	the	the	DET
ejpam-93	82	15	maximum	maximum	ADJ
ejpam-93	82	16	principle	principle	NOUN
ejpam-93	82	17	we	we	PRON
ejpam-93	82	18	have	have	VERB
ejpam-93	82	19	l	l	NOUN
ejpam-93	82	20	=	=	SYM
ejpam-93	82	21	a(w)wt	a(w)wt	PROPN
ejpam-93	82	22	−	−	PROPN
ejpam-93	82	23	b(w)≤	b(w)≤	PROPN
ejpam-93	82	24	0	0	NUM
ejpam-93	82	25	,	,	PUNCT
ejpam-93	82	26	i.e.	i.e.	X
ejpam-93	82	27	,	,	PUNCT
ejpam-93	82	28	wt	wt	PROPN
ejpam-93	82	29	≤	≤	NUM
ejpam-93	82	30	b(w	b(w	NOUN
ejpam-93	82	31	)	)	PUNCT
ejpam-93	82	32	a(w	a(w	PROPN
ejpam-93	82	33	)	)	PUNCT
ejpam-93	82	34	in	in	ADP
ejpam-93	82	35	ω×	ω×	PROPN
ejpam-93	82	36	(	(	PUNCT
ejpam-93	82	37	0	0	NUM
ejpam-93	82	38	,	,	PUNCT
ejpam-93	82	39	t	t	NOUN
ejpam-93	82	40	)	)	PUNCT
ejpam-93	82	41	.	.	PUNCT
ejpam-93	83	1	(	(	PUNCT
ejpam-93	83	2	15	15	NUM
ejpam-93	83	3	)	)	PUNCT
ejpam-93	83	4	for	for	ADP
ejpam-93	83	5	each	each	DET
ejpam-93	83	6	fixed	fix	VERB
ejpam-93	83	7	x	x	SYM
ejpam-93	83	8	∈	∈	PROPN
ejpam-93	83	9	ω	ω	NOUN
ejpam-93	83	10	,	,	PUNCT
ejpam-93	83	11	we	we	PRON
ejpam-93	83	12	get	get	VERB
ejpam-93	83	13	by	by	ADP
ejpam-93	83	14	integration	integration	NOUN
ejpam-93	83	15	(	(	PUNCT
ejpam-93	83	16	15	15	NUM
ejpam-93	83	17	)	)	PUNCT
ejpam-93	83	18	∫	∫	PROPN
ejpam-93	84	1	w(x	w(x	PROPN
ejpam-93	84	2	,	,	PUNCT
ejpam-93	84	3	t	t	PROPN
ejpam-93	84	4	)	)	PUNCT
ejpam-93	84	5	m	m	VERB
ejpam-93	84	6	a(s	a(s	ADJ
ejpam-93	84	7	)	)	PUNCT
ejpam-93	84	8	b(s	b(	NOUN
ejpam-93	84	9	)	)	PUNCT
ejpam-93	84	10	ds	ds	ADJ
ejpam-93	84	11	≤	≤	NUM
ejpam-93	84	12	t.	t.	NOUN
ejpam-93	84	13	(	(	PUNCT
ejpam-93	84	14	16	16	NUM
ejpam-93	84	15	)	)	PUNCT
ejpam-93	84	16	it	it	PRON
ejpam-93	84	17	follows	follow	VERB
ejpam-93	84	18	from	from	ADP
ejpam-93	84	19	assumptions	assumption	NOUN
ejpam-93	84	20	that	that	SCONJ
ejpam-93	84	21	w(x	w(x	PRON
ejpam-93	84	22	,	,	PUNCT
ejpam-93	84	23	t	t	PROPN
ejpam-93	84	24	)	)	PUNCT
ejpam-93	84	25	must	must	AUX
ejpam-93	84	26	be	be	AUX
ejpam-93	84	27	a	a	DET
ejpam-93	84	28	global	global	ADJ
ejpam-93	84	29	solution	solution	NOUN
ejpam-93	84	30	.	.	PUNCT
ejpam-93	85	1	with	with	ADP
ejpam-93	85	2	inequality	inequality	NOUN
ejpam-93	85	3	(	(	PUNCT
ejpam-93	85	4	16	16	NUM
ejpam-93	85	5	)	)	PUNCT
ejpam-93	85	6	,	,	PUNCT
ejpam-93	85	7	one	one	PRON
ejpam-93	85	8	gets	get	VERB
ejpam-93	85	9	g(w(x	g(w(x	NOUN
ejpam-93	85	10	,	,	PUNCT
ejpam-93	85	11	t))−	t))−	NOUN
ejpam-93	85	12	g(m	g(m	NOUN
ejpam-93	85	13	)	)	PUNCT
ejpam-93	86	1	=	=	SYM
ejpam-93	86	2	∫	∫	PROPN
ejpam-93	86	3	w(x	w(x	NUM
ejpam-93	86	4	,	,	PUNCT
ejpam-93	86	5	t	t	PROPN
ejpam-93	86	6	)	)	PUNCT
ejpam-93	86	7	c	c	NOUN
ejpam-93	86	8	dβ(s	dβ(	NOUN
ejpam-93	86	9	)	)	PUNCT
ejpam-93	86	10	f	f	NOUN
ejpam-93	86	11	(	(	PUNCT
ejpam-93	86	12	s	s	NOUN
ejpam-93	86	13	)	)	PUNCT
ejpam-93	86	14	≤	≤	NOUN
ejpam-93	86	15	t	t	NOUN
ejpam-93	86	16	and	and	CCONJ
ejpam-93	86	17	w(x	w(x	NOUN
ejpam-93	86	18	,	,	PUNCT
ejpam-93	86	19	t)≤	t)≤	PROPN
ejpam-93	86	20	g−1(t	g−1(t	PROPN
ejpam-93	86	21	+	+	CCONJ
ejpam-93	86	22	g(m	g(m	NOUN
ejpam-93	86	23	)	)	PUNCT
ejpam-93	86	24	)	)	PUNCT
ejpam-93	86	25	.	.	PUNCT
ejpam-93	87	1	by	by	ADP
ejpam-93	87	2	the	the	DET
ejpam-93	87	3	comparison	comparison	NOUN
ejpam-93	87	4	principle	principle	NOUN
ejpam-93	87	5	we	we	PRON
ejpam-93	87	6	know	know	VERB
ejpam-93	87	7	that	that	SCONJ
ejpam-93	87	8	w(x	w(x	PROPN
ejpam-93	87	9	,	,	PUNCT
ejpam-93	87	10	t	t	PROPN
ejpam-93	87	11	)	)	PUNCT
ejpam-93	87	12	is	be	AUX
ejpam-93	87	13	an	an	DET
ejpam-93	87	14	upper	upper	ADJ
ejpam-93	87	15	solution	solution	NOUN
ejpam-93	87	16	of	of	ADP
ejpam-93	87	17	(	(	PUNCT
ejpam-93	87	18	1)-(3	1)-(3	NUM
ejpam-93	87	19	)	)	PUNCT
ejpam-93	87	20	.	.	PUNCT
ejpam-93	88	1	thus	thus	ADV
ejpam-93	88	2	u(x	u(x	NOUN
ejpam-93	88	3	,	,	PUNCT
ejpam-93	88	4	t)≤	t)≤	PRON
ejpam-93	88	5	w(x	w(x	PROPN
ejpam-93	88	6	,	,	PUNCT
ejpam-93	88	7	t	t	PROPN
ejpam-93	88	8	)	)	PUNCT
ejpam-93	88	9	in	in	ADP
ejpam-93	88	10	ω×	ω×	PROPN
ejpam-93	88	11	(	(	PUNCT
ejpam-93	88	12	0	0	NUM
ejpam-93	88	13	,	,	PUNCT
ejpam-93	88	14	t	t	NOUN
ejpam-93	88	15	)	)	PUNCT
ejpam-93	88	16	.	.	PUNCT
ejpam-93	89	1	the	the	DET
ejpam-93	89	2	proof	proof	NOUN
ejpam-93	89	3	of	of	ADP
ejpam-93	89	4	corollary	corollary	ADJ
ejpam-93	89	5	1	1	NUM
ejpam-93	89	6	is	be	AUX
ejpam-93	89	7	complete	complete	ADJ
ejpam-93	89	8	.	.	PUNCT
ejpam-93	90	1	we	we	PRON
ejpam-93	90	2	shall	shall	AUX
ejpam-93	90	3	prove	prove	VERB
ejpam-93	90	4	in	in	ADP
ejpam-93	90	5	the	the	DET
ejpam-93	90	6	following	following	NOUN
ejpam-93	90	7	theorem	theorem	NOUN
ejpam-93	90	8	that	that	SCONJ
ejpam-93	90	9	the	the	DET
ejpam-93	90	10	blowup	blowup	NOUN
ejpam-93	90	11	will	will	AUX
ejpam-93	90	12	occur	occur	VERB
ejpam-93	90	13	only	only	ADV
ejpam-93	90	14	at	at	ADP
ejpam-93	90	15	the	the	DET
ejpam-93	90	16	boundary	boundary	NOUN
ejpam-93	90	17	of	of	ADP
ejpam-93	90	18	the	the	DET
ejpam-93	90	19	domain	domain	NOUN
ejpam-93	90	20	.	.	PUNCT
ejpam-93	91	1	theorem	theorem	NOUN
ejpam-93	91	2	2	2	NUM
ejpam-93	91	3	.	.	PUNCT
ejpam-93	91	4	suppose	suppose	VERB
ejpam-93	91	5	that	that	SCONJ
ejpam-93	91	6	the	the	DET
ejpam-93	91	7	assumptions	assumption	NOUN
ejpam-93	91	8	of	of	ADP
ejpam-93	91	9	theorem	theorem	ADJ
ejpam-93	91	10	1	1	NUM
ejpam-93	91	11	hold	hold	NOUN
ejpam-93	91	12	,	,	PUNCT
ejpam-93	91	13	and	and	CCONJ
ejpam-93	91	14	there	there	PRON
ejpam-93	91	15	exists	exist	VERB
ejpam-93	91	16	a	a	DET
ejpam-93	91	17	positive	positive	ADJ
ejpam-93	91	18	constant	constant	ADJ
ejpam-93	91	19	c0	c0	NOUN
ejpam-93	91	20	such	such	ADJ
ejpam-93	91	21	that	that	SCONJ
ejpam-93	91	22	s	s	X
ejpam-93	91	23	(	(	PUNCT
ejpam-93	91	24	b	b	NOUN
ejpam-93	91	25	a	a	PRON
ejpam-93	91	26	)	)	PUNCT
ejpam-93	91	27	′(h(s))≤	′(h(s))≤	ADJ
ejpam-93	91	28	c0	c0	NOUN
ejpam-93	91	29	for	for	ADP
ejpam-93	91	30	s	s	PROPN
ejpam-93	91	31	>	>	X
ejpam-93	91	32	0	0	NUM
ejpam-93	91	33	.	.	PUNCT
ejpam-93	92	1	then	then	ADV
ejpam-93	92	2	for	for	ADP
ejpam-93	92	3	any	any	DET
ejpam-93	92	4	ω′	ω′	PROPN
ejpam-93	92	5	⊂⊂	⊂⊂	PROPN
ejpam-93	92	6	ω	ω	PROPN
ejpam-93	92	7	and	and	CCONJ
ejpam-93	92	8	ε0	ε0	PROPN
ejpam-93	92	9	>	>	X
ejpam-93	92	10	0	0	NUM
ejpam-93	92	11	,	,	PUNCT
ejpam-93	92	12	sup	sup	NOUN
ejpam-93	92	13	x∈ω′	x∈ω′	NOUN
ejpam-93	92	14	,	,	PUNCT
ejpam-93	92	15	t∈[ε0,t	t∈[ε0,t	NOUN
ejpam-93	92	16	)	)	PUNCT
ejpam-93	92	17	u(x	u(x	PROPN
ejpam-93	92	18	,	,	PUNCT
ejpam-93	92	19	t)<+∞.	t)<+∞.	PROPN
ejpam-93	92	20	h.	h.	PROPN
ejpam-93	92	21	zhang	zhang	PROPN
ejpam-93	92	22	,	,	PUNCT
ejpam-93	92	23	x.	x.	PROPN
ejpam-93	92	24	guo	guo	PROPN
ejpam-93	92	25	/	/	SYM
ejpam-93	92	26	eur	eur	PROPN
ejpam-93	92	27	.	.	PUNCT
ejpam-93	93	1	j.	j.	PROPN
ejpam-93	93	2	pure	pure	PROPN
ejpam-93	93	3	appl	appl	PROPN
ejpam-93	93	4	.	.	PROPN
ejpam-93	93	5	math	math	PROPN
ejpam-93	93	6	,	,	PUNCT
ejpam-93	93	7	1	1	NUM
ejpam-93	93	8	(	(	PUNCT
ejpam-93	93	9	2008	2008	NUM
ejpam-93	93	10	)	)	PUNCT
ejpam-93	93	11	,	,	PUNCT
ejpam-93	93	12	(	(	PUNCT
ejpam-93	93	13	33	33	NUM
ejpam-93	93	14	-	-	SYM
ejpam-93	93	15	39	39	NUM
ejpam-93	93	16	)	)	PUNCT
ejpam-93	93	17	37	37	NUM
ejpam-93	93	18	proof	proof	NOUN
ejpam-93	93	19	.	.	PUNCT
ejpam-93	94	1	we	we	PRON
ejpam-93	94	2	will	will	AUX
ejpam-93	94	3	use	use	VERB
ejpam-93	94	4	the	the	DET
ejpam-93	94	5	ideas	idea	NOUN
ejpam-93	94	6	of	of	ADP
ejpam-93	94	7	[	[	X
ejpam-93	94	8	6	6	NUM
ejpam-93	94	9	]	]	PUNCT
ejpam-93	94	10	.	.	PUNCT
ejpam-93	95	1	let	let	VERB
ejpam-93	95	2	d(x	d(x	NOUN
ejpam-93	95	3	)	)	PUNCT
ejpam-93	96	1	=	=	SYM
ejpam-93	97	1	dist(x	dist(x	INTJ
ejpam-93	97	2	,	,	PUNCT
ejpam-93	97	3	∂ω	∂ω	ADJ
ejpam-93	97	4	)	)	PUNCT
ejpam-93	97	5	and	and	CCONJ
ejpam-93	97	6	v(x	v(x	PROPN
ejpam-93	97	7	)	)	PUNCT
ejpam-93	97	8	=	=	SYM
ejpam-93	97	9	d2(x	d2(x	PROPN
ejpam-93	97	10	)	)	PUNCT
ejpam-93	97	11	for	for	ADP
ejpam-93	97	12	x	x	PROPN
ejpam-93	97	13	∈	∈	PROPN
ejpam-93	97	14	nε(∂ω	nε(∂ω	NOUN
ejpam-93	97	15	)	)	PUNCT
ejpam-93	97	16	where	where	SCONJ
ejpam-93	97	17	nε(∂ω	nε(∂ω	VERB
ejpam-93	97	18	)	)	PUNCT
ejpam-93	97	19	=	=	PRON
ejpam-93	98	1	{	{	PUNCT
ejpam-93	98	2	x	x	PUNCT
ejpam-93	98	3	∈	∈	PROPN
ejpam-93	98	4	ω	ω	NOUN
ejpam-93	98	5	:	:	PUNCT
ejpam-93	98	6	d(x	d(x	NOUN
ejpam-93	98	7	)	)	PUNCT
ejpam-93	98	8	<	<	X
ejpam-93	98	9	ε	ε	PROPN
ejpam-93	98	10	}	}	PUNCT
ejpam-93	98	11	.	.	PUNCT
ejpam-93	99	1	since	since	SCONJ
ejpam-93	99	2	∂ω	∂ω	PROPN
ejpam-93	99	3	is	be	AUX
ejpam-93	99	4	c2	c2	PROPN
ejpam-93	99	5	,	,	PUNCT
ejpam-93	99	6	the	the	DET
ejpam-93	99	7	function	function	NOUN
ejpam-93	99	8	v(x	v(x	PROPN
ejpam-93	99	9	)	)	PUNCT
ejpam-93	99	10	is	be	AUX
ejpam-93	99	11	in	in	ADP
ejpam-93	99	12	c2(nε(∂ω	c2(nε(∂ω	NOUN
ejpam-93	99	13	)	)	PUNCT
ejpam-93	99	14	)	)	PUNCT
ejpam-93	100	1	if	if	SCONJ
ejpam-93	100	2	ε	ε	PROPN
ejpam-93	100	3	is	be	AUX
ejpam-93	100	4	small	small	ADJ
ejpam-93	100	5	enough	enough	ADV
ejpam-93	100	6	.	.	PUNCT
ejpam-93	101	1	therefore	therefore	ADV
ejpam-93	101	2	,	,	PUNCT
ejpam-93	101	3	there	there	PRON
ejpam-93	101	4	exists	exist	VERB
ejpam-93	101	5	a	a	DET
ejpam-93	101	6	constant	constant	ADJ
ejpam-93	101	7	c	c	NOUN
ejpam-93	101	8	>	>	X
ejpam-93	101	9	0	0	NUM
ejpam-93	102	1	such	such	ADJ
ejpam-93	102	2	that	that	SCONJ
ejpam-93	102	3	div(a(v)∇v)−	div(a(v)∇v)−	ADJ
ejpam-93	102	4	c0	c0	NOUN
ejpam-93	102	5	v	v	NOUN
ejpam-93	102	6	|∇v|2	|∇v|2	PRON
ejpam-93	102	7	≥−c	≥−c	PROPN
ejpam-93	102	8	in	in	ADP
ejpam-93	102	9	nε0(∂ω	nε0(∂ω	NOUN
ejpam-93	102	10	)	)	PUNCT
ejpam-93	102	11	if	if	SCONJ
ejpam-93	102	12	ε0	ε0	PROPN
ejpam-93	102	13	is	be	AUX
ejpam-93	102	14	small	small	ADJ
ejpam-93	102	15	enough	enough	ADV
ejpam-93	102	16	.	.	PUNCT
ejpam-93	103	1	we	we	PRON
ejpam-93	103	2	next	next	ADV
ejpam-93	103	3	extend	extend	VERB
ejpam-93	103	4	v(x	v(x	PROPN
ejpam-93	103	5	)	)	PUNCT
ejpam-93	103	6	to	to	ADP
ejpam-93	103	7	a	a	DET
ejpam-93	103	8	function	function	NOUN
ejpam-93	103	9	on	on	ADP
ejpam-93	103	10	ω	ω	NUM
ejpam-93	103	11	such	such	ADJ
ejpam-93	103	12	that	that	PRON
ejpam-93	103	13	v	v	ADP
ejpam-93	103	14	∈	∈	PROPN
ejpam-93	103	15	c2(ω	c2(ω	PRON
ejpam-93	103	16	)	)	PUNCT
ejpam-93	103	17	and	and	CCONJ
ejpam-93	103	18	v	v	ADP
ejpam-93	103	19	≥	≥	NOUN
ejpam-93	103	20	c0	c0	X
ejpam-93	103	21	>	>	X
ejpam-93	103	22	0	0	PUNCT
ejpam-93	104	1	on	on	ADP
ejpam-93	104	2	ω	ω	PROPN
ejpam-93	104	3	/	/	SYM
ejpam-93	104	4	nε0(∂ω	nε0(∂ω	NOUN
ejpam-93	104	5	)	)	PUNCT
ejpam-93	104	6	.	.	PUNCT
ejpam-93	105	1	then	then	ADV
ejpam-93	105	2	div(a(v)∇v)−	div(a(v)∇v)−	NOUN
ejpam-93	105	3	c0	c0	PROPN
ejpam-93	105	4	v	v	NOUN
ejpam-93	105	5	|∇v|2	|∇v|2	X
ejpam-93	105	6	≥−c∗	≥−c∗	PROPN
ejpam-93	105	7	on	on	ADP
ejpam-93	105	8	ω	ω	NUM
ejpam-93	105	9	for	for	ADP
ejpam-93	105	10	some	some	DET
ejpam-93	105	11	1≥	1≥	NUM
ejpam-93	105	12	c∗	c∗	PROPN
ejpam-93	105	13	>	>	X
ejpam-93	105	14	0	0	X
ejpam-93	105	15	.	.	PUNCT
ejpam-93	106	1	set	set	VERB
ejpam-93	106	2	w(x	w(x	PROPN
ejpam-93	106	3	,	,	PUNCT
ejpam-93	106	4	t	t	PROPN
ejpam-93	106	5	)	)	PUNCT
ejpam-93	106	6	=	=	SYM
ejpam-93	106	7	c1h(τ	c1h(τ	PROPN
ejpam-93	106	8	)	)	PUNCT
ejpam-93	106	9	,	,	PUNCT
ejpam-93	106	10	where	where	SCONJ
ejpam-93	106	11	τ=	τ=	NOUN
ejpam-93	106	12	δ(v(x	δ(v(x	VERB
ejpam-93	106	13	)	)	PUNCT
ejpam-93	107	1	+	+	CCONJ
ejpam-93	107	2	c∗(t	c∗(t	PROPN
ejpam-93	107	3	−	−	PROPN
ejpam-93	107	4	t	t	PROPN
ejpam-93	107	5	)	)	PUNCT
ejpam-93	107	6	)	)	PUNCT
ejpam-93	107	7	and	and	CCONJ
ejpam-93	107	8	c1	c1	PROPN
ejpam-93	107	9	>	>	X
ejpam-93	108	1	0	0	X
ejpam-93	108	2	.	.	PUNCT
ejpam-93	109	1	then	then	ADV
ejpam-93	109	2	wt	wt	ADP
ejpam-93	109	3	−	−	PROPN
ejpam-93	109	4	div(a(w)∇w	div(a(w)∇w	PUNCT
ejpam-93	109	5	)	)	PUNCT
ejpam-93	110	1	+	+	CCONJ
ejpam-93	110	2	f	f	X
ejpam-93	110	3	(	(	PUNCT
ejpam-93	110	4	w)≥	w)≥	PROPN
ejpam-93	110	5	0	0	NUM
ejpam-93	110	6	in	in	ADP
ejpam-93	110	7	ω×	ω×	PROPN
ejpam-93	110	8	(	(	PUNCT
ejpam-93	110	9	ε0	ε0	PROPN
ejpam-93	110	10	,	,	PUNCT
ejpam-93	110	11	t	t	PROPN
ejpam-93	110	12	)	)	PUNCT
ejpam-93	110	13	.	.	PUNCT
ejpam-93	111	1	by	by	ADP
ejpam-93	111	2	theorem	theorem	NOUN
ejpam-93	111	3	1	1	NUM
ejpam-93	111	4	we	we	PRON
ejpam-93	111	5	have	have	VERB
ejpam-93	111	6	sup	sup	NOUN
ejpam-93	111	7	x∈ω	x∈ω	NOUN
ejpam-93	111	8	u(x	u(x	NOUN
ejpam-93	111	9	,	,	PUNCT
ejpam-93	111	10	t)≤	t)≤	DET
ejpam-93	111	11	h(δ(t	h(δ(t	PROPN
ejpam-93	111	12	−	−	PROPN
ejpam-93	111	13	t	t	PROPN
ejpam-93	111	14	)	)	PUNCT
ejpam-93	111	15	)	)	PUNCT
ejpam-93	111	16	on	on	ADP
ejpam-93	111	17	∂ω×	∂ω×	PROPN
ejpam-93	111	18	(	(	PUNCT
ejpam-93	111	19	ε0	ε0	PROPN
ejpam-93	111	20	,	,	PUNCT
ejpam-93	111	21	t	t	PROPN
ejpam-93	111	22	)	)	PUNCT
ejpam-93	111	23	.	.	PUNCT
ejpam-93	112	1	thus	thus	ADV
ejpam-93	112	2	w(x	w(x	NUM
ejpam-93	112	3	,	,	PUNCT
ejpam-93	112	4	t	t	PROPN
ejpam-93	112	5	)	)	PUNCT
ejpam-93	112	6	=	=	NOUN
ejpam-93	112	7	c1h(δc∗(t	c1h(δc∗(t	PROPN
ejpam-93	112	8	−	−	PROPN
ejpam-93	112	9	t	t	PROPN
ejpam-93	112	10	)	)	PUNCT
ejpam-93	112	11	)	)	PUNCT
ejpam-93	112	12	)	)	PUNCT
ejpam-93	112	13	>	>	X
ejpam-93	113	1	h(δ(t	h(δ(t	PROPN
ejpam-93	113	2	−	−	NOUN
ejpam-93	113	3	t))≥	t))≥	PROPN
ejpam-93	113	4	u(x	u(x	PROPN
ejpam-93	113	5	,	,	PUNCT
ejpam-93	113	6	t	t	PROPN
ejpam-93	113	7	)	)	PUNCT
ejpam-93	113	8	on	on	ADP
ejpam-93	113	9	∂ω×	∂ω×	PROPN
ejpam-93	113	10	(	(	PUNCT
ejpam-93	113	11	ε0	ε0	PROPN
ejpam-93	113	12	,	,	PUNCT
ejpam-93	113	13	t	t	PROPN
ejpam-93	113	14	)	)	PUNCT
ejpam-93	114	1	if	if	SCONJ
ejpam-93	114	2	c1	c1	PROPN
ejpam-93	114	3	>	>	X
ejpam-93	114	4	1	1	X
ejpam-93	114	5	.	.	X
ejpam-93	114	6	take	take	VERB
ejpam-93	114	7	c1	c1	PROPN
ejpam-93	114	8	to	to	PART
ejpam-93	114	9	be	be	AUX
ejpam-93	114	10	large	large	ADJ
ejpam-93	114	11	enough	enough	ADV
ejpam-93	114	12	so	so	SCONJ
ejpam-93	114	13	that	that	SCONJ
ejpam-93	114	14	w(x	w(x	NOUN
ejpam-93	114	15	,	,	PUNCT
ejpam-93	114	16	ε0)≥	ε0)≥	CCONJ
ejpam-93	114	17	u(x	u(x	PROPN
ejpam-93	114	18	,	,	PUNCT
ejpam-93	114	19	ε0	ε0	PROPN
ejpam-93	114	20	)	)	PUNCT
ejpam-93	114	21	.	.	PUNCT
ejpam-93	115	1	then	then	ADV
ejpam-93	115	2	the	the	DET
ejpam-93	115	3	maximum	maximum	ADJ
ejpam-93	115	4	principle	principle	NOUN
ejpam-93	115	5	implies	imply	VERB
ejpam-93	115	6	that	that	SCONJ
ejpam-93	115	7	w(x	w(x	NOUN
ejpam-93	115	8	,	,	PUNCT
ejpam-93	115	9	t)≥	t)≥	PROPN
ejpam-93	115	10	u(x	u(x	PROPN
ejpam-93	115	11	,	,	PUNCT
ejpam-93	115	12	t	t	PROPN
ejpam-93	115	13	)	)	PUNCT
ejpam-93	115	14	in	in	ADP
ejpam-93	115	15	ω×	ω×	PROPN
ejpam-93	115	16	(	(	PUNCT
ejpam-93	115	17	ε0	ε0	PROPN
ejpam-93	115	18	,	,	PUNCT
ejpam-93	115	19	t	t	PROPN
ejpam-93	115	20	)	)	PUNCT
ejpam-93	115	21	.	.	PUNCT
ejpam-93	116	1	therefore	therefore	ADV
ejpam-93	116	2	for	for	ADP
ejpam-93	116	3	ω′	ω′	PROPN
ejpam-93	116	4	⊂⊂	⊂⊂	PROPN
ejpam-93	116	5	ω	ω	NUM
ejpam-93	116	6	u(x	u(x	PROPN
ejpam-93	116	7	,	,	PUNCT
ejpam-93	116	8	t)≤	t)≤	DET
ejpam-93	116	9	c1h(δ(v(x	c1h(δ(v(x	NOUN
ejpam-93	116	10	)	)	PUNCT
ejpam-93	116	11	+	+	CCONJ
ejpam-93	116	12	c∗(t	c∗(t	NOUN
ejpam-93	116	13	−	−	PROPN
ejpam-93	116	14	t)))≤	t)))≤	PUNCT
ejpam-93	116	15	c1h(δv(x	c1h(δv(x	PROPN
ejpam-93	116	16	)	)	PUNCT
ejpam-93	116	17	)	)	PUNCT
ejpam-93	117	1	i.e.	i.e.	X
ejpam-93	117	2	,	,	PUNCT
ejpam-93	117	3	sup	sup	NOUN
ejpam-93	117	4	x∈ω′	x∈ω′	NOUN
ejpam-93	117	5	,	,	PUNCT
ejpam-93	117	6	t∈[ε0,t	t∈[ε0,t	NOUN
ejpam-93	117	7	)	)	PUNCT
ejpam-93	117	8	u(x	u(x	PROPN
ejpam-93	117	9	,	,	PUNCT
ejpam-93	117	10	t)<+∞.	t)<+∞.	NOUN
ejpam-93	117	11	the	the	DET
ejpam-93	117	12	theorem	theorem	NOUN
ejpam-93	117	13	2	2	NUM
ejpam-93	117	14	is	be	AUX
ejpam-93	117	15	proved	prove	VERB
ejpam-93	117	16	.	.	PUNCT
ejpam-93	118	1	in	in	ADP
ejpam-93	118	2	our	our	PRON
ejpam-93	118	3	theorems	theorem	NOUN
ejpam-93	118	4	,	,	PUNCT
ejpam-93	118	5	if	if	SCONJ
ejpam-93	118	6	f	f	PROPN
ejpam-93	118	7	(	(	PUNCT
ejpam-93	118	8	u	u	NOUN
ejpam-93	118	9	)	)	PUNCT
ejpam-93	118	10	≡	≡	PROPN
ejpam-93	118	11	0	0	NUM
ejpam-93	118	12	,	,	PUNCT
ejpam-93	118	13	a(u	a(u	X
ejpam-93	118	14	)	)	PUNCT
ejpam-93	118	15	≡	≡	PROPN
ejpam-93	118	16	1	1	NUM
ejpam-93	118	17	and	and	CCONJ
ejpam-93	118	18	b(u	b(u	PROPN
ejpam-93	118	19	)	)	PUNCT
ejpam-93	118	20	=	=	PUNCT
ejpam-93	118	21	up	up	ADV
ejpam-93	118	22	(	(	PUNCT
ejpam-93	118	23	p	p	X
ejpam-93	118	24	>	>	X
ejpam-93	118	25	1	1	NUM
ejpam-93	118	26	)	)	PUNCT
ejpam-93	118	27	,	,	PUNCT
ejpam-93	118	28	then	then	ADV
ejpam-93	118	29	the	the	DET
ejpam-93	118	30	following	follow	VERB
ejpam-93	118	31	conclusion	conclusion	NOUN
ejpam-93	118	32	holds	hold	VERB
ejpam-93	118	33	:	:	PUNCT
ejpam-93	118	34	corollary	corollary	ADJ
ejpam-93	118	35	2	2	X
ejpam-93	118	36	.	.	PUNCT
ejpam-93	119	1	let	let	VERB
ejpam-93	119	2	u(x	u(x	PROPN
ejpam-93	119	3	,	,	PUNCT
ejpam-93	119	4	t	t	PROPN
ejpam-93	119	5	)	)	PUNCT
ejpam-93	119	6	be	be	AUX
ejpam-93	119	7	a	a	DET
ejpam-93	119	8	smooth	smooth	ADJ
ejpam-93	119	9	solution	solution	NOUN
ejpam-93	119	10	of	of	ADP
ejpam-93	119	11	the	the	DET
ejpam-93	119	12	following	following	ADJ
ejpam-93	119	13	problem	problem	NOUN
ejpam-93	119	14	:	:	PUNCT
ejpam-93	119	15			PROPN
ejpam-93	119	16			ADP
ejpam-93	119	17			NOUN
ejpam-93	119	18	ut	ut	PROPN
ejpam-93	120	1	=	=	NOUN
ejpam-93	120	2	4u	4u	NOUN
ejpam-93	120	3	in	in	ADP
ejpam-93	120	4	ω×	ω×	PROPN
ejpam-93	120	5	(	(	PUNCT
ejpam-93	120	6	0	0	NUM
ejpam-93	120	7	,	,	PUNCT
ejpam-93	120	8	t	t	NOUN
ejpam-93	120	9	)	)	PUNCT
ejpam-93	120	10	∂	∂	NUM
ejpam-93	120	11	u	u	NOUN
ejpam-93	120	12	∂	∂	NOUN
ejpam-93	120	13	n	n	NOUN
ejpam-93	120	14	=	=	X
ejpam-93	120	15	up	up	ADV
ejpam-93	120	16	on	on	ADP
ejpam-93	120	17	∂ω×	∂ω×	PROPN
ejpam-93	120	18	(	(	PUNCT
ejpam-93	120	19	0	0	NUM
ejpam-93	120	20	,	,	PUNCT
ejpam-93	120	21	t	t	NOUN
ejpam-93	120	22	)	)	PUNCT
ejpam-93	120	23	u(x	u(x	PROPN
ejpam-93	120	24	,	,	PUNCT
ejpam-93	120	25	0	0	NUM
ejpam-93	120	26	)	)	PUNCT
ejpam-93	120	27	=	=	SYM
ejpam-93	120	28	u0(x	u0(x	NOUN
ejpam-93	120	29	)	)	PUNCT
ejpam-93	120	30	>	>	X
ejpam-93	120	31	0	0	PUNCT
ejpam-93	120	32	in	in	ADP
ejpam-93	120	33	ω	ω	PROPN
ejpam-93	120	34	.	.	PUNCT
ejpam-93	121	1	if	if	SCONJ
ejpam-93	121	2	4u0	4u0	NUM
ejpam-93	121	3	≥	≥	NOUN
ejpam-93	121	4	0	0	NUM
ejpam-93	121	5	,	,	PUNCT
ejpam-93	121	6	then	then	ADV
ejpam-93	121	7	u(x	u(x	PROPN
ejpam-93	121	8	,	,	PUNCT
ejpam-93	121	9	t	t	PROPN
ejpam-93	121	10	)	)	PUNCT
ejpam-93	121	11	blows	blow	VERB
ejpam-93	121	12	up	up	ADP
ejpam-93	121	13	in	in	ADP
ejpam-93	121	14	finite	finite	ADJ
ejpam-93	121	15	time	time	NOUN
ejpam-93	121	16	and	and	CCONJ
ejpam-93	121	17	blowup	blowup	ADJ
ejpam-93	121	18	will	will	AUX
ejpam-93	121	19	occur	occur	VERB
ejpam-93	121	20	only	only	ADV
ejpam-93	121	21	at	at	ADP
ejpam-93	121	22	the	the	DET
ejpam-93	121	23	boundary	boundary	NOUN
ejpam-93	121	24	of	of	ADP
ejpam-93	121	25	the	the	DET
ejpam-93	121	26	domain	domain	NOUN
ejpam-93	121	27	.	.	PUNCT
ejpam-93	122	1	this	this	PRON
ejpam-93	122	2	is	be	AUX
ejpam-93	122	3	the	the	DET
ejpam-93	122	4	case	case	NOUN
ejpam-93	122	5	of	of	ADP
ejpam-93	122	6	[	[	X
ejpam-93	122	7	6	6	NUM
ejpam-93	122	8	]	]	PUNCT
ejpam-93	122	9	.	.	PUNCT
ejpam-93	123	1	references	reference	NOUN
ejpam-93	123	2	38	38	NUM
ejpam-93	123	3	3	3	NUM
ejpam-93	123	4	.	.	PUNCT
ejpam-93	123	5	concluding	conclude	VERB
ejpam-93	123	6	remarks	remark	NOUN
ejpam-93	123	7	and	and	CCONJ
ejpam-93	123	8	applications	application	NOUN
ejpam-93	123	9	problem	problem	NOUN
ejpam-93	123	10	(	(	PUNCT
ejpam-93	123	11	1)-(3	1)-(3	NOUN
ejpam-93	123	12	)	)	PUNCT
ejpam-93	123	13	arises	arise	VERB
ejpam-93	123	14	in	in	ADP
ejpam-93	123	15	the	the	DET
ejpam-93	123	16	nonlinear	nonlinear	ADJ
ejpam-93	123	17	diffusion	diffusion	NOUN
ejpam-93	123	18	process	process	NOUN
ejpam-93	123	19	,	,	PUNCT
ejpam-93	123	20	in	in	ADP
ejpam-93	123	21	which	which	PRON
ejpam-93	123	22	div(a(u)∇u	div(a(u)∇u	NOUN
ejpam-93	123	23	)	)	PUNCT
ejpam-93	123	24	denotes	denote	VERB
ejpam-93	123	25	the	the	DET
ejpam-93	123	26	nonlinear	nonlinear	ADJ
ejpam-93	123	27	diffusion	diffusion	NOUN
ejpam-93	123	28	effect	effect	NOUN
ejpam-93	123	29	,	,	PUNCT
ejpam-93	123	30	f	f	PROPN
ejpam-93	123	31	(	(	PUNCT
ejpam-93	123	32	u	u	NOUN
ejpam-93	123	33	)	)	PUNCT
ejpam-93	123	34	denotes	denote	VERB
ejpam-93	123	35	absorption	absorption	NOUN
ejpam-93	123	36	in	in	ADP
ejpam-93	123	37	the	the	DET
ejpam-93	123	38	interior	interior	NOUN
ejpam-93	123	39	of	of	ADP
ejpam-93	123	40	the	the	DET
ejpam-93	123	41	domain	domain	NOUN
ejpam-93	123	42	,	,	PUNCT
ejpam-93	123	43	and	and	CCONJ
ejpam-93	123	44	∂	∂	NUM
ejpam-93	123	45	u	u	NOUN
ejpam-93	123	46	∂	∂	PROPN
ejpam-93	123	47	n	n	NOUN
ejpam-93	123	48	denotes	denote	VERB
ejpam-93	123	49	the	the	DET
ejpam-93	123	50	boundary	boundary	ADJ
ejpam-93	123	51	flux	flux	NOUN
ejpam-93	123	52	along	along	ADP
ejpam-93	123	53	the	the	DET
ejpam-93	123	54	outward	outward	ADJ
ejpam-93	123	55	normal	normal	ADJ
ejpam-93	123	56	direction	direction	NOUN
ejpam-93	123	57	to	to	ADP
ejpam-93	123	58	the	the	DET
ejpam-93	123	59	domain	domain	NOUN
ejpam-93	123	60	.	.	PUNCT
ejpam-93	124	1	with	with	ADP
ejpam-93	124	2	this	this	DET
ejpam-93	124	3	model	model	NOUN
ejpam-93	124	4	,	,	PUNCT
ejpam-93	124	5	all	all	PRON
ejpam-93	124	6	of	of	ADP
ejpam-93	124	7	the	the	DET
ejpam-93	124	8	results	result	NOUN
ejpam-93	124	9	obtained	obtain	VERB
ejpam-93	124	10	in	in	ADP
ejpam-93	124	11	the	the	DET
ejpam-93	124	12	preceding	precede	VERB
ejpam-93	124	13	sections	section	NOUN
ejpam-93	124	14	are	be	AUX
ejpam-93	124	15	physically	physically	ADV
ejpam-93	124	16	meaningful	meaningful	ADJ
ejpam-93	124	17	.	.	PUNCT
ejpam-93	125	1	our	our	PRON
ejpam-93	125	2	results	result	NOUN
ejpam-93	125	3	show	show	VERB
ejpam-93	125	4	that	that	SCONJ
ejpam-93	125	5	the	the	DET
ejpam-93	125	6	strength	strength	NOUN
ejpam-93	125	7	of	of	ADP
ejpam-93	125	8	the	the	DET
ejpam-93	125	9	boundary	boundary	ADJ
ejpam-93	125	10	flux	flux	NOUN
ejpam-93	125	11	plays	play	VERB
ejpam-93	125	12	a	a	DET
ejpam-93	125	13	key	key	ADJ
ejpam-93	125	14	role	role	NOUN
ejpam-93	125	15	in	in	ADP
ejpam-93	125	16	the	the	DET
ejpam-93	125	17	blowup	blowup	ADJ
ejpam-93	125	18	properties	property	NOUN
ejpam-93	125	19	of	of	ADP
ejpam-93	125	20	the	the	DET
ejpam-93	125	21	problem	problem	NOUN
ejpam-93	125	22	(	(	PUNCT
ejpam-93	125	23	1)-(3	1)-(3	NUM
ejpam-93	125	24	)	)	PUNCT
ejpam-93	125	25	.	.	PUNCT
ejpam-93	126	1	if	if	SCONJ
ejpam-93	126	2	the	the	DET
ejpam-93	126	3	boundary	boundary	ADJ
ejpam-93	126	4	flux	flux	NOUN
ejpam-93	126	5	is	be	AUX
ejpam-93	126	6	sufficiently	sufficiently	ADV
ejpam-93	126	7	strong	strong	ADJ
ejpam-93	126	8	,	,	PUNCT
ejpam-93	126	9	then	then	ADV
ejpam-93	126	10	it	it	PRON
ejpam-93	126	11	will	will	AUX
ejpam-93	126	12	bring	bring	VERB
ejpam-93	126	13	about	about	ADP
ejpam-93	126	14	blowup	blowup	VERB
ejpam-93	126	15	in	in	ADP
ejpam-93	126	16	a	a	DET
ejpam-93	126	17	finite	finite	ADJ
ejpam-93	126	18	time	time	NOUN
ejpam-93	126	19	,	,	PUNCT
ejpam-93	126	20	and	and	CCONJ
ejpam-93	126	21	the	the	DET
ejpam-93	126	22	blowup	blowup	NOUN
ejpam-93	126	23	will	will	AUX
ejpam-93	126	24	occur	occur	VERB
ejpam-93	126	25	only	only	ADV
ejpam-93	126	26	at	at	ADP
ejpam-93	126	27	the	the	DET
ejpam-93	126	28	boundary	boundary	NOUN
ejpam-93	126	29	of	of	ADP
ejpam-93	126	30	the	the	DET
ejpam-93	126	31	domain	domain	NOUN
ejpam-93	126	32	.	.	PUNCT
ejpam-93	127	1	if	if	SCONJ
ejpam-93	127	2	the	the	DET
ejpam-93	127	3	boundary	boundary	ADJ
ejpam-93	127	4	flux	flux	NOUN
ejpam-93	127	5	is	be	AUX
ejpam-93	127	6	not	not	PART
ejpam-93	127	7	sufficiently	sufficiently	ADV
ejpam-93	127	8	strong	strong	ADJ
ejpam-93	127	9	,	,	PUNCT
ejpam-93	127	10	it	it	PRON
ejpam-93	127	11	is	be	AUX
ejpam-93	127	12	probable	probable	ADJ
ejpam-93	127	13	that	that	SCONJ
ejpam-93	127	14	the	the	DET
ejpam-93	127	15	solution	solution	NOUN
ejpam-93	127	16	may	may	AUX
ejpam-93	127	17	never	never	ADV
ejpam-93	127	18	blow	blow	VERB
ejpam-93	127	19	up	up	ADP
ejpam-93	127	20	.	.	PUNCT
ejpam-93	128	1	as	as	ADP
ejpam-93	128	2	the	the	DET
ejpam-93	128	3	application	application	NOUN
ejpam-93	128	4	of	of	ADP
ejpam-93	128	5	theorems	theorem	NOUN
ejpam-93	128	6	,	,	PUNCT
ejpam-93	128	7	now	now	ADV
ejpam-93	128	8	we	we	PRON
ejpam-93	128	9	consider	consider	VERB
ejpam-93	128	10	the	the	DET
ejpam-93	128	11	following	follow	VERB
ejpam-93	128	12	porous	porous	ADJ
ejpam-93	128	13	medium	medium	ADJ
ejpam-93	128	14	problem	problem	NOUN
ejpam-93	128	15	ut	ut	PROPN
ejpam-93	129	1	=	=	NOUN
ejpam-93	129	2	4up	4up	NOUN
ejpam-93	129	3	−	−	PROPN
ejpam-93	129	4	uq	uq	NOUN
ejpam-93	129	5	in	in	ADP
ejpam-93	129	6	ω×	ω×	PROPN
ejpam-93	129	7	(	(	PUNCT
ejpam-93	129	8	0	0	NUM
ejpam-93	129	9	,	,	PUNCT
ejpam-93	129	10	t	t	NOUN
ejpam-93	129	11	)	)	PUNCT
ejpam-93	129	12	,	,	PUNCT
ejpam-93	129	13	∂	∂	NUM
ejpam-93	129	14	u	u	NOUN
ejpam-93	129	15	∂	∂	NOUN
ejpam-93	129	16	n	n	NOUN
ejpam-93	129	17	=	=	PRON
ejpam-93	129	18	ur	ur	PROPN
ejpam-93	129	19	on	on	ADP
ejpam-93	129	20	∂ω×	∂ω×	PROPN
ejpam-93	129	21	(	(	PUNCT
ejpam-93	129	22	0	0	NUM
ejpam-93	129	23	,	,	PUNCT
ejpam-93	129	24	t	t	NOUN
ejpam-93	129	25	)	)	PUNCT
ejpam-93	129	26	,	,	PUNCT
ejpam-93	129	27	u(x	u(x	PROPN
ejpam-93	129	28	,	,	PUNCT
ejpam-93	129	29	0	0	NUM
ejpam-93	129	30	)	)	PUNCT
ejpam-93	129	31	=	=	SYM
ejpam-93	129	32	u0(x	u0(x	NOUN
ejpam-93	129	33	)	)	PUNCT
ejpam-93	129	34	>	>	X
ejpam-93	129	35	0	0	PUNCT
ejpam-93	129	36	in	in	ADP
ejpam-93	129	37	ω	ω	PROPN
ejpam-93	129	38	,	,	PUNCT
ejpam-93	129	39	where	where	SCONJ
ejpam-93	129	40	p	p	X
ejpam-93	129	41	,	,	PUNCT
ejpam-93	129	42	q	q	ADJ
ejpam-93	129	43	,	,	PUNCT
ejpam-93	129	44	r	r	NOUN
ejpam-93	129	45	>	>	X
ejpam-93	129	46	0	0	NUM
ejpam-93	129	47	.	.	PUNCT
ejpam-93	130	1	if	if	SCONJ
ejpam-93	130	2	r	r	NOUN
ejpam-93	130	3	≤	≤	X
ejpam-93	130	4	p	p	X
ejpam-93	130	5	≤	≤	NUM
ejpam-93	130	6	1	1	NUM
ejpam-93	130	7	,	,	PUNCT
ejpam-93	130	8	then	then	ADV
ejpam-93	130	9	corollary	corollary	ADJ
ejpam-93	130	10	1	1	NUM
ejpam-93	130	11	hold	hold	NOUN
ejpam-93	130	12	,	,	PUNCT
ejpam-93	130	13	every	every	DET
ejpam-93	130	14	positive	positive	ADJ
ejpam-93	130	15	solution	solution	NOUN
ejpam-93	130	16	u(x	u(x	PROPN
ejpam-93	130	17	,	,	PUNCT
ejpam-93	130	18	t	t	PROPN
ejpam-93	130	19	)	)	PUNCT
ejpam-93	130	20	of	of	ADP
ejpam-93	130	21	the	the	DET
ejpam-93	130	22	problem	problem	NOUN
ejpam-93	130	23	exists	exist	VERB
ejpam-93	130	24	globally	globally	ADV
ejpam-93	130	25	.	.	PUNCT
ejpam-93	131	1	if	if	SCONJ
ejpam-93	131	2	r	r	NOUN
ejpam-93	131	3	≥	≥	NOUN
ejpam-93	131	4	max{1	max{1	NOUN
ejpam-93	131	5	,	,	PUNCT
ejpam-93	131	6	p	p	X
ejpam-93	131	7	,	,	PUNCT
ejpam-93	131	8	q	q	ADJ
ejpam-93	131	9	}	}	PUNCT
ejpam-93	131	10	and	and	CCONJ
ejpam-93	131	11	4up	4up	ADJ
ejpam-93	131	12	0	0	NUM
ejpam-93	131	13	≥	≥	NOUN
ejpam-93	131	14	uq	uq	NOUN
ejpam-93	131	15	0	0	NUM
ejpam-93	131	16	,	,	PUNCT
ejpam-93	131	17	by	by	ADP
ejpam-93	131	18	theorems	theorem	NOUN
ejpam-93	131	19	1	1	NUM
ejpam-93	131	20	-	-	SYM
ejpam-93	131	21	2	2	NUM
ejpam-93	131	22	we	we	PRON
ejpam-93	131	23	know	know	VERB
ejpam-93	131	24	that	that	SCONJ
ejpam-93	131	25	every	every	DET
ejpam-93	131	26	positive	positive	ADJ
ejpam-93	131	27	solution	solution	NOUN
ejpam-93	131	28	u(x	u(x	PROPN
ejpam-93	131	29	,	,	PUNCT
ejpam-93	131	30	t	t	PROPN
ejpam-93	131	31	)	)	PUNCT
ejpam-93	131	32	of	of	ADP
ejpam-93	131	33	the	the	DET
ejpam-93	131	34	problem	problem	NOUN
ejpam-93	131	35	blows	blow	VERB
ejpam-93	131	36	up	up	ADP
ejpam-93	131	37	in	in	ADP
ejpam-93	131	38	a	a	DET
ejpam-93	131	39	finite	finite	ADJ
ejpam-93	131	40	time	time	NOUN
ejpam-93	131	41	t	t	PROPN
ejpam-93	131	42	and	and	CCONJ
ejpam-93	131	43	the	the	DET
ejpam-93	131	44	blowup	blowup	NOUN
ejpam-93	131	45	will	will	AUX
ejpam-93	131	46	occur	occur	VERB
ejpam-93	131	47	only	only	ADV
ejpam-93	131	48	at	at	ADP
ejpam-93	131	49	the	the	DET
ejpam-93	131	50	boundary	boundary	NOUN
ejpam-93	131	51	of	of	ADP
ejpam-93	131	52	the	the	DET
ejpam-93	131	53	domain	domain	NOUN
ejpam-93	131	54	.	.	PUNCT
ejpam-93	132	1	moreover	moreover	ADV
ejpam-93	132	2	,	,	PUNCT
ejpam-93	132	3	there	there	PRON
ejpam-93	132	4	exits	exit	VERB
ejpam-93	132	5	a	a	DET
ejpam-93	132	6	constant	constant	ADJ
ejpam-93	132	7	c	c	NOUN
ejpam-93	132	8	>	>	X
ejpam-93	132	9	0	0	NUM
ejpam-93	132	10	such	such	ADJ
ejpam-93	132	11	that	that	DET
ejpam-93	132	12	sup	sup	PROPN
ejpam-93	132	13	x∈ω	x∈ω	X
ejpam-93	132	14	u(x	u(x	PROPN
ejpam-93	132	15	,	,	PUNCT
ejpam-93	132	16	t)≤	t)≤	PRON
ejpam-93	132	17	c	c	X
ejpam-93	132	18	(	(	PUNCT
ejpam-93	132	19	t	t	PROPN
ejpam-93	132	20	−	−	PROPN
ejpam-93	132	21	t	t	PROPN
ejpam-93	132	22	)	)	PUNCT
ejpam-93	132	23	1	1	NUM
ejpam-93	132	24	r−p	r−p	NOUN
ejpam-93	132	25	ε0	ε0	NOUN
ejpam-93	132	26	<	<	X
ejpam-93	132	27	t	t	X
ejpam-93	132	28	<	<	X
ejpam-93	132	29	t	t	PROPN
ejpam-93	132	30	,	,	PUNCT
ejpam-93	132	31	ε0	ε0	PROPN
ejpam-93	132	32	>	>	X
ejpam-93	132	33	0	0	X
ejpam-93	132	34	.	.	PUNCT
ejpam-93	133	1	acknowledgements	acknowledgement	NOUN
ejpam-93	133	2	the	the	DET
ejpam-93	133	3	authors	author	NOUN
ejpam-93	133	4	would	would	AUX
ejpam-93	133	5	like	like	VERB
ejpam-93	133	6	to	to	PART
ejpam-93	133	7	thank	thank	VERB
ejpam-93	133	8	professor	professor	PROPN
ejpam-93	133	9	c.v.pao	c.v.pao	PROPN
ejpam-93	133	10	for	for	ADP
ejpam-93	133	11	his	his	PRON
ejpam-93	133	12	helpful	helpful	ADJ
ejpam-93	133	13	discussion	discussion	NOUN
ejpam-93	133	14	.	.	PUNCT
ejpam-93	134	1	we	we	PRON
ejpam-93	134	2	should	should	AUX
ejpam-93	134	3	also	also	ADV
ejpam-93	134	4	like	like	VERB
ejpam-93	134	5	to	to	PART
ejpam-93	134	6	thank	thank	VERB
ejpam-93	134	7	the	the	DET
ejpam-93	134	8	referees	referee	NOUN
ejpam-93	134	9	for	for	ADP
ejpam-93	134	10	their	their	PRON
ejpam-93	134	11	advice	advice	NOUN
ejpam-93	134	12	on	on	ADP
ejpam-93	134	13	amendments	amendment	NOUN
ejpam-93	134	14	.	.	PUNCT
ejpam-93	135	1	this	this	DET
ejpam-93	135	2	work	work	NOUN
ejpam-93	135	3	is	be	AUX
ejpam-93	135	4	supported	support	VERB
ejpam-93	135	5	by	by	ADP
ejpam-93	135	6	the	the	DET
ejpam-93	135	7	national	national	ADJ
ejpam-93	135	8	natural	natural	PROPN
ejpam-93	135	9	science	science	PROPN
ejpam-93	135	10	foundation	foundation	PROPN
ejpam-93	135	11	of	of	ADP
ejpam-93	135	12	china	china	PROPN
ejpam-93	135	13	and	and	CCONJ
ejpam-93	135	14	the	the	DET
ejpam-93	135	15	key	key	ADJ
ejpam-93	135	16	project	project	NOUN
ejpam-93	135	17	of	of	ADP
ejpam-93	135	18	zhejiang	zhejiang	PROPN
ejpam-93	135	19	ocean	ocean	PROPN
ejpam-93	135	20	university	university	PROPN
ejpam-93	135	21	.	.	PUNCT
ejpam-93	136	1	references	reference	NOUN
ejpam-93	136	2	[	[	X
ejpam-93	136	3	1	1	NUM
ejpam-93	136	4	]	]	PUNCT
ejpam-93	136	5	a.	a.	NOUN
ejpam-93	136	6	amann	amann	PROPN
ejpam-93	136	7	,	,	PUNCT
ejpam-93	136	8	quasilinear	quasilinear	PROPN
ejpam-93	136	9	parabolic	parabolic	NOUN
ejpam-93	136	10	systems	system	NOUN
ejpam-93	136	11	under	under	ADP
ejpam-93	136	12	nonlinear	nonlinear	ADJ
ejpam-93	136	13	boundary	boundary	ADJ
ejpam-93	136	14	conditions	condition	NOUN
ejpam-93	136	15	,	,	PUNCT
ejpam-93	136	16	arch	arch	NOUN
ejpam-93	136	17	.	.	PUNCT
ejpam-93	137	1	rational	rational	ADJ
ejpam-93	137	2	mech	mech	NOUN
ejpam-93	137	3	.	.	PUNCT
ejpam-93	138	1	anal	anal	PROPN
ejpam-93	138	2	.	.	PUNCT
ejpam-93	139	1	92(1986	92(1986	NUM
ejpam-93	139	2	)	)	PUNCT
ejpam-93	139	3	153	153	NUM
ejpam-93	139	4	-	-	SYM
ejpam-93	139	5	192	192	NUM
ejpam-93	139	6	.	.	PUNCT
ejpam-93	140	1	[	[	X
ejpam-93	140	2	2	2	X
ejpam-93	140	3	]	]	PUNCT
ejpam-93	140	4	t.	t.	PROPN
ejpam-93	140	5	k.	k.	PROPN
ejpam-93	140	6	boni	boni	PROPN
ejpam-93	140	7	,	,	PUNCT
ejpam-93	140	8	sur	sur	PROPN
ejpam-93	140	9	i’explosion	i’explosion	PROPN
ejpam-93	140	10	et	et	PROPN
ejpam-93	140	11	le	le	X
ejpam-93	140	12	comportement	comportement	PROPN
ejpam-93	140	13	asymptotique	asymptotique	NOUN
ejpam-93	140	14	de	de	X
ejpam-93	140	15	la	la	PROPN
ejpam-93	140	16	solution	solution	NOUN
ejpam-93	140	17	d’une	d’une	ADJ
ejpam-93	140	18	equation	equation	NOUN
ejpam-93	140	19	parabolique	parabolique	VERB
ejpam-93	140	20	semilinaire	semilinaire	NOUN
ejpam-93	140	21	du	du	PROPN
ejpam-93	140	22	second	second	ADJ
ejpam-93	140	23	ordre	ordre	PROPN
ejpam-93	140	24	,	,	PUNCT
ejpam-93	140	25	c.	c.	PROPN
ejpam-93	140	26	r.	r.	PROPN
ejpam-93	140	27	acad	acad	PROPN
ejpam-93	140	28	.	.	PUNCT
ejpam-93	141	1	sci	sci	PROPN
ejpam-93	141	2	.	.	PROPN
ejpam-93	141	3	paris	paris	PROPN
ejpam-93	141	4	,	,	PUNCT
ejpam-93	141	5	ser.i	ser.i	PROPN
ejpam-93	141	6	326(1998	326(1998	NUM
ejpam-93	141	7	)	)	PUNCT
ejpam-93	141	8	317	317	NUM
ejpam-93	141	9	-	-	SYM
ejpam-93	141	10	322	322	NUM
ejpam-93	141	11	.	.	PUNCT
ejpam-93	142	1	[	[	X
ejpam-93	142	2	3	3	X
ejpam-93	142	3	]	]	X
ejpam-93	142	4	j.	j.	PROPN
ejpam-93	142	5	ding	ding	PROPN
ejpam-93	142	6	,	,	PUNCT
ejpam-93	142	7	s.	s.	PROPN
ejpam-93	142	8	li	li	PROPN
ejpam-93	142	9	,	,	PUNCT
ejpam-93	142	10	blow	blow	NOUN
ejpam-93	142	11	-	-	PUNCT
ejpam-93	142	12	up	up	ADP
ejpam-93	142	13	solutions	solution	NOUN
ejpam-93	142	14	and	and	CCONJ
ejpam-93	142	15	global	global	ADJ
ejpam-93	142	16	solutions	solution	NOUN
ejpam-93	142	17	for	for	ADP
ejpam-93	142	18	a	a	DET
ejpam-93	142	19	class	class	NOUN
ejpam-93	142	20	of	of	ADP
ejpam-93	142	21	quasilinear	quasilinear	PROPN
ejpam-93	142	22	parabolic	parabolic	PROPN
ejpam-93	142	23	equations	equation	NOUN
ejpam-93	142	24	with	with	ADP
ejpam-93	142	25	robin	robin	PROPN
ejpam-93	142	26	boundary	boundary	PROPN
ejpam-93	142	27	conditions	condition	NOUN
ejpam-93	142	28	,	,	PUNCT
ejpam-93	142	29	comput	comput	NOUN
ejpam-93	142	30	.	.	PUNCT
ejpam-93	142	31	math	math	NOUN
ejpam-93	142	32	.	.	PUNCT
ejpam-93	143	1	appl	appl	PROPN
ejpam-93	143	2	.	.	PUNCT
ejpam-93	144	1	49(2005	49(2005	NUM
ejpam-93	144	2	)	)	PUNCT
ejpam-93	145	1	689	689	NUM
ejpam-93	145	2	-	-	SYM
ejpam-93	145	3	701	701	NUM
ejpam-93	145	4	.	.	PUNCT
ejpam-93	146	1	references	reference	NOUN
ejpam-93	146	2	39	39	NUM
ejpam-93	146	3	[	[	X
ejpam-93	146	4	4	4	NUM
ejpam-93	146	5	]	]	PUNCT
ejpam-93	146	6	a.	a.	NOUN
ejpam-93	146	7	friedman	friedman	PROPN
ejpam-93	146	8	,	,	PUNCT
ejpam-93	146	9	j.	j.	PROPN
ejpam-93	146	10	b.	b.	PROPN
ejpam-93	146	11	mcleod	mcleod	PROPN
ejpam-93	146	12	,	,	PUNCT
ejpam-93	146	13	blow	blow	NOUN
ejpam-93	146	14	-	-	PUNCT
ejpam-93	146	15	up	up	NOUN
ejpam-93	146	16	of	of	ADP
ejpam-93	146	17	positive	positive	ADJ
ejpam-93	146	18	solutions	solution	NOUN
ejpam-93	146	19	of	of	ADP
ejpam-93	146	20	semi	semi	ADJ
ejpam-93	146	21	-	-	ADJ
ejpam-93	146	22	linear	linear	ADJ
ejpam-93	146	23	heat	heat	NOUN
ejpam-93	146	24	equations	equation	NOUN
ejpam-93	146	25	,	,	PUNCT
ejpam-93	146	26	indiana	indiana	PROPN
ejpam-93	146	27	univ	univ	PROPN
ejpam-93	146	28	.	.	PUNCT
ejpam-93	147	1	math	math	PROPN
ejpam-93	147	2	.	.	PUNCT
ejpam-93	148	1	j.	j.	PROPN
ejpam-93	148	2	34(1985	34(1985	NUM
ejpam-93	148	3	)	)	PUNCT
ejpam-93	148	4	425	425	NUM
ejpam-93	148	5	-	-	SYM
ejpam-93	148	6	447	447	NUM
ejpam-93	148	7	.	.	PUNCT
ejpam-93	149	1	[	[	X
ejpam-93	149	2	5	5	X
ejpam-93	149	3	]	]	PUNCT
ejpam-93	149	4	h.	h.	PROPN
ejpam-93	149	5	fujita	fujita	PROPN
ejpam-93	149	6	,	,	PUNCT
ejpam-93	149	7	on	on	ADP
ejpam-93	149	8	the	the	DET
ejpam-93	149	9	blow	blow	NOUN
ejpam-93	149	10	-	-	PUNCT
ejpam-93	149	11	up	up	NOUN
ejpam-93	149	12	of	of	ADP
ejpam-93	149	13	solutions	solution	NOUN
ejpam-93	149	14	of	of	ADP
ejpam-93	149	15	the	the	DET
ejpam-93	149	16	cauchy	cauchy	ADJ
ejpam-93	149	17	problem	problem	NOUN
ejpam-93	149	18	for	for	ADP
ejpam-93	149	19	ut	ut	PROPN
ejpam-93	149	20	=	=	NOUN
ejpam-93	149	21	4u	4u	NOUN
ejpam-93	149	22	+	+	X
ejpam-93	149	23	u1+α	u1+α	PROPN
ejpam-93	149	24	,	,	PUNCT
ejpam-93	149	25	j.fac.sci.univ.tokyo	j.fac.sci.univ.tokyo	PROPN
ejpam-93	149	26	sec.1a	sec.1a	PROPN
ejpam-93	149	27	math	math	NOUN
ejpam-93	149	28	.	.	PUNCT
ejpam-93	150	1	16	16	NUM
ejpam-93	150	2	(	(	PUNCT
ejpam-93	150	3	1966	1966	NUM
ejpam-93	150	4	)	)	PUNCT
ejpam-93	150	5	105	105	NUM
ejpam-93	150	6	-	-	SYM
ejpam-93	150	7	113	113	NUM
ejpam-93	150	8	.	.	PUNCT
ejpam-93	151	1	[	[	X
ejpam-93	151	2	6	6	NUM
ejpam-93	151	3	]	]	PUNCT
ejpam-93	151	4	bei	bei	X
ejpam-93	151	5	hu	hu	PROPN
ejpam-93	151	6	,	,	PUNCT
ejpam-93	151	7	h.	h.	PROPN
ejpam-93	151	8	m.	m.	PROPN
ejpam-93	151	9	yin	yin	PROPN
ejpam-93	151	10	,	,	PUNCT
ejpam-93	151	11	the	the	DET
ejpam-93	151	12	profile	profile	NOUN
ejpam-93	151	13	near	near	ADP
ejpam-93	151	14	blowup	blowup	ADJ
ejpam-93	151	15	time	time	NOUN
ejpam-93	151	16	for	for	ADP
ejpam-93	151	17	solution	solution	NOUN
ejpam-93	151	18	of	of	ADP
ejpam-93	151	19	the	the	DET
ejpam-93	151	20	heat	heat	NOUN
ejpam-93	151	21	equation	equation	NOUN
ejpam-93	151	22	with	with	ADP
ejpam-93	151	23	a	a	DET
ejpam-93	151	24	nonlinear	nonlinear	ADJ
ejpam-93	151	25	boundary	boundary	ADJ
ejpam-93	151	26	condition	condition	NOUN
ejpam-93	151	27	,	,	PUNCT
ejpam-93	151	28	transactions	transaction	NOUN
ejpam-93	151	29	of	of	ADP
ejpam-93	151	30	the	the	DET
ejpam-93	151	31	american	american	PROPN
ejpam-93	151	32	mathematical	mathematical	PROPN
ejpam-93	151	33	society	society	NOUN
ejpam-93	151	34	,	,	PUNCT
ejpam-93	151	35	346(1994	346(1994	NUM
ejpam-93	151	36	)	)	PUNCT
ejpam-93	151	37	117	117	NUM
ejpam-93	151	38	-	-	SYM
ejpam-93	151	39	135	135	NUM
ejpam-93	151	40	.	.	PUNCT
ejpam-93	152	1	[	[	X
ejpam-93	152	2	7	7	X
ejpam-93	152	3	]	]	PUNCT
ejpam-93	152	4	a.	a.	PROPN
ejpam-93	152	5	w.	w.	PROPN
ejpam-93	152	6	leung	leung	PROPN
ejpam-93	152	7	,	,	PUNCT
ejpam-93	152	8	q.zhang	q.zhang	NOUN
ejpam-93	152	9	,	,	PUNCT
ejpam-93	152	10	finite	finite	ADJ
ejpam-93	152	11	extinction	extinction	NOUN
ejpam-93	152	12	time	time	NOUN
ejpam-93	152	13	for	for	ADP
ejpam-93	152	14	nonlinear	nonlinear	ADJ
ejpam-93	152	15	parabolic	parabolic	ADJ
ejpam-93	152	16	equations	equation	NOUN
ejpam-93	152	17	with	with	ADP
ejpam-93	152	18	nonlinear	nonlinear	ADJ
ejpam-93	152	19	mixed	mixed	ADJ
ejpam-93	152	20	boundary	boundary	ADJ
ejpam-93	152	21	data	datum	NOUN
ejpam-93	152	22	,	,	PUNCT
ejpam-93	152	23	nonlinear	nonlinear	ADJ
ejpam-93	152	24	analysis	analysis	NOUN
ejpam-93	152	25	31(1998	31(1998	NUM
ejpam-93	152	26	)	)	PUNCT
ejpam-93	152	27	1	1	NUM
ejpam-93	152	28	-	-	SYM
ejpam-93	152	29	13	13	NUM
ejpam-93	152	30	.	.	PUNCT
ejpam-93	153	1	[	[	X
ejpam-93	153	2	8	8	NUM
ejpam-93	153	3	]	]	X
ejpam-93	153	4	h.	h.	PROPN
ejpam-93	153	5	levine	levine	PROPN
ejpam-93	153	6	,	,	PUNCT
ejpam-93	153	7	l.	l.	PROPN
ejpam-93	153	8	payne	payne	PROPN
ejpam-93	153	9	,	,	PUNCT
ejpam-93	153	10	nonexistce	nonexistce	PROPN
ejpam-93	153	11	theorems	theorem	NOUN
ejpam-93	153	12	for	for	ADP
ejpam-93	153	13	the	the	DET
ejpam-93	153	14	heat	heat	NOUN
ejpam-93	153	15	equation	equation	NOUN
ejpam-93	153	16	with	with	ADP
ejpam-93	153	17	nonlinear	nonlinear	ADJ
ejpam-93	153	18	boundary	boundary	ADJ
ejpam-93	153	19	conditions	condition	NOUN
ejpam-93	153	20	and	and	CCONJ
ejpam-93	153	21	for	for	ADP
ejpam-93	153	22	the	the	DET
ejpam-93	153	23	porous	porous	ADJ
ejpam-93	153	24	medium	medium	ADJ
ejpam-93	153	25	equation	equation	NOUN
ejpam-93	153	26	backward	backward	ADV
ejpam-93	153	27	in	in	ADP
ejpam-93	153	28	time	time	NOUN
ejpam-93	153	29	,	,	PUNCT
ejpam-93	153	30	j.	j.	PROPN
ejpam-93	153	31	differential	differential	PROPN
ejpam-93	153	32	equations	equations	PROPN
ejpam-93	153	33	,	,	PUNCT
ejpam-93	153	34	16(1974	16(1974	NUM
ejpam-93	153	35	)	)	PUNCT
ejpam-93	153	36	319	319	NUM
ejpam-93	153	37	-	-	SYM
ejpam-93	153	38	334	334	NUM
ejpam-93	153	39	.	.	PUNCT
ejpam-93	154	1	[	[	X
ejpam-93	154	2	9	9	NUM
ejpam-93	154	3	]	]	X
ejpam-93	154	4	r.	r.	PROPN
ejpam-93	154	5	pinsky	pinsky	PROPN
ejpam-93	154	6	,	,	PUNCT
ejpam-93	154	7	existence	existence	NOUN
ejpam-93	154	8	and	and	CCONJ
ejpam-93	154	9	noexistence	noexistence	NOUN
ejpam-93	154	10	of	of	ADP
ejpam-93	154	11	global	global	ADJ
ejpam-93	154	12	solutions	solution	NOUN
ejpam-93	154	13	for	for	ADP
ejpam-93	154	14	ut	ut	PROPN
ejpam-93	154	15	=	=	NOUN
ejpam-93	154	16	4u+	4u+	NUM
ejpam-93	154	17	a(x)up	a(x)up	PUNCT
ejpam-93	154	18	in	in	ADP
ejpam-93	154	19	rd	rd	PROPN
ejpam-93	154	20	,	,	PUNCT
ejpam-93	154	21	j.	j.	PROPN
ejpam-93	154	22	differential	differential	PROPN
ejpam-93	154	23	equations	equation	NOUN
ejpam-93	154	24	,	,	PUNCT
ejpam-93	154	25	133(1997	133(1997	NUM
ejpam-93	154	26	)	)	PUNCT
ejpam-93	154	27	152	152	NUM
ejpam-93	154	28	-	-	SYM
ejpam-93	154	29	177	177	NUM
ejpam-93	154	30	.	.	PUNCT
ejpam-93	155	1	[	[	X
ejpam-93	155	2	10	10	NUM
ejpam-93	155	3	]	]	X
ejpam-93	155	4	p.	p.	NOUN
ejpam-93	155	5	quittner	quittner	NOUN
ejpam-93	155	6	,	,	PUNCT
ejpam-93	155	7	on	on	ADP
ejpam-93	155	8	global	global	ADJ
ejpam-93	155	9	existence	existence	NOUN
ejpam-93	155	10	and	and	CCONJ
ejpam-93	155	11	stationary	stationary	ADJ
ejpam-93	155	12	solutions	solution	NOUN
ejpam-93	155	13	for	for	ADP
ejpam-93	155	14	two	two	NUM
ejpam-93	155	15	classes	class	NOUN
ejpam-93	155	16	of	of	ADP
ejpam-93	155	17	semilinear	semilinear	PROPN
ejpam-93	155	18	parabolic	parabolic	PROPN
ejpam-93	155	19	problems	problem	NOUN
ejpam-93	155	20	,	,	PUNCT
ejpam-93	155	21	comment	comment	NOUN
ejpam-93	155	22	.	.	PUNCT
ejpam-93	156	1	math	math	NOUN
ejpam-93	156	2	.	.	PUNCT
ejpam-93	157	1	univ	univ	PROPN
ejpam-93	157	2	.	.	PUNCT
ejpam-93	157	3	carolinae	carolinae	PROPN
ejpam-93	157	4	.	.	PUNCT
ejpam-93	158	1	34	34	NUM
ejpam-93	158	2	(	(	PUNCT
ejpam-93	158	3	1993	1993	NUM
ejpam-93	158	4	)	)	PUNCT
ejpam-93	159	1	105–124	105–124	NUM
ejpam-93	159	2	.	.	PUNCT
ejpam-93	160	1	[	[	X
ejpam-93	160	2	11	11	NUM
ejpam-93	160	3	]	]	PUNCT
ejpam-93	160	4	r.	r.	PROPN
ejpam-93	160	5	p.	p.	PROPN
ejpam-93	160	6	sperp	sperp	PROPN
ejpam-93	160	7	,	,	PUNCT
ejpam-93	160	8	growth	growth	NOUN
ejpam-93	160	9	estimates	estimate	NOUN
ejpam-93	160	10	in	in	ADP
ejpam-93	160	11	diffusion	diffusion	NOUN
ejpam-93	160	12	-	-	PUNCT
ejpam-93	160	13	reaction	reaction	NOUN
ejpam-93	160	14	problems	problem	NOUN
ejpam-93	160	15	,	,	PUNCT
ejpam-93	160	16	arch	arch	NOUN
ejpam-93	160	17	.	.	PUNCT
ejpam-93	161	1	rational	rational	ADJ
ejpam-93	161	2	mech	mech	NOUN
ejpam-93	161	3	.	.	PUNCT
ejpam-93	162	1	anal	anal	NOUN
ejpam-93	162	2	.	.	PUNCT
ejpam-93	163	1	75(1980	75(1980	X
ejpam-93	163	2	)	)	PUNCT
ejpam-93	163	3	127	127	NUM
ejpam-93	163	4	-	-	SYM
ejpam-93	163	5	145	145	NUM
ejpam-93	163	6	.	.	PUNCT
ejpam-93	164	1	[	[	X
ejpam-93	164	2	12	12	NUM
ejpam-93	164	3	]	]	PUNCT
ejpam-93	164	4	m.	m.	NOUN
ejpam-93	164	5	wang	wang	PROPN
ejpam-93	164	6	,	,	PUNCT
ejpam-93	164	7	y.	y.	PROPN
ejpam-93	164	8	wu	wu	PROPN
ejpam-93	164	9	,	,	PUNCT
ejpam-93	164	10	global	global	ADJ
ejpam-93	164	11	existence	existence	NOUN
ejpam-93	164	12	and	and	CCONJ
ejpam-93	164	13	blow	blow	NOUN
ejpam-93	164	14	-	-	PUNCT
ejpam-93	164	15	up	up	ADP
ejpam-93	164	16	problems	problem	NOUN
ejpam-93	164	17	for	for	ADP
ejpam-93	164	18	quasilinear	quasilinear	PROPN
ejpam-93	164	19	parabolic	parabolic	PROPN
ejpam-93	164	20	equations	equation	NOUN
ejpam-93	164	21	with	with	ADP
ejpam-93	164	22	nonlinear	nonlinear	ADJ
ejpam-93	164	23	boundary	boundary	ADJ
ejpam-93	164	24	conditions	condition	NOUN
ejpam-93	164	25	,	,	PUNCT
ejpam-93	164	26	siam	siam	PROPN
ejpam-93	164	27	j.	j.	PROPN
ejpam-93	164	28	math	math	PROPN
ejpam-93	164	29	.	.	PUNCT
ejpam-93	165	1	anal	anal	PROPN
ejpam-93	165	2	.	.	PUNCT
ejpam-93	166	1	24(1993	24(1993	NUM
ejpam-93	166	2	)	)	PUNCT
ejpam-93	166	3	1515	1515	NUM
ejpam-93	166	4	-	-	SYM
ejpam-93	166	5	1521	1521	NUM
ejpam-93	166	6	.	.	PUNCT
ejpam-93	167	1	[	[	X
ejpam-93	167	2	13	13	NUM
ejpam-93	167	3	]	]	X
ejpam-93	167	4	h.	h.	PROPN
ejpam-93	167	5	m.	m.	PROPN
ejpam-93	167	6	ying	ying	PROPN
ejpam-93	167	7	,	,	PUNCT
ejpam-93	167	8	blow	blow	NOUN
ejpam-93	167	9	-	-	PUNCT
ejpam-93	167	10	up	up	NOUN
ejpam-93	167	11	versus	versus	ADP
ejpam-93	167	12	global	global	ADJ
ejpam-93	167	13	solvability	solvability	NOUN
ejpam-93	167	14	for	for	ADP
ejpam-93	167	15	a	a	DET
ejpam-93	167	16	class	class	NOUN
ejpam-93	167	17	of	of	ADP
ejpam-93	167	18	nonlinear	nonlinear	ADJ
ejpam-93	167	19	parabolic	parabolic	PROPN
ejpam-93	167	20	equations	equation	NOUN
ejpam-93	167	21	,	,	PUNCT
ejpam-93	167	22	nonlinear	nonlinear	ADJ
ejpam-93	167	23	ananlysis	ananlysis	NOUN
ejpam-93	167	24	,	,	PUNCT
ejpam-93	167	25	23	23	NUM
ejpam-93	167	26	(	(	PUNCT
ejpam-93	167	27	1994	1994	NUM
ejpam-93	167	28	)	)	PUNCT
ejpam-93	167	29	911	911	NUM
ejpam-93	167	30	-	-	SYM
ejpam-93	167	31	924	924	NUM
ejpam-93	167	32	.	.	PUNCT
ejpam-93	168	1	[	[	X
ejpam-93	168	2	14	14	NUM
ejpam-93	168	3	]	]	X
ejpam-93	168	4	h.	h.	PROPN
ejpam-93	168	5	zhang	zhang	PROPN
ejpam-93	168	6	,	,	PUNCT
ejpam-93	168	7	z.	z.	PROPN
ejpam-93	168	8	liu	liu	PROPN
ejpam-93	168	9	,	,	PUNCT
ejpam-93	168	10	w.	w.	PROPN
ejpam-93	168	11	zhang	zhang	PROPN
ejpam-93	168	12	,	,	PUNCT
ejpam-93	168	13	growth	growth	NOUN
ejpam-93	168	14	estimates	estimate	NOUN
ejpam-93	168	15	and	and	CCONJ
ejpam-93	168	16	blow	blow	NOUN
ejpam-93	168	17	-	-	PUNCT
ejpam-93	168	18	up	up	NOUN
ejpam-93	168	19	in	in	ADP
ejpam-93	168	20	quasilinear	quasilinear	PROPN
ejpam-93	168	21	parabolic	parabolic	NOUN
ejpam-93	168	22	problems	problem	NOUN
ejpam-93	168	23	,	,	PUNCT
ejpam-93	168	24	applicable	applicable	ADJ
ejpam-93	168	25	analysis	analysis	NOUN
ejpam-93	168	26	,	,	PUNCT
ejpam-93	168	27	86	86	NUM
ejpam-93	168	28	(	(	PUNCT
ejpam-93	168	29	2007	2007	NUM
ejpam-93	168	30	)	)	PUNCT
ejpam-93	168	31	261	261	NUM
ejpam-93	168	32	268	268	NUM
ejpam-93	168	33	.	.	PUNCT