id	sid	tid	token	lemma	pos
m-1057	1	1	ijo	ijo	PROPN
m-1057	1	2	international	international	PROPN
m-1057	1	3	journal	journal	PROPN
m-1057	1	4	of	of	ADP
m-1057	1	5	mathematics	mathematics	PROPN
m-1057	1	6	(	(	PUNCT
m-1057	1	7	issn	issn	PROPN
m-1057	1	8	:	:	PUNCT
m-1057	1	9	2992	2992	NUM
m-1057	1	10	-	-	SYM
m-1057	1	11	4421	4421	NUM
m-1057	1	12	)	)	PUNCT
m-1057	1	13	otobong	otobong	PROPN
m-1057	1	14	j.	j.	PROPN
m-1057	1	15	tom1	tom1	PROPN
m-1057	2	1	*	*	PUNCT
m-1057	2	2	https://ijojournals.com/	https://ijojournals.com/	PROPN
m-1057	2	3	volume	volume	NOUN
m-1057	2	4	08	08	NUM
m-1057	2	5	||	||	PROPN
m-1057	2	6	issue	issue	NOUN
m-1057	2	7	04	04	NUM
m-1057	2	8	||	||	NOUN
m-1057	2	9	april	april	PROPN
m-1057	2	10	,	,	PUNCT
m-1057	2	11	2025	2025	NUM
m-1057	2	12	||	||	PUNCT
m-1057	3	1	“	"	PUNCT
m-1057	3	2	semigroup	semigroup	ADJ
m-1057	3	3	approach	approach	NOUN
m-1057	3	4	for	for	ADP
m-1057	3	5	the	the	DET
m-1057	3	6	solution	solution	NOUN
m-1057	3	7	of	of	ADP
m-1057	3	8	boundary	boundary	ADJ
m-1057	3	9	layer	layer	NOUN
m-1057	3	10	equation	equation	NOUN
m-1057	3	11	with	with	ADP
m-1057	3	12	sinc	sinc	ADJ
m-1057	3	13	function	function	NOUN
m-1057	3	14	term	term	NOUN
m-1057	3	15	"	"	PUNCT
m-1057	3	16	semigroup	semigroup	ADJ
m-1057	3	17	approach	approach	NOUN
m-1057	3	18	for	for	ADP
m-1057	3	19	the	the	DET
m-1057	3	20	solution	solution	NOUN
m-1057	3	21	of	of	ADP
m-1057	3	22	boundary	boundary	ADJ
m-1057	3	23	layer	layer	NOUN
m-1057	3	24	equation	equation	NOUN
m-1057	3	25	with	with	ADP
m-1057	3	26	sinc	sinc	PROPN
m-1057	3	27	function	function	NOUN
m-1057	3	28	term	term	NOUN
m-1057	3	29	otobong	otobong	PROPN
m-1057	3	30	j.	j.	PROPN
m-1057	3	31	tom1	tom1	PROPN
m-1057	3	32	&	&	CCONJ
m-1057	3	33	otobong	otobong	PROPN
m-1057	3	34	g.	g.	PROPN
m-1057	3	35	udoaka2	udoaka2	PROPN
m-1057	4	1	1federal	1federal	NUM
m-1057	4	2	university	university	NOUN
m-1057	4	3	of	of	ADP
m-1057	4	4	technology	technology	NOUN
m-1057	4	5	,	,	PUNCT
m-1057	4	6	ikot	ikot	PROPN
m-1057	4	7	abasi	abasi	NOUN
m-1057	4	8	.	.	PUNCT
m-1057	5	1	2akwa	2akwa	NUM
m-1057	5	2	ibom	ibom	ADJ
m-1057	5	3	state	state	NOUN
m-1057	5	4	university	university	NOUN
m-1057	5	5	,	,	PUNCT
m-1057	5	6	ikot	ikot	PROPN
m-1057	5	7	akpaden	akpaden	NOUN
m-1057	5	8	declarations	declaration	NOUN
m-1057	5	9	1	1	NUM
m-1057	5	10	.	.	X
m-1057	6	1	funding	funding	NOUN
m-1057	6	2	:	:	PUNCT
m-1057	6	3	not	not	PART
m-1057	6	4	applicable	applicable	ADJ
m-1057	6	5	2	2	NUM
m-1057	6	6	.	.	PUNCT
m-1057	6	7	informed	informed	ADJ
m-1057	6	8	consent	consent	NOUN
m-1057	6	9	statement	statement	NOUN
m-1057	6	10	:	:	PUNCT
m-1057	6	11	not	not	PART
m-1057	6	12	applicable	applicable	ADJ
m-1057	6	13	3	3	NUM
m-1057	6	14	.	.	PUNCT
m-1057	6	15	data	datum	NOUN
m-1057	6	16	availability	availability	NOUN
m-1057	6	17	:	:	PUNCT
m-1057	6	18	not	not	PART
m-1057	6	19	applicable	applicable	ADJ
m-1057	6	20	4	4	NUM
m-1057	6	21	.	.	PUNCT
m-1057	7	1	conflict	conflict	NOUN
m-1057	7	2	of	of	ADP
m-1057	7	3	interest	interest	NOUN
m-1057	7	4	statement	statement	NOUN
m-1057	7	5	:	:	PUNCT
m-1057	7	6	no	no	DET
m-1057	7	7	conflict	conflict	NOUN
m-1057	7	8	of	of	ADP
m-1057	7	9	interest	interest	NOUN
m-1057	7	10	.	.	PUNCT
m-1057	8	1	abstract	abstract	ADJ
m-1057	8	2	boundary	boundary	ADJ
m-1057	8	3	layer	layer	NOUN
m-1057	8	4	equation	equation	NOUN
m-1057	8	5	is	be	AUX
m-1057	8	6	crucial	crucial	ADJ
m-1057	8	7	in	in	ADP
m-1057	8	8	fluid	fluid	ADJ
m-1057	8	9	dynamics	dynamic	NOUN
m-1057	8	10	for	for	ADP
m-1057	8	11	modeling	model	VERB
m-1057	8	12	viscous	viscous	ADJ
m-1057	8	13	flow	flow	NOUN
m-1057	8	14	near	near	ADP
m-1057	8	15	surfaces	surface	NOUN
m-1057	8	16	.	.	PUNCT
m-1057	9	1	it	it	PRON
m-1057	9	2	provides	provide	VERB
m-1057	9	3	insight	insight	NOUN
m-1057	9	4	into	into	ADP
m-1057	9	5	flow	flow	NOUN
m-1057	9	6	behaviour	behaviour	NOUN
m-1057	9	7	,	,	PUNCT
m-1057	9	8	drag	drag	NOUN
m-1057	9	9	reduction	reduction	NOUN
m-1057	9	10	,	,	PUNCT
m-1057	9	11	heat	heat	NOUN
m-1057	9	12	transfer	transfer	NOUN
m-1057	9	13	and	and	CCONJ
m-1057	9	14	stability	stability	NOUN
m-1057	9	15	,	,	PUNCT
m-1057	9	16	making	make	VERB
m-1057	9	17	it	it	PRON
m-1057	9	18	essential	essential	ADJ
m-1057	9	19	in	in	ADP
m-1057	9	20	both	both	CCONJ
m-1057	9	21	theoretical	theoretical	ADJ
m-1057	9	22	and	and	CCONJ
m-1057	9	23	applied	applied	ADJ
m-1057	9	24	fluid	fluid	ADJ
m-1057	9	25	mechanics	mechanic	NOUN
m-1057	9	26	.	.	PUNCT
m-1057	10	1	this	this	DET
m-1057	10	2	paper	paper	NOUN
m-1057	10	3	examines	examine	VERB
m-1057	10	4	the	the	DET
m-1057	10	5	semigroup	semigroup	ADJ
m-1057	10	6	approach	approach	NOUN
m-1057	10	7	for	for	ADP
m-1057	10	8	solving	solve	VERB
m-1057	10	9	the	the	DET
m-1057	10	10	boundary	boundary	ADJ
m-1057	10	11	layer	layer	NOUN
m-1057	10	12	equation	equation	NOUN
m-1057	10	13	incorporating	incorporate	VERB
m-1057	10	14	a	a	DET
m-1057	10	15	sinc	sinc	ADJ
m-1057	10	16	function	function	NOUN
m-1057	10	17	term.the	term.the	DET
m-1057	10	18	addition	addition	NOUN
m-1057	10	19	of	of	ADP
m-1057	10	20	the	the	DET
m-1057	10	21	sinc	sinc	PROPN
m-1057	10	22	function	function	NOUN
m-1057	10	23	term	term	NOUN
m-1057	10	24	necessitates	necessitate	VERB
m-1057	10	25	specialized	specialized	ADJ
m-1057	10	26	functional	functional	ADJ
m-1057	10	27	analysis	analysis	NOUN
m-1057	10	28	techniques	technique	NOUN
m-1057	10	29	and	and	CCONJ
m-1057	10	30	its	its	PRON
m-1057	10	31	effects	effect	NOUN
m-1057	10	32	are	be	AUX
m-1057	10	33	analyzed	analyze	VERB
m-1057	10	34	.	.	PUNCT
m-1057	11	1	we	we	PRON
m-1057	11	2	establish	establish	VERB
m-1057	11	3	well	well	ADJ
m-1057	11	4	-	-	PUNCT
m-1057	11	5	posedness	posedness	NOUN
m-1057	11	6	in	in	ADP
m-1057	11	7	a	a	DET
m-1057	11	8	suitable	suitable	ADJ
m-1057	11	9	function	function	NOUN
m-1057	11	10	space	space	NOUN
m-1057	11	11	by	by	ADP
m-1057	11	12	analyzing	analyze	VERB
m-1057	11	13	the	the	DET
m-1057	11	14	existence	existence	NOUN
m-1057	11	15	,	,	PUNCT
m-1057	11	16	uniqueness	uniqueness	NOUN
m-1057	11	17	of	of	ADP
m-1057	11	18	the	the	DET
m-1057	11	19	mild	mild	ADJ
m-1057	11	20	solution	solution	NOUN
m-1057	11	21	.	.	PUNCT
m-1057	12	1	we	we	PRON
m-1057	12	2	demonstrate	demonstrate	VERB
m-1057	12	3	the	the	DET
m-1057	12	4	semigroup	semigroup	PROPN
m-1057	12	5	method	method	NOUN
m-1057	12	6	's	's	PART
m-1057	12	7	effectiveness	effectiveness	NOUN
m-1057	12	8	in	in	ADP
m-1057	12	9	capturing	capture	VERB
m-1057	12	10	boundary	boundary	ADJ
m-1057	12	11	layer	layer	NOUN
m-1057	12	12	dynamics	dynamic	NOUN
m-1057	12	13	,	,	PUNCT
m-1057	12	14	contributing	contribute	VERB
m-1057	12	15	to	to	ADP
m-1057	12	16	the	the	DET
m-1057	12	17	study	study	NOUN
m-1057	12	18	of	of	ADP
m-1057	12	19	semigroup	semigroup	ADJ
m-1057	12	20	methods	method	NOUN
m-1057	12	21	in	in	ADP
m-1057	12	22	fluid	fluid	ADJ
m-1057	12	23	mechanics	mechanic	NOUN
m-1057	12	24	and	and	CCONJ
m-1057	12	25	partial	partial	ADJ
m-1057	12	26	differential	differential	NOUN
m-1057	12	27	equations	equation	NOUN
m-1057	12	28	.	.	PUNCT
m-1057	13	1	the	the	DET
m-1057	13	2	influences	influence	NOUN
m-1057	13	3	of	of	ADP
m-1057	13	4	the	the	DET
m-1057	13	5	sinc	sinc	PROPN
m-1057	13	6	function	function	NOUN
m-1057	13	7	term	term	NOUN
m-1057	13	8	are	be	AUX
m-1057	13	9	analyzed	analyze	VERB
m-1057	13	10	and	and	CCONJ
m-1057	13	11	illustrative	illustrative	ADJ
m-1057	13	12	examples	example	NOUN
m-1057	13	13	are	be	AUX
m-1057	13	14	included	include	VERB
m-1057	13	15	to	to	PART
m-1057	13	16	validate	validate	VERB
m-1057	13	17	the	the	DET
m-1057	13	18	approach	approach	NOUN
m-1057	13	19	and	and	CCONJ
m-1057	13	20	to	to	PART
m-1057	13	21	also	also	ADV
m-1057	13	22	highlight	highlight	VERB
m-1057	13	23	its	its	PRON
m-1057	13	24	applicability	applicability	NOUN
m-1057	13	25	.	.	PUNCT
m-1057	14	1	key	key	ADJ
m-1057	14	2	words	word	NOUN
m-1057	14	3	:	:	PUNCT
m-1057	14	4	boundary	boundary	ADJ
m-1057	14	5	layer	layer	NOUN
m-1057	14	6	equation	equation	NOUN
m-1057	14	7	,	,	PUNCT
m-1057	14	8	banach	banach	NOUN
m-1057	14	9	spaces	space	NOUN
m-1057	14	10	,	,	PUNCT
m-1057	14	11	sinc	sinc	PROPN
m-1057	14	12	function	function	NOUN
m-1057	14	13	,	,	PUNCT
m-1057	14	14	strongly	strongly	ADV
m-1057	14	15	continuous	continuous	ADJ
m-1057	14	16	semigroup	semigroup	NOUN
m-1057	14	17	,	,	PUNCT
m-1057	14	18	mild	mild	ADJ
m-1057	14	19	solution	solution	NOUN
m-1057	14	20	.	.	PUNCT
m-1057	15	1	ijo	ijo	PROPN
m-1057	15	2	journals	journal	NOUN
m-1057	15	3	volume	volume	NOUN
m-1057	15	4	08	08	NUM
m-1057	16	1	|	|	ADV
m-1057	16	2	issue	issue	VERB
m-1057	16	3	04	04	NUM
m-1057	17	1	|	|	CCONJ
m-1057	17	2	april	april	PROPN
m-1057	17	3	2025	2025	NUM
m-1057	17	4	|	|	ADV
m-1057	17	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	PROPN
m-1057	17	6	22	22	NUM
m-1057	17	7	ijo	ijo	PROPN
m-1057	17	8	international	international	PROPN
m-1057	17	9	journal	journal	PROPN
m-1057	17	10	of	of	ADP
m-1057	17	11	mathematics	mathematics	PROPN
m-1057	17	12	(	(	PUNCT
m-1057	17	13	issn	issn	PROPN
m-1057	17	14	:	:	PUNCT
m-1057	17	15	2992	2992	NUM
m-1057	17	16	-	-	SYM
m-1057	17	17	4421	4421	NUM
m-1057	17	18	)	)	PUNCT
m-1057	17	19	otobong	otobong	PROPN
m-1057	17	20	j.	j.	PROPN
m-1057	17	21	tom1	tom1	PROPN
m-1057	18	1	*	*	PUNCT
m-1057	18	2	https://ijojournals.com/	https://ijojournals.com/	PROPN
m-1057	18	3	volume	volume	NOUN
m-1057	18	4	08	08	NUM
m-1057	18	5	||	||	PROPN
m-1057	18	6	issue	issue	NOUN
m-1057	18	7	04	04	NUM
m-1057	18	8	||	||	NOUN
m-1057	18	9	april	april	PROPN
m-1057	18	10	,	,	PUNCT
m-1057	18	11	2025	2025	NUM
m-1057	18	12	||	||	PUNCT
m-1057	19	1	“	"	PUNCT
m-1057	19	2	semigroup	semigroup	ADJ
m-1057	19	3	approach	approach	NOUN
m-1057	19	4	for	for	ADP
m-1057	19	5	the	the	DET
m-1057	19	6	solution	solution	NOUN
m-1057	19	7	of	of	ADP
m-1057	19	8	boundary	boundary	ADJ
m-1057	19	9	layer	layer	NOUN
m-1057	19	10	equation	equation	NOUN
m-1057	19	11	with	with	ADP
m-1057	19	12	sinc	sinc	ADJ
m-1057	19	13	function	function	NOUN
m-1057	19	14	term	term	NOUN
m-1057	19	15	"	"	PUNCT
m-1057	19	16	1	1	NUM
m-1057	19	17	.	.	X
m-1057	19	18	introduction	introduction	NOUN
m-1057	19	19	the	the	DET
m-1057	19	20	boundary	boundary	ADJ
m-1057	19	21	layer	layer	NOUN
m-1057	19	22	equation	equation	NOUN
m-1057	19	23	plays	play	VERB
m-1057	19	24	a	a	DET
m-1057	19	25	crucial	crucial	ADJ
m-1057	19	26	role	role	NOUN
m-1057	19	27	in	in	ADP
m-1057	19	28	fluid	fluid	ADJ
m-1057	19	29	dynamics	dynamic	NOUN
m-1057	19	30	,	,	PUNCT
m-1057	19	31	describing	describe	VERB
m-1057	19	32	the	the	DET
m-1057	19	33	behavior	behavior	NOUN
m-1057	19	34	of	of	ADP
m-1057	19	35	viscous	viscous	ADJ
m-1057	19	36	fluid	fluid	NOUN
m-1057	19	37	flow	flow	NOUN
m-1057	19	38	near	near	ADP
m-1057	19	39	solid	solid	ADJ
m-1057	19	40	surfaces	surface	NOUN
m-1057	19	41	.	.	PUNCT
m-1057	20	1	prandtl	prandtl	NOUN
m-1057	21	1	[	[	X
m-1057	21	2	1	1	NUM
m-1057	21	3	]	]	PUNCT
m-1057	21	4	initiated	initiate	VERB
m-1057	21	5	the	the	DET
m-1057	21	6	boundary	boundary	ADJ
m-1057	21	7	layer	layer	NOUN
m-1057	21	8	theory	theory	NOUN
m-1057	21	9	,	,	PUNCT
m-1057	21	10	significantly	significantly	ADV
m-1057	21	11	advancing	advance	VERB
m-1057	21	12	the	the	DET
m-1057	21	13	study	study	NOUN
m-1057	21	14	of	of	ADP
m-1057	21	15	viscous	viscous	ADJ
m-1057	21	16	flows	flow	NOUN
m-1057	21	17	.	.	PUNCT
m-1057	22	1	this	this	DET
m-1057	22	2	equation	equation	NOUN
m-1057	22	3	has	have	AUX
m-1057	22	4	been	be	AUX
m-1057	22	5	extensively	extensively	ADV
m-1057	22	6	studied	study	VERB
m-1057	22	7	due	due	ADP
m-1057	22	8	to	to	ADP
m-1057	22	9	its	its	PRON
m-1057	22	10	in	in	ADP
m-1057	22	11	aerodynamics	aerodynamic	NOUN
m-1057	22	12	,	,	PUNCT
m-1057	22	13	heat	heat	NOUN
m-1057	22	14	transfer	transfer	NOUN
m-1057	22	15	,	,	PUNCT
m-1057	22	16	and	and	CCONJ
m-1057	22	17	hydrodynamics	hydrodynamic	NOUN
m-1057	22	18	stability	stability	NOUN
m-1057	22	19	.	.	PUNCT
m-1057	23	1	the	the	DET
m-1057	23	2	traditional	traditional	ADJ
m-1057	23	3	method	method	NOUN
m-1057	23	4	for	for	ADP
m-1057	23	5	solving	solve	VERB
m-1057	23	6	the	the	DET
m-1057	23	7	boundary	boundary	ADJ
m-1057	23	8	layer	layer	NOUN
m-1057	23	9	equation	equation	NOUN
m-1057	23	10	include	include	VERB
m-1057	23	11	similarity	similarity	NOUN
m-1057	23	12	transformations	transformation	NOUN
m-1057	23	13	,	,	PUNCT
m-1057	23	14	perturbation	perturbation	NOUN
m-1057	23	15	methods	method	NOUN
m-1057	23	16	,	,	PUNCT
m-1057	23	17	and	and	CCONJ
m-1057	23	18	numerical	numerical	ADJ
m-1057	23	19	simulations	simulation	NOUN
m-1057	23	20	.	.	PUNCT
m-1057	24	1	however	however	ADV
m-1057	24	2	,	,	PUNCT
m-1057	24	3	in	in	ADP
m-1057	24	4	recent	recent	ADJ
m-1057	24	5	years	year	NOUN
m-1057	24	6	,	,	PUNCT
m-1057	24	7	the	the	DET
m-1057	24	8	semigroup	semigroup	PROPN
m-1057	24	9	approach	approach	NOUN
m-1057	24	10	has	have	AUX
m-1057	24	11	emerged	emerge	VERB
m-1057	24	12	as	as	ADP
m-1057	24	13	a	a	DET
m-1057	24	14	powerful	powerful	ADJ
m-1057	24	15	tool	tool	NOUN
m-1057	24	16	for	for	ADP
m-1057	24	17	the	the	DET
m-1057	24	18	existence	existence	NOUN
m-1057	24	19	,	,	PUNCT
m-1057	24	20	uniqueness	uniqueness	NOUN
m-1057	24	21	,	,	PUNCT
m-1057	24	22	and	and	CCONJ
m-1057	24	23	stability	stability	NOUN
m-1057	24	24	of	of	ADP
m-1057	24	25	solutions	solution	NOUN
m-1057	24	26	to	to	ADP
m-1057	24	27	partial	partial	ADJ
m-1057	24	28	differential	differential	ADJ
m-1057	24	29	equations	equation	NOUN
m-1057	24	30	(	(	PUNCT
m-1057	24	31	pdes	pde	NOUN
m-1057	24	32	)	)	PUNCT
m-1057	24	33	.	.	PUNCT
m-1057	25	1	this	this	DET
m-1057	25	2	method	method	NOUN
m-1057	25	3	leverages	leverage	VERB
m-1057	25	4	the	the	DET
m-1057	25	5	properties	property	NOUN
m-1057	25	6	of	of	ADP
m-1057	25	7	operator	operator	NOUN
m-1057	25	8	semigroups	semigroup	NOUN
m-1057	25	9	to	to	PART
m-1057	25	10	study	study	VERB
m-1057	25	11	the	the	DET
m-1057	25	12	time	time	NOUN
m-1057	25	13	evolution	evolution	NOUN
m-1057	25	14	of	of	ADP
m-1057	25	15	solutions	solution	NOUN
m-1057	25	16	in	in	ADP
m-1057	25	17	appropriate	appropriate	ADJ
m-1057	25	18	functional	functional	ADJ
m-1057	25	19	spaces	space	NOUN
m-1057	25	20	.	.	PUNCT
m-1057	26	1	semigroup	semigroup	PROPN
m-1057	26	2	theory	theory	NOUN
m-1057	26	3	provides	provide	VERB
m-1057	26	4	a	a	DET
m-1057	26	5	robust	robust	ADJ
m-1057	26	6	framework	framework	NOUN
m-1057	26	7	for	for	ADP
m-1057	26	8	studying	study	VERB
m-1057	26	9	time	time	NOUN
m-1057	26	10	-	-	PUNCT
m-1057	26	11	dependent	dependent	ADJ
m-1057	26	12	pdes	pde	NOUN
m-1057	26	13	.	.	PUNCT
m-1057	27	1	hille	hille	PROPN
m-1057	27	2	and	and	CCONJ
m-1057	27	3	phillips	phillip	NOUN
m-1057	28	1	[	[	X
m-1057	28	2	2	2	NUM
m-1057	28	3	]	]	PUNCT
m-1057	28	4	laid	lay	VERB
m-1057	28	5	the	the	DET
m-1057	28	6	foundation	foundation	NOUN
m-1057	28	7	of	of	ADP
m-1057	28	8	semigroup	semigroup	PROPN
m-1057	28	9	analysis	analysis	NOUN
m-1057	28	10	,	,	PUNCT
m-1057	28	11	later	later	ADV
m-1057	28	12	extended	extend	VERB
m-1057	28	13	by	by	ADP
m-1057	28	14	pazy	pazy	NOUN
m-1057	29	1	[	[	X
m-1057	29	2	3	3	X
m-1057	29	3	]	]	PUNCT
m-1057	29	4	to	to	PART
m-1057	29	5	cover	cover	VERB
m-1057	29	6	evolutionary	evolutionary	ADJ
m-1057	29	7	equations	equation	NOUN
m-1057	29	8	in	in	ADP
m-1057	29	9	banach	banach	NOUN
m-1057	29	10	spaces	space	NOUN
m-1057	29	11	.	.	PUNCT
m-1057	30	1	the	the	DET
m-1057	30	2	semigroup	semigroup	PROPN
m-1057	30	3	approach	approach	NOUN
m-1057	30	4	has	have	AUX
m-1057	30	5	been	be	AUX
m-1057	30	6	successfully	successfully	ADV
m-1057	30	7	applied	apply	VERB
m-1057	30	8	to	to	ADP
m-1057	30	9	fluid	fluid	ADJ
m-1057	30	10	dynamics	dynamic	NOUN
m-1057	30	11	problems	problem	NOUN
m-1057	30	12	,	,	PUNCT
m-1057	30	13	including	include	VERB
m-1057	30	14	the	the	DET
m-1057	30	15	navier	navier	NOUN
m-1057	30	16	-	-	PUNCT
m-1057	30	17	stokes	stokes	PROPN
m-1057	30	18	equations	equation	NOUN
m-1057	31	1	[	[	X
m-1057	31	2	4]and	4]and	NUM
m-1057	31	3	parabolic	parabolic	ADJ
m-1057	31	4	pdes	pde	NOUN
m-1057	31	5	[	[	X
m-1057	31	6	5	5	NUM
m-1057	31	7	]	]	PUNCT
m-1057	31	8	.	.	PUNCT
m-1057	32	1	henry	henry	PROPN
m-1057	33	1	[	[	X
m-1057	33	2	6	6	NUM
m-1057	33	3	]	]	PUNCT
m-1057	33	4	applied	apply	VERB
m-1057	33	5	semigroup	semigroup	NOUN
m-1057	33	6	method	method	NOUN
m-1057	33	7	for	for	ADP
m-1057	33	8	nonlinear	nonlinear	ADJ
m-1057	33	9	equations	equation	NOUN
m-1057	33	10	where	where	SCONJ
m-1057	33	11	he	he	PRON
m-1057	33	12	showed	show	VERB
m-1057	33	13	that	that	SCONJ
m-1057	33	14	the	the	DET
m-1057	33	15	mild	mild	ADJ
m-1057	33	16	solution	solution	NOUN
m-1057	33	17	method	method	NOUN
m-1057	33	18	could	could	AUX
m-1057	33	19	be	be	AUX
m-1057	33	20	used	use	VERB
m-1057	33	21	to	to	PART
m-1057	33	22	establish	establish	VERB
m-1057	33	23	the	the	DET
m-1057	33	24	well	well	NOUN
m-1057	33	25	-	-	PUNCT
m-1057	33	26	posedness	posedness	NOUN
m-1057	33	27	of	of	ADP
m-1057	33	28	these	these	DET
m-1057	33	29	equations	equation	NOUN
m-1057	33	30	in	in	ADP
m-1057	33	31	various	various	ADJ
m-1057	33	32	function	function	NOUN
m-1057	33	33	spaces	space	NOUN
m-1057	33	34	.	.	PUNCT
m-1057	34	1	recently	recently	ADV
m-1057	34	2	,	,	PUNCT
m-1057	34	3	the	the	DET
m-1057	34	4	work	work	NOUN
m-1057	34	5	of	of	ADP
m-1057	34	6	pruss	pruss	NOUN
m-1057	34	7	[	[	X
m-1057	34	8	7	7	X
m-1057	34	9	]	]	PUNCT
m-1057	34	10	extended	extend	VERB
m-1057	34	11	the	the	DET
m-1057	34	12	semigroup	semigroup	ADJ
m-1057	34	13	approach	approach	NOUN
m-1057	34	14	to	to	PART
m-1057	34	15	treat	treat	VERB
m-1057	34	16	boundary	boundary	ADJ
m-1057	34	17	boundary	boundary	ADJ
m-1057	34	18	value	value	NOUN
m-1057	34	19	problems	problem	NOUN
m-1057	34	20	with	with	ADP
m-1057	34	21	non	non	ADJ
m-1057	34	22	-	-	ADJ
m-1057	34	23	homogeneous	homogeneous	ADJ
m-1057	34	24	conditions	condition	NOUN
m-1057	34	25	,	,	PUNCT
m-1057	34	26	which	which	PRON
m-1057	34	27	arise	arise	VERB
m-1057	34	28	in	in	ADP
m-1057	34	29	practical	practical	ADJ
m-1057	34	30	fluid	fluid	ADJ
m-1057	34	31	dynamics	dynamic	NOUN
m-1057	34	32	applications	application	NOUN
m-1057	34	33	.	.	PUNCT
m-1057	35	1	husssian	husssian	PROPN
m-1057	35	2	and	and	CCONJ
m-1057	35	3	kato	kato	PROPN
m-1057	36	1	[	[	X
m-1057	36	2	8	8	NUM
m-1057	36	3	]	]	PUNCT
m-1057	36	4	explored	explore	VERB
m-1057	36	5	the	the	DET
m-1057	36	6	use	use	NOUN
m-1057	36	7	of	of	ADP
m-1057	36	8	semigroup	semigroup	ADJ
m-1057	36	9	approach	approach	NOUN
m-1057	36	10	to	to	PART
m-1057	36	11	solve	solve	VERB
m-1057	36	12	boundary	boundary	ADJ
m-1057	36	13	layer	layer	NOUN
m-1057	36	14	equation	equation	NOUN
m-1057	36	15	numerically	numerically	ADV
m-1057	36	16	.	.	PUNCT
m-1057	37	1	their	their	PRON
m-1057	37	2	research	research	NOUN
m-1057	37	3	showed	show	VERB
m-1057	37	4	that	that	SCONJ
m-1057	37	5	semigroup	semigroup	NOUN
m-1057	37	6	-	-	PUNCT
m-1057	37	7	based	base	VERB
m-1057	37	8	numerical	numerical	ADJ
m-1057	37	9	methods	method	NOUN
m-1057	37	10	offer	offer	VERB
m-1057	37	11	significant	significant	ADJ
m-1057	37	12	advantages	advantage	NOUN
m-1057	37	13	in	in	ADP
m-1057	37	14	terms	term	NOUN
m-1057	37	15	of	of	ADP
m-1057	37	16	stability	stability	NOUN
m-1057	37	17	compared	compare	VERB
m-1057	37	18	to	to	ADP
m-1057	37	19	other	other	ADJ
m-1057	37	20	methods	method	NOUN
m-1057	37	21	like	like	ADP
m-1057	37	22	finite	finite	ADJ
m-1057	37	23	difference	difference	NOUN
m-1057	37	24	schemes	scheme	NOUN
m-1057	37	25	,	,	PUNCT
m-1057	37	26	particularly	particularly	ADV
m-1057	37	27	for	for	ADP
m-1057	37	28	complex	complex	ADJ
m-1057	37	29	flow	flow	NOUN
m-1057	37	30	configurations	configuration	NOUN
m-1057	37	31	and	and	CCONJ
m-1057	37	32	high	high	ADJ
m-1057	37	33	renolds	renold	NOUN
m-1057	37	34	numbers	number	NOUN
m-1057	37	35	.	.	PUNCT
m-1057	38	1	the	the	DET
m-1057	38	2	sinc	sinc	PROPN
m-1057	38	3	function	function	PROPN
m-1057	38	4	and	and	CCONJ
m-1057	38	5	its	its	PRON
m-1057	38	6	interpolation	interpolation	NOUN
m-1057	38	7	techniques	technique	NOUN
m-1057	38	8	have	have	AUX
m-1057	38	9	been	be	AUX
m-1057	38	10	widely	widely	ADV
m-1057	38	11	studied	study	VERB
m-1057	38	12	in	in	ADP
m-1057	38	13	numerical	numerical	ADJ
m-1057	38	14	analysis	analysis	NOUN
m-1057	38	15	[	[	X
m-1057	38	16	10	10	NUM
m-1057	38	17	,	,	PUNCT
m-1057	38	18	11,12	11,12	NUM
m-1057	38	19	]	]	PUNCT
m-1057	38	20	.	.	PUNCT
m-1057	39	1	the	the	DET
m-1057	39	2	function	function	NOUN
m-1057	39	3	is	be	AUX
m-1057	39	4	well	well	ADV
m-1057	39	5	known	known	ADJ
m-1057	39	6	for	for	ADP
m-1057	39	7	its	its	PRON
m-1057	39	8	applications	application	NOUN
m-1057	39	9	in	in	ADP
m-1057	39	10	signal	signal	NOUN
m-1057	39	11	processing	processing	NOUN
m-1057	39	12	and	and	CCONJ
m-1057	39	13	numerical	numerical	ADJ
m-1057	39	14	analysis	analysis	NOUN
m-1057	39	15	,	,	PUNCT
m-1057	39	16	introducing	introduce	VERB
m-1057	39	17	oscillatory	oscillatory	ADJ
m-1057	39	18	behavior	behavior	NOUN
m-1057	39	19	into	into	ADP
m-1057	39	20	the	the	DET
m-1057	39	21	equation	equation	NOUN
m-1057	39	22	,	,	PUNCT
m-1057	39	23	which	which	PRON
m-1057	39	24	affects	affect	VERB
m-1057	39	25	the	the	DET
m-1057	39	26	solution	solution	NOUN
m-1057	39	27	properties	property	NOUN
m-1057	39	28	.	.	PUNCT
m-1057	40	1	also	also	ADV
m-1057	40	2	,	,	PUNCT
m-1057	40	3	the	the	DET
m-1057	40	4	function	function	NOUN
m-1057	40	5	’s	’s	PART
m-1057	40	6	unique	unique	ADJ
m-1057	40	7	properties	property	NOUN
m-1057	40	8	such	such	ADJ
m-1057	40	9	as	as	ADP
m-1057	40	10	band	band	NOUN
m-1057	40	11	-	-	PUNCT
m-1057	40	12	limited	limit	VERB
m-1057	40	13	representation	representation	NOUN
m-1057	40	14	and	and	CCONJ
m-1057	40	15	rapid	rapid	ADJ
m-1057	40	16	decay	decay	NOUN
m-1057	40	17	,	,	PUNCT
m-1057	40	18	makes	make	VERB
m-1057	40	19	it	it	PRON
m-1057	40	20	useful	useful	ADJ
m-1057	40	21	for	for	ADP
m-1057	40	22	solving	solve	VERB
m-1057	40	23	differential	differential	ADJ
m-1057	40	24	equations	equation	NOUN
m-1057	40	25	.	.	PUNCT
m-1057	41	1	lund	lund	PROPN
m-1057	41	2	and	and	CCONJ
m-1057	41	3	bowers	bower	NOUN
m-1057	42	1	[	[	X
m-1057	42	2	10	10	NUM
m-1057	42	3	]	]	PUNCT
m-1057	42	4	have	have	AUX
m-1057	42	5	explored	explore	VERB
m-1057	42	6	sinc	sinc	ADJ
m-1057	42	7	-	-	PUNCT
m-1057	42	8	base	base	NOUN
m-1057	42	9	methods	method	NOUN
m-1057	42	10	for	for	ADP
m-1057	42	11	approximating	approximate	VERB
m-1057	42	12	pde	pde	NOUN
m-1057	42	13	solutions	solution	NOUN
m-1057	42	14	,	,	PUNCT
m-1057	42	15	but	but	CCONJ
m-1057	42	16	their	their	PRON
m-1057	42	17	interaction	interaction	NOUN
m-1057	42	18	with	with	ADP
m-1057	42	19	semigroup	semigroup	ADJ
m-1057	42	20	methods	method	NOUN
m-1057	42	21	remains	remain	VERB
m-1057	42	22	an	an	DET
m-1057	42	23	open	open	ADJ
m-1057	42	24	area	area	NOUN
m-1057	42	25	of	of	ADP
m-1057	42	26	research	research	NOUN
m-1057	42	27	.	.	PUNCT
m-1057	43	1	this	this	DET
m-1057	43	2	study	study	NOUN
m-1057	43	3	aims	aim	VERB
m-1057	43	4	to	to	PART
m-1057	43	5	bridge	bridge	VERB
m-1057	43	6	this	this	DET
m-1057	43	7	gap	gap	NOUN
m-1057	43	8	by	by	ADP
m-1057	43	9	developing	develop	VERB
m-1057	43	10	a	a	DET
m-1057	43	11	semigroup	semigroup	ADJ
m-1057	43	12	-	-	PUNCT
m-1057	43	13	theoretic	theoretic	ADJ
m-1057	43	14	approach	approach	NOUN
m-1057	43	15	for	for	ADP
m-1057	43	16	analyzing	analyze	VERB
m-1057	43	17	the	the	DET
m-1057	43	18	well	well	NOUN
m-1057	43	19	-	-	PUNCT
m-1057	43	20	posedness	posedness	NOUN
m-1057	43	21	of	of	ADP
m-1057	43	22	boundary	boundary	ADJ
m-1057	43	23	layer	layer	NOUN
m-1057	43	24	equation	equation	NOUN
m-1057	43	25	with	with	ADP
m-1057	43	26	sinc	sinc	ADJ
m-1057	43	27	function	function	NOUN
m-1057	43	28	term	term	NOUN
m-1057	43	29	.	.	PUNCT
m-1057	44	1	the	the	DET
m-1057	44	2	integration	integration	NOUN
m-1057	44	3	of	of	ADP
m-1057	44	4	sinc	sinc	PROPN
m-1057	44	5	function	function	NOUN
m-1057	44	6	term	term	NOUN
m-1057	44	7	in	in	ADP
m-1057	44	8	the	the	DET
m-1057	44	9	equation	equation	NOUN
m-1057	44	10	introduces	introduce	VERB
m-1057	44	11	additional	additional	ADJ
m-1057	44	12	complexities	complexity	NOUN
m-1057	44	13	,	,	PUNCT
m-1057	44	14	requiring	require	VERB
m-1057	44	15	additional	additional	ADJ
m-1057	44	16	mathematical	mathematical	ADJ
m-1057	44	17	techniques	technique	NOUN
m-1057	44	18	for	for	ADP
m-1057	44	19	analysis	analysis	NOUN
m-1057	44	20	and	and	CCONJ
m-1057	44	21	solution	solution	NOUN
m-1057	44	22	.	.	PUNCT
m-1057	45	1	our	our	PRON
m-1057	45	2	approach	approach	NOUN
m-1057	45	3	focuses	focus	VERB
m-1057	45	4	on	on	ADP
m-1057	45	5	establishing	establish	VERB
m-1057	45	6	well	well	ADJ
m-1057	45	7	-	-	PUNCT
m-1057	45	8	posedess	posedess	NOUN
m-1057	45	9	of	of	ADP
m-1057	45	10	the	the	DET
m-1057	45	11	equation	equation	NOUN
m-1057	45	12	with	with	ADP
m-1057	45	13	the	the	DET
m-1057	45	14	inclusion	inclusion	NOUN
m-1057	45	15	of	of	ADP
m-1057	45	16	the	the	DET
m-1057	45	17	sinc	sinc	PROPN
m-1057	45	18	function	function	NOUN
m-1057	45	19	term	term	NOUN
m-1057	45	20	.	.	PUNCT
m-1057	46	1	ijo	ijo	PROPN
m-1057	46	2	journals	journal	NOUN
m-1057	46	3	volume	volume	NOUN
m-1057	46	4	08	08	NUM
m-1057	47	1	|	|	ADV
m-1057	47	2	issue	issue	VERB
m-1057	47	3	04	04	NUM
m-1057	48	1	|	|	CCONJ
m-1057	48	2	april	april	PROPN
m-1057	48	3	2025	2025	NUM
m-1057	48	4	|	|	ADV
m-1057	48	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1057	48	6	23	23	NUM
m-1057	48	7	ijo	ijo	PROPN
m-1057	48	8	international	international	ADJ
m-1057	48	9	journal	journal	PROPN
m-1057	48	10	of	of	ADP
m-1057	48	11	mathematics	mathematics	PROPN
m-1057	48	12	(	(	PUNCT
m-1057	48	13	issn	issn	PROPN
m-1057	48	14	:	:	PUNCT
m-1057	48	15	2992	2992	NUM
m-1057	48	16	-	-	SYM
m-1057	48	17	4421	4421	NUM
m-1057	48	18	)	)	PUNCT
m-1057	48	19	otobong	otobong	PROPN
m-1057	48	20	j.	j.	PROPN
m-1057	48	21	tom1	tom1	PROPN
m-1057	49	1	*	*	PUNCT
m-1057	49	2	https://ijojournals.com/	https://ijojournals.com/	PROPN
m-1057	49	3	volume	volume	NOUN
m-1057	49	4	08	08	NUM
m-1057	49	5	||	||	PROPN
m-1057	49	6	issue	issue	NOUN
m-1057	49	7	04	04	NUM
m-1057	49	8	||	||	NOUN
m-1057	49	9	april	april	PROPN
m-1057	49	10	,	,	PUNCT
m-1057	49	11	2025	2025	NUM
m-1057	49	12	||	||	PUNCT
m-1057	50	1	“	"	PUNCT
m-1057	50	2	semigroup	semigroup	ADJ
m-1057	50	3	approach	approach	NOUN
m-1057	50	4	for	for	ADP
m-1057	50	5	the	the	DET
m-1057	50	6	solution	solution	NOUN
m-1057	50	7	of	of	ADP
m-1057	50	8	boundary	boundary	ADJ
m-1057	50	9	layer	layer	NOUN
m-1057	50	10	equation	equation	NOUN
m-1057	50	11	with	with	ADP
m-1057	50	12	sinc	sinc	ADJ
m-1057	50	13	function	function	NOUN
m-1057	50	14	term	term	NOUN
m-1057	50	15	"	"	PUNCT
m-1057	50	16	2	2	NUM
m-1057	50	17	.	.	PUNCT
m-1057	50	18	preliminaries	preliminary	NOUN
m-1057	50	19	in	in	ADP
m-1057	50	20	this	this	DET
m-1057	50	21	section	section	NOUN
m-1057	50	22	,	,	PUNCT
m-1057	50	23	we	we	PRON
m-1057	50	24	introduce	introduce	VERB
m-1057	50	25	the	the	DET
m-1057	50	26	fundamental	fundamental	ADJ
m-1057	50	27	mathematical	mathematical	ADJ
m-1057	50	28	concepts	concept	NOUN
m-1057	50	29	and	and	CCONJ
m-1057	50	30	notations	notation	NOUN
m-1057	50	31	required	require	VERB
m-1057	50	32	for	for	ADP
m-1057	50	33	our	our	PRON
m-1057	50	34	analysis	analysis	NOUN
m-1057	50	35	of	of	ADP
m-1057	50	36	the	the	DET
m-1057	50	37	boundary	boundary	ADJ
m-1057	50	38	layer	layer	NOUN
m-1057	50	39	equation	equation	NOUN
m-1057	50	40	with	with	ADP
m-1057	50	41	a	a	DET
m-1057	50	42	sinc	sinc	ADJ
m-1057	50	43	function	function	NOUN
m-1057	50	44	term	term	NOUN
m-1057	50	45	using	use	VERB
m-1057	50	46	the	the	DET
m-1057	50	47	semigroup	semigroup	PROPN
m-1057	50	48	approach	approach	NOUN
m-1057	50	49	.	.	PUNCT
m-1057	51	1	2.1	2.1	NUM
m-1057	51	2	.	.	PUNCT
m-1057	51	3	functional	functional	ADJ
m-1057	51	4	space	space	NOUN
m-1057	51	5	and	and	CCONJ
m-1057	51	6	operators	operator	NOUN
m-1057	51	7	let	let	VERB
m-1057	51	8	x	x	PART
m-1057	51	9	be	be	AUX
m-1057	51	10	a	a	DET
m-1057	51	11	banach	banach	NOUN
m-1057	51	12	space	space	NOUN
m-1057	51	13	,	,	PUNCT
m-1057	51	14	and	and	CCONJ
m-1057	51	15	consider	consider	VERB
m-1057	51	16	a	a	DET
m-1057	51	17	differential	differential	ADJ
m-1057	51	18	operator	operator	NOUN
m-1057	51	19	a	a	PRON
m-1057	51	20	on	on	ADP
m-1057	51	21	a	a	DET
m-1057	51	22	dense	dense	ADJ
m-1057	51	23	subspace	subspace	NOUN
m-1057	51	24			NOUN
m-1057	51	25	d	d	VERB
m-1057	51	26	a	a	DET
m-1057	51	27	x	x	X
m-1057	51	28	.	.	PUNCT
m-1057	52	1	we	we	PRON
m-1057	52	2	work	work	VERB
m-1057	52	3	within	within	ADP
m-1057	52	4	the	the	DET
m-1057	52	5	frame	frame	NOUN
m-1057	52	6	work	work	NOUN
m-1057	52	7	of	of	ADP
m-1057	52	8	semigroup	semigroup	PROPN
m-1057	52	9	theory	theory	NOUN
m-1057	52	10	,	,	PUNCT
m-1057	52	11	requiring	require	VERB
m-1057	52	12	the	the	DET
m-1057	52	13	following	follow	VERB
m-1057	52	14	definitions	definition	NOUN
m-1057	52	15	:	:	PUNCT
m-1057	52	16	2.2	2.2	NUM
m-1057	52	17	.	.	PUNCT
m-1057	53	1	normed	normed	PROPN
m-1057	53	2	and	and	CCONJ
m-1057	53	3	banach	banach	NOUN
m-1057	53	4	spaces	space	VERB
m-1057	53	5	:	:	PUNCT
m-1057	53	6	a	a	DET
m-1057	53	7	normed	normed	ADJ
m-1057	53	8	space	space	NOUN
m-1057	53	9			NOUN
m-1057	53	10	,x	,x	PUNCT
m-1057	53	11			PROPN
m-1057	53	12	is	be	AUX
m-1057	53	13	a	a	DET
m-1057	53	14	vector	vector	NOUN
m-1057	53	15	space	space	NOUN
m-1057	53	16	if	if	SCONJ
m-1057	53	17	it	it	PRON
m-1057	53	18	is	be	AUX
m-1057	53	19	complete	complete	ADJ
m-1057	53	20	with	with	ADP
m-1057	53	21	respect	respect	NOUN
m-1057	53	22	to	to	ADP
m-1057	53	23	this	this	DET
m-1057	53	24	norm	norm	NOUN
m-1057	53	25	.	.	PUNCT
m-1057	54	1	a	a	DET
m-1057	54	2	normed	normed	ADJ
m-1057	54	3	space	space	NOUN
m-1057	54	4			NOUN
m-1057	54	5	,x	,x	PUNCT
m-1057	54	6			PROPN
m-1057	54	7	is	be	AUX
m-1057	54	8	called	call	VERB
m-1057	54	9	banach	banach	NOUN
m-1057	54	10	space	space	NOUN
m-1057	54	11	if	if	SCONJ
m-1057	54	12	every	every	DET
m-1057	54	13	cauchy	cauchy	ADJ
m-1057	54	14	sequence	sequence	NOUN
m-1057	54	15	in	in	ADP
m-1057	54	16			NOUN
m-1057	54	17	,x	,x	PUNCT
m-1057	54	18			ADJ
m-1057	54	19	converges	converge	NOUN
m-1057	54	20	.	.	PUNCT
m-1057	55	1	2.3	2.3	NUM
m-1057	55	2	.	.	PUNCT
m-1057	56	1	hilbert	hilbert	NOUN
m-1057	56	2	space	space	NOUN
m-1057	56	3	:	:	PUNCT
m-1057	56	4	a	a	DET
m-1057	56	5	special	special	ADJ
m-1057	56	6	case	case	NOUN
m-1057	56	7	of	of	ADP
m-1057	56	8	banach	banach	NOUN
m-1057	56	9	space	space	NOUN
m-1057	56	10	where	where	SCONJ
m-1057	56	11	the	the	DET
m-1057	56	12	norm	norm	NOUN
m-1057	56	13	is	be	AUX
m-1057	56	14	induced	induce	VERB
m-1057	56	15	by	by	ADP
m-1057	56	16	an	an	DET
m-1057	56	17	inner	inner	ADJ
m-1057	56	18	product	product	NOUN
m-1057	56	19	,	,	PUNCT
m-1057	56	20			PROPN
m-1057	56	21			PROPN
m-1057	56	22	.	.	PUNCT
m-1057	57	1	we	we	PRON
m-1057	57	2	primarily	primarily	ADV
m-1057	57	3	consider	consider	VERB
m-1057	57	4	function	function	NOUN
m-1057	57	5	spaces	space	NOUN
m-1057	57	6	such	such	ADJ
m-1057	57	7	as	as	ADP
m-1057	57	8			NOUN
m-1057	57	9	pl	pl	PROPN
m-1057	57	10	ω	ω	NUM
m-1057	57	11	and	and	CCONJ
m-1057	57	12	sobolevspaces	sobolevspace	NOUN
m-1057	57	13			PROPN
m-1057	57	14	kh	kh	PROPN
m-1057	57	15	ω	ω	NOUN
m-1057	57	16	,	,	PUNCT
m-1057	57	17	which	which	PRON
m-1057	57	18	are	be	AUX
m-1057	57	19	crucial	crucial	ADJ
m-1057	57	20	in	in	ADP
m-1057	57	21	studying	study	VERB
m-1057	57	22	pdes	pde	NOUN
m-1057	57	23	[	[	PUNCT
m-1057	57	24	5	5	NUM
m-1057	57	25	,	,	PUNCT
m-1057	57	26	13	13	NUM
m-1057	57	27	,	,	PUNCT
m-1057	57	28	14	14	NUM
m-1057	57	29	,	,	PUNCT
m-1057	57	30	21	21	NUM
m-1057	57	31	]	]	PUNCT
m-1057	57	32	.	.	PUNCT
m-1057	58	1	3	3	X
m-1057	58	2	.	.	NOUN
m-1057	58	3	boundary	boundary	ADJ
m-1057	58	4	layer	layer	NOUN
m-1057	58	5	equation	equation	NOUN
m-1057	58	6	with	with	ADP
m-1057	58	7	sinc	sinc	ADJ
m-1057	58	8	term	term	NOUN
m-1057	58	9	the	the	DET
m-1057	58	10	general	general	ADJ
m-1057	58	11	form	form	NOUN
m-1057	58	12	of	of	ADP
m-1057	58	13	the	the	DET
m-1057	58	14	boundary	boundary	ADJ
m-1057	58	15	layer	layer	NOUN
m-1057	58	16	equation	equation	NOUN
m-1057	58	17	with	with	ADP
m-1057	58	18	a	a	DET
m-1057	58	19	sinc	sinc	ADJ
m-1057	58	20	function	function	NOUN
m-1057	58	21	term	term	NOUN
m-1057	58	22	can	can	AUX
m-1057	58	23	be	be	AUX
m-1057	58	24	written	write	VERB
m-1057	58	25	as	as	ADP
m-1057	58	26	:	:	PUNCT
m-1057	58	27			NOUN
m-1057	58	28			PROPN
m-1057	58	29			NOUN
m-1057	58	30			PUNCT
m-1057	58	31			PROPN
m-1057	58	32			PROPN
m-1057	58	33	,	,	PUNCT
m-1057	58	34	,	,	PUNCT
m-1057	58	35	1	1	NUM
m-1057	58	36	u	u	NOUN
m-1057	58	37	au	au	PROPN
m-1057	58	38	f	f	PROPN
m-1057	58	39	x	x	X
m-1057	58	40	t	t	PROPN
m-1057	58	41	s	s	X
m-1057	58	42	x	x	X
m-1057	58	43	t	t	PROPN
m-1057	58	44	t	t	PROPN
m-1057	58	45			PROPN
m-1057	58	46			PROPN
m-1057	58	47			NUM
m-1057	58	48			ADV
m-1057	58	49			ADJ
m-1057	58	50	were	be	AUX
m-1057	58	51	:	:	PUNCT
m-1057	58	52			X
m-1057	58	53			NOUN
m-1057	58	54	,u	,u	NOUN
m-1057	59	1	x	x	PUNCT
m-1057	59	2	t	t	PROPN
m-1057	59	3	represents	represent	VERB
m-1057	59	4	the	the	DET
m-1057	59	5	velocity	velocity	NOUN
m-1057	59	6	field	field	NOUN
m-1057	59	7	,	,	PUNCT
m-1057	59	8			PRON
m-1057	59	9	a	a	PRON
m-1057	59	10	is	be	AUX
m-1057	59	11	a	a	DET
m-1057	59	12	differential	differential	ADJ
m-1057	59	13	operator	operator	NOUN
m-1057	59	14	capturing	capture	VERB
m-1057	59	15	the	the	DET
m-1057	59	16	viscous	viscous	ADJ
m-1057	59	17	effects	effect	NOUN
m-1057	59	18	,	,	PUNCT
m-1057	59	19			PRON
m-1057	59	20			PROPN
m-1057	59	21	,f	,f	VERB
m-1057	59	22	x	x	X
m-1057	59	23	t	t	PROPN
m-1057	59	24	is	be	AUX
m-1057	59	25	an	an	DET
m-1057	59	26	external	external	ADJ
m-1057	59	27	forcing	force	VERB
m-1057	59	28	term	term	NOUN
m-1057	59	29	,	,	PUNCT
m-1057	59	30	ijo	ijo	PROPN
m-1057	59	31	journals	journal	NOUN
m-1057	59	32	volume	volume	NOUN
m-1057	59	33	08	08	NUM
m-1057	60	1	|	|	ADV
m-1057	60	2	issue	issue	VERB
m-1057	60	3	04	04	NUM
m-1057	61	1	|	|	CCONJ
m-1057	61	2	april	april	PROPN
m-1057	61	3	2025	2025	NUM
m-1057	61	4	|	|	ADV
m-1057	61	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1057	61	6	24	24	NUM
m-1057	61	7	ijo	ijo	PROPN
m-1057	61	8	international	international	PROPN
m-1057	61	9	journal	journal	PROPN
m-1057	61	10	of	of	ADP
m-1057	61	11	mathematics	mathematics	PROPN
m-1057	61	12	(	(	PUNCT
m-1057	61	13	issn	issn	PROPN
m-1057	61	14	:	:	PUNCT
m-1057	61	15	2992	2992	NUM
m-1057	61	16	-	-	SYM
m-1057	61	17	4421	4421	NUM
m-1057	61	18	)	)	PUNCT
m-1057	62	1	otobong	otobong	PROPN
m-1057	62	2	j.	j.	PROPN
m-1057	62	3	tom1	tom1	PROPN
m-1057	62	4	*	*	PUNCT
m-1057	63	1	https://ijojournals.com/	https://ijojournals.com/	PROPN
m-1057	63	2	volume	volume	NOUN
m-1057	63	3	08	08	NUM
m-1057	63	4	||	||	PROPN
m-1057	63	5	issue	issue	NOUN
m-1057	63	6	04	04	NUM
m-1057	63	7	||	||	NOUN
m-1057	63	8	april	april	PROPN
m-1057	63	9	,	,	PUNCT
m-1057	63	10	2025	2025	NUM
m-1057	63	11	||	||	PUNCT
m-1057	64	1	“	"	PUNCT
m-1057	64	2	semigroup	semigroup	ADJ
m-1057	64	3	approach	approach	NOUN
m-1057	64	4	for	for	ADP
m-1057	64	5	the	the	DET
m-1057	64	6	solution	solution	NOUN
m-1057	64	7	of	of	ADP
m-1057	64	8	boundary	boundary	ADJ
m-1057	64	9	layer	layer	NOUN
m-1057	64	10	equation	equation	NOUN
m-1057	64	11	with	with	ADP
m-1057	64	12	sinc	sinc	ADJ
m-1057	64	13	function	function	NOUN
m-1057	64	14	term	term	NOUN
m-1057	64	15	"	"	PUNCT
m-1057	64	16			NOUN
m-1057	64	17			NOUN
m-1057	64	18	,s	,s	X
m-1057	64	19	x	x	PUNCT
m-1057	65	1	t	t	NOUN
m-1057	65	2	is	be	AUX
m-1057	65	3	a	a	DET
m-1057	65	4	sinc	sinc	PROPN
m-1057	65	5	function	function	NOUN
m-1057	65	6	-	-	PUNCT
m-1057	65	7	modulated	modulate	VERB
m-1057	65	8	term	term	NOUN
m-1057	65	9	affecting	affect	VERB
m-1057	65	10	the	the	DET
m-1057	65	11	solution	solution	NOUN
m-1057	65	12	structure	structure	NOUN
m-1057	65	13	.	.	PUNCT
m-1057	66	1	the	the	DET
m-1057	66	2	boundary	boundary	ADJ
m-1057	66	3	conditions	condition	NOUN
m-1057	66	4	and	and	CCONJ
m-1057	66	5	initial	initial	ADJ
m-1057	66	6	conditions	condition	NOUN
m-1057	66	7	depend	depend	VERB
m-1057	66	8	on	on	ADP
m-1057	66	9	the	the	DET
m-1057	66	10	physical	physical	ADJ
m-1057	66	11	context	context	NOUN
m-1057	66	12	.	.	PUNCT
m-1057	67	1	4	4	X
m-1057	67	2	.	.	X
m-1057	67	3	semigroup	semigroup	PROPN
m-1057	67	4	theory	theory	NOUN
m-1057	67	5	let	let	VERB
m-1057	67	6	x	x	PRON
m-1057	67	7	be	be	AUX
m-1057	67	8	a	a	DET
m-1057	67	9	banach	banach	NOUN
m-1057	67	10	space	space	NOUN
m-1057	67	11	,	,	PUNCT
m-1057	67	12	and	and	CCONJ
m-1057	67	13	let	let	VERB
m-1057	67	14			NOUN
m-1057	67	15	:a	:a	VERB
m-1057	68	1	d	d	NOUN
m-1057	68	2	a	a	X
m-1057	68	3	x	x	INTJ
m-1057	68	4	x	x	AUX
m-1057	68	5			PROPN
m-1057	68	6	be	be	AUX
m-1057	68	7	a	a	DET
m-1057	68	8	densely	densely	ADV
m-1057	68	9	defined	define	VERB
m-1057	68	10	,	,	PUNCT
m-1057	68	11	closed	close	VERB
m-1057	68	12	linear	linear	ADJ
m-1057	68	13	operator	operator	NOUN
m-1057	68	14	.	.	PUNCT
m-1057	69	1	a	a	DET
m-1057	69	2	strongly	strongly	ADV
m-1057	69	3	continuous	continuous	ADJ
m-1057	69	4	semigroup	semigroup	NOUN
m-1057	69	5	(	(	PUNCT
m-1057	69	6	or	or	CCONJ
m-1057	69	7	0c	0c	NUM
m-1057	69	8	semigroup	semigroup	PROPN
m-1057	69	9	,	,	PUNCT
m-1057	69	10	or	or	CCONJ
m-1057	69	11	a	a	DET
m-1057	69	12	semigroup	semigroup	NOUN
m-1057	69	13	of	of	ADP
m-1057	69	14	class	class	NOUN
m-1057	69	15	0c	0c	NOUN
m-1057	69	16	)	)	PUNCT
m-1057	69	17			NOUN
m-1057	70	1			PUNCT
m-1057	70	2	0	0	NUM
m-1057	70	3	t	t	PROPN
m-1057	70	4	t	t	PROPN
m-1057	70	5	t	t	PROPN
m-1057	70	6			NUM
m-1057	70	7	on	on	ADP
m-1057	70	8	the	the	DET
m-1057	70	9	banach	banach	NOUN
m-1057	70	10	space	space	NOUN
m-1057	70	11	x	x	PUNCT
m-1057	70	12	is	be	AUX
m-1057	70	13	a	a	DET
m-1057	70	14	family	family	NOUN
m-1057	70	15	of	of	ADP
m-1057	70	16	bounded	bounded	ADJ
m-1057	70	17	linear	linear	PROPN
m-1057	70	18	operators	operator	NOUN
m-1057	70	19	such	such	ADJ
m-1057	70	20	that	that	DET
m-1057	70	21			NOUN
m-1057	70	22			SYM
m-1057	70	23			NOUN
m-1057	70	24			SYM
m-1057	70	25			NOUN
m-1057	70	26			SYM
m-1057	70	27			NOUN
m-1057	70	28			SYM
m-1057	70	29			NOUN
m-1057	70	30			SYM
m-1057	70	31			NOUN
m-1057	70	32			SYM
m-1057	70	33			NOUN
m-1057	70	34			PROPN
m-1057	70	35	0	0	SYM
m-1057	70	36	0	0	NUM
m-1057	70	37	the	the	DET
m-1057	70	38	identity	identity	NOUN
m-1057	70	39	operator	operator	NOUN
m-1057	70	40	for	for	ADP
m-1057	70	41	all	all	PRON
m-1057	70	42	,	,	PUNCT
m-1057	70	43	0	0	NUM
m-1057	70	44	2	2	NUM
m-1057	70	45	lim	lim	NOUN
m-1057	70	46	for	for	ADP
m-1057	70	47	all	all	DET
m-1057	70	48	t	t	NOUN
m-1057	70	49	t	t	NOUN
m-1057	71	1	i	i	PRON
m-1057	71	2	t	t	PROPN
m-1057	71	3	s	s	PROPN
m-1057	71	4	t	t	PROPN
m-1057	71	5	t	t	PROPN
m-1057	71	6	s	s	PROPN
m-1057	71	7	t	t	PROPN
m-1057	71	8	t	t	PROPN
m-1057	71	9	t	t	PROPN
m-1057	71	10	s	s	PROPN
m-1057	71	11	t	t	PROPN
m-1057	71	12	t	t	NOUN
m-1057	71	13	x	x	PUNCT
m-1057	71	14	x	x	PUNCT
m-1057	71	15	x	x	PUNCT
m-1057	71	16	x	x	NOUN
m-1057	71	17			NOUN
m-1057	71	18			ADV
m-1057	72	1			PRON
m-1057	73	1			NUM
m-1057	73	2			NOUN
m-1057	73	3			PROPN
m-1057	73	4			PROPN
m-1057	73	5			NUM
m-1057	73	6			NOUN
m-1057	73	7			NOUN
m-1057	73	8			PROPN
m-1057	74	1	the	the	DET
m-1057	74	2	generator	generator	NOUN
m-1057	74	3	of	of	ADP
m-1057	74	4	the	the	DET
m-1057	74	5	semigroup	semigroup	NOUN
m-1057	74	6	,	,	PUNCT
m-1057	74	7	denoted	denote	VERB
m-1057	74	8	by	by	ADP
m-1057	74	9	a	a	PRON
m-1057	74	10	,	,	PUNCT
m-1057	74	11	is	be	AUX
m-1057	74	12	defined	define	VERB
m-1057	74	13	as	as	ADP
m-1057	74	14			NOUN
m-1057	74	15			PROPN
m-1057	74	16	0	0	NUM
m-1057	75	1	lim	lim	PROPN
m-1057	75	2	,	,	PUNCT
m-1057	75	3	t	t	PROPN
m-1057	75	4	t	t	PROPN
m-1057	75	5	t	t	NOUN
m-1057	75	6	x	x	PUNCT
m-1057	75	7	x	x	PUNCT
m-1057	75	8	ax	ax	NOUN
m-1057	75	9	t	t	NUM
m-1057	75	10			PROPN
m-1057	75	11			NOUN
m-1057	75	12	whenever	whenever	SCONJ
m-1057	75	13	the	the	DET
m-1057	75	14	limit	limit	NOUN
m-1057	75	15	exists	exist	VERB
m-1057	75	16	.	.	PUNCT
m-1057	76	1	the	the	DET
m-1057	76	2	well	well	ADV
m-1057	76	3	-	-	PUNCT
m-1057	76	4	posedness	posedness	NOUN
m-1057	76	5	of	of	ADP
m-1057	76	6	the	the	DET
m-1057	76	7	equation	equation	NOUN
m-1057	76	8	depends	depend	VERB
m-1057	76	9	on	on	ADP
m-1057	76	10	whether	whether	SCONJ
m-1057	76	11	a	a	PRON
m-1057	76	12	generates	generate	VERB
m-1057	76	13	a	a	DET
m-1057	76	14	semigroup	semigroup	NOUN
m-1057	76	15	on	on	ADP
m-1057	76	16	x	x	PUNCT
m-1057	77	1	[	[	X
m-1057	77	2	3	3	NUM
m-1057	77	3	,	,	PUNCT
m-1057	77	4	18	18	NUM
m-1057	77	5	,	,	PUNCT
m-1057	77	6	19	19	NUM
m-1057	77	7	,	,	PUNCT
m-1057	77	8	22	22	NUM
m-1057	77	9	,	,	PUNCT
m-1057	77	10	24	24	NUM
m-1057	77	11	]	]	PUNCT
m-1057	77	12	.	.	PUNCT
m-1057	78	1	4.1	4.1	NUM
m-1057	78	2	.	.	PUNCT
m-1057	78	3	spectral	spectral	ADJ
m-1057	78	4	properties	property	NOUN
m-1057	78	5	of	of	ADP
m-1057	78	6	the	the	DET
m-1057	78	7	operators	operator	NOUN
m-1057	78	8	:	:	PUNCT
m-1057	78	9	the	the	DET
m-1057	78	10	spectrum	spectrum	NOUN
m-1057	78	11	of	of	ADP
m-1057	78	12	a	a	DET
m-1057	78	13	denoted	denote	VERB
m-1057	78	14	by	by	ADP
m-1057	78	15			NOUN
m-1057	78	16	a	a	NOUN
m-1057	78	17	,	,	PUNCT
m-1057	78	18	plays	play	VERB
m-1057	78	19	a	a	DET
m-1057	78	20	crucial	crucial	ADJ
m-1057	78	21	role	role	NOUN
m-1057	78	22	in	in	ADP
m-1057	78	23	determining	determine	VERB
m-1057	78	24	the	the	DET
m-1057	78	25	stability	stability	NOUN
m-1057	78	26	of	of	ADP
m-1057	78	27	the	the	DET
m-1057	78	28	solutions	solution	NOUN
m-1057	78	29	.	.	PUNCT
m-1057	79	1	the	the	DET
m-1057	79	2	resolvent	resolvent	ADJ
m-1057	79	3	operator	operator	NOUN
m-1057	79	4			NOUN
m-1057	79	5			SYM
m-1057	79	6			NOUN
m-1057	79	7			PROPN
m-1057	79	8	1	1	NUM
m-1057	79	9	,	,	PUNCT
m-1057	79	10	r	r	NOUN
m-1057	79	11	a	a	PRON
m-1057	79	12	i	i	PROPN
m-1057	79	13	a	a	PROPN
m-1057	79	14			ADJ
m-1057	79	15			PROPN
m-1057	79	16			PROPN
m-1057	79	17			PROPN
m-1057	79	18	helps	help	VERB
m-1057	79	19	analyze	analyze	VERB
m-1057	79	20	whether	whether	SCONJ
m-1057	79	21	a	a	DET
m-1057	79	22	an	an	DET
m-1057	79	23	exponentially	exponentially	ADV
m-1057	79	24	stable	stable	ADJ
m-1057	79	25	semigroup	semigroup	NOUN
m-1057	79	26	.	.	PUNCT
m-1057	80	1	4.2	4.2	NUM
m-1057	80	2	.	.	PUNCT
m-1057	80	3	sinc	sinc	PROPN
m-1057	80	4	function	function	PROPN
m-1057	80	5	and	and	CCONJ
m-1057	80	6	its	its	PRON
m-1057	80	7	properties	property	NOUN
m-1057	80	8	the	the	DET
m-1057	80	9	sinc	sinc	PROPN
m-1057	80	10	function	function	NOUN
m-1057	80	11	is	be	AUX
m-1057	80	12	define	define	VERB
m-1057	80	13	as	as	ADP
m-1057	80	14			NOUN
m-1057	81	1			PROPN
m-1057	81	2			NOUN
m-1057	81	3			SYM
m-1057	81	4			NOUN
m-1057	81	5			SYM
m-1057	81	6			NOUN
m-1057	81	7			PROPN
m-1057	81	8	sin	sin	NOUN
m-1057	81	9	sinc	sinc	PROPN
m-1057	81	10	,	,	PUNCT
m-1057	81	11	0	0	NUM
m-1057	81	12	,	,	PUNCT
m-1057	81	13	sinc	sinc	NOUN
m-1057	81	14	0	0	NUM
m-1057	81	15	1	1	NUM
m-1057	81	16	3	3	NUM
m-1057	81	17	x	x	SYM
m-1057	81	18	x	x	SYM
m-1057	81	19	x	x	PUNCT
m-1057	81	20	x	x	SYM
m-1057	81	21			PROPN
m-1057	81	22			PROPN
m-1057	81	23			PROPN
m-1057	81	24			NOUN
m-1057	81	25			PROPN
m-1057	81	26	ijo	ijo	PROPN
m-1057	81	27	journals	journal	NOUN
m-1057	81	28	volume	volume	NOUN
m-1057	81	29	08	08	NUM
m-1057	82	1	|	|	ADV
m-1057	82	2	issue	issue	VERB
m-1057	82	3	04	04	NUM
m-1057	83	1	|	|	CCONJ
m-1057	83	2	april	april	PROPN
m-1057	83	3	2025	2025	NUM
m-1057	83	4	|	|	ADV
m-1057	83	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1057	83	6	25	25	NUM
m-1057	83	7	ijo	ijo	PROPN
m-1057	83	8	international	international	ADJ
m-1057	83	9	journal	journal	PROPN
m-1057	83	10	of	of	ADP
m-1057	83	11	mathematics	mathematics	PROPN
m-1057	83	12	(	(	PUNCT
m-1057	83	13	issn	issn	PROPN
m-1057	83	14	:	:	PUNCT
m-1057	83	15	2992	2992	NUM
m-1057	83	16	-	-	SYM
m-1057	83	17	4421	4421	NUM
m-1057	83	18	)	)	PUNCT
m-1057	83	19	otobong	otobong	PROPN
m-1057	83	20	j.	j.	PROPN
m-1057	83	21	tom1	tom1	PROPN
m-1057	84	1	*	*	PUNCT
m-1057	84	2	https://ijojournals.com/	https://ijojournals.com/	PROPN
m-1057	84	3	volume	volume	NOUN
m-1057	84	4	08	08	NUM
m-1057	84	5	||	||	PROPN
m-1057	84	6	issue	issue	NOUN
m-1057	84	7	04	04	NUM
m-1057	84	8	||	||	NOUN
m-1057	84	9	april	april	PROPN
m-1057	84	10	,	,	PUNCT
m-1057	84	11	2025	2025	NUM
m-1057	84	12	||	||	PUNCT
m-1057	85	1	“	"	PUNCT
m-1057	85	2	semigroup	semigroup	ADJ
m-1057	85	3	approach	approach	NOUN
m-1057	85	4	for	for	ADP
m-1057	85	5	the	the	DET
m-1057	85	6	solution	solution	NOUN
m-1057	85	7	of	of	ADP
m-1057	85	8	boundary	boundary	ADJ
m-1057	85	9	layer	layer	NOUN
m-1057	85	10	equation	equation	NOUN
m-1057	85	11	with	with	ADP
m-1057	85	12	sinc	sinc	ADJ
m-1057	85	13	function	function	NOUN
m-1057	85	14	term	term	NOUN
m-1057	85	15	"	"	PUNCT
m-1057	85	16	it	it	PRON
m-1057	85	17	has	have	VERB
m-1057	85	18	useful	useful	ADJ
m-1057	85	19	properties	property	NOUN
m-1057	85	20	such	such	ADJ
m-1057	85	21	as	as	ADP
m-1057	85	22	rapid	rapid	ADJ
m-1057	85	23	decay	decay	NOUN
m-1057	85	24	and	and	CCONJ
m-1057	85	25	interpolation	interpolation	NOUN
m-1057	85	26	capabilities	capability	NOUN
m-1057	85	27	,	,	PUNCT
m-1057	85	28	making	make	VERB
m-1057	85	29	it	it	PRON
m-1057	85	30	a	a	DET
m-1057	85	31	valuable	valuable	ADJ
m-1057	85	32	tool	tool	NOUN
m-1057	85	33	in	in	ADP
m-1057	85	34	numerical	numerical	ADJ
m-1057	85	35	method	method	NOUN
m-1057	85	36	and	and	CCONJ
m-1057	85	37	spectral	spectral	ADJ
m-1057	85	38	analysis	analysis	NOUN
m-1057	85	39	[	[	X
m-1057	85	40	12	12	NUM
m-1057	85	41	]	]	PUNCT
m-1057	85	42	.	.	PUNCT
m-1057	86	1	4.3	4.3	NUM
m-1057	86	2	.	.	PUNCT
m-1057	86	3	mild	mild	ADJ
m-1057	86	4	solution	solution	NOUN
m-1057	86	5	through	through	ADP
m-1057	86	6	semigroup	semigroup	PROPN
m-1057	86	7	approach	approach	NOUN
m-1057	86	8	:	:	PUNCT
m-1057	86	9	a	a	DET
m-1057	86	10	mild	mild	ADJ
m-1057	86	11	solution	solution	NOUN
m-1057	86	12	to	to	ADP
m-1057	86	13	a	a	DET
m-1057	86	14	differential	differential	ADJ
m-1057	86	15	equation	equation	NOUN
m-1057	86	16	is	be	AUX
m-1057	86	17	a	a	DET
m-1057	86	18	solution	solution	NOUN
m-1057	86	19	that	that	PRON
m-1057	86	20	is	be	AUX
m-1057	86	21	defined	define	VERB
m-1057	86	22	through	through	ADP
m-1057	86	23	an	an	DET
m-1057	86	24	integral	integral	ADJ
m-1057	86	25	equation	equation	NOUN
m-1057	86	26	involving	involve	VERB
m-1057	86	27	a	a	DET
m-1057	86	28	semigroup	semigroup	NOUN
m-1057	86	29	.	.	PUNCT
m-1057	87	1	for	for	ADP
m-1057	87	2	an	an	DET
m-1057	87	3	evolution	evolution	NOUN
m-1057	87	4	equation	equation	NOUN
m-1057	87	5	of	of	ADP
m-1057	87	6	the	the	DET
m-1057	87	7	form	form	NOUN
m-1057	87	8			PROPN
m-1057	87	9			PROPN
m-1057	87	10	,	,	PUNCT
m-1057	87	11	du	du	PROPN
m-1057	87	12	au	au	PROPN
m-1057	87	13	f	f	PROPN
m-1057	87	14	t	t	PROPN
m-1057	87	15	dt	dt	PROPN
m-1057	87	16			PROPN
m-1057	87	17			NUM
m-1057	87	18	the	the	DET
m-1057	87	19	mild	mild	ADJ
m-1057	87	20	solution	solution	NOUN
m-1057	87	21	is	be	AUX
m-1057	87	22	obtain	obtain	VERB
m-1057	87	23	using	use	VERB
m-1057	87	24	duhamel	duhamel	PROPN
m-1057	87	25	’s	’s	PART
m-1057	87	26	formula	formula	NOUN
m-1057	87	27	and	and	CCONJ
m-1057	87	28	is	be	AUX
m-1057	87	29	given	give	VERB
m-1057	87	30	by	by	ADP
m-1057	87	31			NOUN
m-1057	88	1			PROPN
m-1057	88	2			NOUN
m-1057	88	3			SYM
m-1057	88	4			NOUN
m-1057	88	5			SYM
m-1057	88	6			NOUN
m-1057	88	7			SYM
m-1057	88	8			NOUN
m-1057	88	9	0	0	NOUN
m-1057	88	10	0	0	NUM
m-1057	88	11	4	4	NUM
m-1057	88	12	t	t	NOUN
m-1057	88	13	u	u	NOUN
m-1057	88	14	t	t	PROPN
m-1057	88	15	t	t	PROPN
m-1057	88	16	t	t	PROPN
m-1057	88	17	u	u	PROPN
m-1057	88	18	t	t	PROPN
m-1057	88	19	t	t	PROPN
m-1057	88	20	s	s	X
m-1057	88	21	f	f	PROPN
m-1057	88	22	s	s	PROPN
m-1057	88	23	ds	ds	PROPN
m-1057	88	24			ADJ
m-1057	88	25			NOUN
m-1057	88	26	where	where	SCONJ
m-1057	88	27			NOUN
m-1057	88	28	t	t	PROPN
m-1057	88	29	t	t	PROPN
m-1057	88	30	is	be	AUX
m-1057	88	31	the	the	DET
m-1057	88	32	semigroup	semigroup	NOUN
m-1057	88	33	generated	generate	VERB
m-1057	88	34	by	by	ADP
m-1057	88	35	the	the	DET
m-1057	88	36	operator	operator	NOUN
m-1057	88	37	a	a	PRON
m-1057	88	38	and	and	CCONJ
m-1057	88	39	0u	0u	ADJ
m-1057	88	40	is	be	AUX
m-1057	88	41	the	the	DET
m-1057	88	42	initial	initial	ADJ
m-1057	88	43	condition.the	condition.the	DET
m-1057	88	44	term	term	NOUN
m-1057	88	45	mild	mild	NOUN
m-1057	88	46	is	be	AUX
m-1057	88	47	used	use	VERB
m-1057	88	48	because	because	SCONJ
m-1057	88	49	the	the	DET
m-1057	88	50	solution	solution	NOUN
m-1057	88	51	is	be	AUX
m-1057	88	52	often	often	ADV
m-1057	88	53	less	less	ADV
m-1057	88	54	regular	regular	ADJ
m-1057	88	55	than	than	ADP
m-1057	88	56	classical	classical	ADJ
m-1057	88	57	solutions	solution	NOUN
m-1057	88	58	but	but	CCONJ
m-1057	88	59	still	still	ADV
m-1057	88	60	provides	provide	VERB
m-1057	88	61	valuable	valuable	ADJ
m-1057	88	62	information	information	NOUN
m-1057	88	63	.	.	PUNCT
m-1057	89	1	also	also	ADV
m-1057	89	2	,	,	PUNCT
m-1057	89	3	if	if	SCONJ
m-1057	89	4			NOUN
m-1057	89	5	t	t	PROPN
m-1057	89	6	t	t	PROPN
m-1057	89	7	is	be	AUX
m-1057	89	8	strongly	strongly	ADV
m-1057	89	9	continuous	continuous	ADJ
m-1057	89	10	semigroup	semigroup	NOUN
m-1057	89	11	generated	generate	VERB
m-1057	89	12	by	by	ADP
m-1057	89	13	a	a	PRON
m-1057	89	14	,	,	PUNCT
m-1057	89	15	then	then	ADV
m-1057	89	16	the	the	DET
m-1057	89	17	mild	mild	ADJ
m-1057	89	18	solution	solution	NOUN
m-1057	89	19	can	can	AUX
m-1057	89	20	be	be	AUX
m-1057	89	21	expressed	express	VERB
m-1057	89	22	as	as	ADP
m-1057	89	23			NOUN
m-1057	89	24			PROPN
m-1057	89	25			NOUN
m-1057	89	26			SYM
m-1057	89	27			NOUN
m-1057	89	28			SYM
m-1057	89	29			NOUN
m-1057	89	30			PUNCT
m-1057	89	31			NOUN
m-1057	90	1			NOUN
m-1057	91	1			PUNCT
m-1057	91	2			NOUN
m-1057	91	3	0	0	NOUN
m-1057	91	4	0	0	NUM
m-1057	91	5	5	5	NUM
m-1057	91	6	t	t	NOUN
m-1057	91	7	u	u	NOUN
m-1057	91	8	t	t	PROPN
m-1057	91	9	t	t	PROPN
m-1057	91	10	t	t	PROPN
m-1057	91	11	u	u	PROPN
m-1057	91	12	t	t	PROPN
m-1057	91	13	t	t	PROPN
m-1057	91	14	s	s	X
m-1057	91	15	f	f	PROPN
m-1057	91	16	s	s	X
m-1057	91	17	s	s	X
m-1057	91	18	s	s	X
m-1057	91	19	ds	ds	NOUN
m-1057	91	20			ADJ
m-1057	91	21			NOUN
m-1057	91	22			NUM
m-1057	91	23	equation	equation	NOUN
m-1057	91	24			PROPN
m-1057	91	25	5	5	PROPN
m-1057	91	26	provides	provide	VERB
m-1057	91	27	insight	insight	NOUN
m-1057	91	28	into	into	ADP
m-1057	91	29	the	the	DET
m-1057	91	30	existence	existence	NOUN
m-1057	91	31	,	,	PUNCT
m-1057	91	32	uniqueness	uniqueness	NOUN
m-1057	91	33	,	,	PUNCT
m-1057	91	34	and	and	CCONJ
m-1057	91	35	stability	stability	NOUN
m-1057	91	36	of	of	ADP
m-1057	91	37	the	the	DET
m-1057	91	38	solution	solution	NOUN
m-1057	91	39	,	,	PUNCT
m-1057	91	40	see	see	VERB
m-1057	91	41	[	[	X
m-1057	91	42	23	23	NUM
m-1057	91	43	,	,	PUNCT
m-1057	91	44	24	24	NUM
m-1057	91	45	]	]	PUNCT
m-1057	91	46	.	.	PUNCT
m-1057	92	1	4.4	4.4	NUM
m-1057	92	2	.	.	PUNCT
m-1057	93	1	mathematical	mathematical	ADJ
m-1057	93	2	formulation	formulation	NOUN
m-1057	93	3	of	of	ADP
m-1057	93	4	the	the	DET
m-1057	93	5	problem	problem	NOUN
m-1057	93	6	we	we	PRON
m-1057	93	7	begin	begin	VERB
m-1057	93	8	by	by	ADP
m-1057	93	9	representing	represent	VERB
m-1057	93	10	the	the	DET
m-1057	93	11	boundary	boundary	ADJ
m-1057	93	12	layer	layer	NOUN
m-1057	93	13	equation	equation	NOUN
m-1057	93	14	as	as	SCONJ
m-1057	93	15	follows	follow	VERB
m-1057	93	16			NOUN
m-1057	93	17			SYM
m-1057	93	18			NOUN
m-1057	93	19			PUNCT
m-1057	93	20			PROPN
m-1057	93	21			PROPN
m-1057	93	22	,	,	PUNCT
m-1057	93	23	,	,	PUNCT
m-1057	93	24	,	,	PUNCT
m-1057	93	25	,	,	PUNCT
m-1057	93	26	0	0	NUM
m-1057	93	27	6	6	NUM
m-1057	93	28	u	u	NOUN
m-1057	93	29	au	au	PROPN
m-1057	93	30	f	f	PROPN
m-1057	93	31	x	x	X
m-1057	93	32	t	t	PROPN
m-1057	93	33	s	s	X
m-1057	93	34	x	x	X
m-1057	93	35	t	t	X
m-1057	93	36	x	x	SYM
m-1057	93	37	t	t	PROPN
m-1057	93	38	t	t	PROPN
m-1057	93	39			PROPN
m-1057	93	40			PROPN
m-1057	93	41			PROPN
m-1057	93	42			PUNCT
m-1057	93	43			PROPN
m-1057	93	44			NUM
m-1057	93	45			PROPN
m-1057	93	46	ω	ω	NUM
m-1057	93	47	where	where	SCONJ
m-1057	93	48			NOUN
m-1057	93	49	,u	,u	NOUN
m-1057	93	50	x	x	PUNCT
m-1057	94	1	t	t	PROPN
m-1057	94	2	represent	represent	VERB
m-1057	94	3	the	the	DET
m-1057	94	4	unknown	unknown	ADJ
m-1057	94	5	function	function	NOUN
m-1057	94	6	(	(	PUNCT
m-1057	94	7	the	the	DET
m-1057	94	8	state	state	NOUN
m-1057	94	9	of	of	ADP
m-1057	94	10	the	the	DET
m-1057	94	11	system	system	NOUN
m-1057	94	12	)	)	PUNCT
m-1057	94	13	at	at	ADP
m-1057	94	14	time	time	NOUN
m-1057	94	15	t	t	NOUN
m-1057	94	16	and	and	CCONJ
m-1057	94	17	position	position	NOUN
m-1057	94	18	x	x	SYM
m-1057	94	19	,	,	PUNCT
m-1057	94	20	a	a	PRON
m-1057	94	21	is	be	AUX
m-1057	94	22	a	a	DET
m-1057	94	23	differential	differential	ADJ
m-1057	94	24	operator	operator	NOUN
m-1057	94	25	(	(	PUNCT
m-1057	94	26	often	often	ADV
m-1057	94	27	related	relate	VERB
m-1057	94	28	to	to	ADP
m-1057	94	29	the	the	DET
m-1057	94	30	laplacian	laplacian	ADJ
m-1057	94	31	or	or	CCONJ
m-1057	94	32	similar	similar	ADJ
m-1057	94	33	operator	operator	NOUN
m-1057	94	34	that	that	PRON
m-1057	94	35	models	model	VERB
m-1057	94	36	ijo	ijo	PROPN
m-1057	94	37	journals	journal	NOUN
m-1057	94	38	volume	volume	NOUN
m-1057	94	39	08	08	NUM
m-1057	95	1	|	|	ADV
m-1057	95	2	issue	issue	VERB
m-1057	95	3	04	04	NUM
m-1057	96	1	|	|	CCONJ
m-1057	96	2	april	april	PROPN
m-1057	96	3	2025	2025	NUM
m-1057	96	4	|	|	ADV
m-1057	96	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1057	96	6	26	26	NUM
m-1057	96	7	ijo	ijo	PROPN
m-1057	96	8	international	international	PROPN
m-1057	96	9	journal	journal	PROPN
m-1057	96	10	of	of	ADP
m-1057	96	11	mathematics	mathematics	PROPN
m-1057	96	12	(	(	PUNCT
m-1057	96	13	issn	issn	PROPN
m-1057	96	14	:	:	PUNCT
m-1057	96	15	2992	2992	NUM
m-1057	96	16	-	-	SYM
m-1057	96	17	4421	4421	NUM
m-1057	96	18	)	)	PUNCT
m-1057	96	19	otobong	otobong	PROPN
m-1057	96	20	j.	j.	PROPN
m-1057	96	21	tom1	tom1	PROPN
m-1057	97	1	*	*	PUNCT
m-1057	97	2	https://ijojournals.com/	https://ijojournals.com/	PROPN
m-1057	97	3	volume	volume	NOUN
m-1057	97	4	08	08	NUM
m-1057	97	5	||	||	PROPN
m-1057	97	6	issue	issue	NOUN
m-1057	97	7	04	04	NUM
m-1057	97	8	||	||	NOUN
m-1057	97	9	april	april	PROPN
m-1057	97	10	,	,	PUNCT
m-1057	97	11	2025	2025	NUM
m-1057	97	12	||	||	PUNCT
m-1057	98	1	“	"	PUNCT
m-1057	98	2	semigroup	semigroup	ADJ
m-1057	98	3	approach	approach	NOUN
m-1057	98	4	for	for	ADP
m-1057	98	5	the	the	DET
m-1057	98	6	solution	solution	NOUN
m-1057	98	7	of	of	ADP
m-1057	98	8	boundary	boundary	ADJ
m-1057	98	9	layer	layer	NOUN
m-1057	98	10	equation	equation	NOUN
m-1057	98	11	with	with	ADP
m-1057	98	12	sinc	sinc	ADJ
m-1057	98	13	function	function	NOUN
m-1057	98	14	term	term	NOUN
m-1057	98	15	"	"	PUNCT
m-1057	98	16	diffusion	diffusion	NOUN
m-1057	98	17	or	or	CCONJ
m-1057	98	18	advection	advection	NOUN
m-1057	98	19	in	in	ADP
m-1057	98	20	fluid	fluid	ADJ
m-1057	98	21	dynamics	dynamic	NOUN
m-1057	98	22	)	)	PUNCT
m-1057	98	23	,	,	PUNCT
m-1057	98	24			PROPN
m-1057	98	25	,f	,f	NOUN
m-1057	98	26	x	x	PUNCT
m-1057	98	27	t	t	NOUN
m-1057	98	28	and	and	CCONJ
m-1057	98	29			PROPN
m-1057	98	30	,s	,s	X
m-1057	98	31	x	x	PUNCT
m-1057	99	1	t	t	NOUN
m-1057	99	2	are	be	AUX
m-1057	99	3	external	external	ADJ
m-1057	99	4	forcing	force	VERB
m-1057	99	5	terms	term	NOUN
m-1057	99	6	.	.	PUNCT
m-1057	100	1	the	the	DET
m-1057	100	2	initial	initial	ADJ
m-1057	100	3	condition	condition	NOUN
m-1057	100	4	for	for	ADP
m-1057	100	5	this	this	DET
m-1057	100	6	equation	equation	NOUN
m-1057	100	7	is	be	AUX
m-1057	100	8	:	:	PUNCT
m-1057	100	9			PROPN
m-1057	100	10			SYM
m-1057	100	11			NOUN
m-1057	100	12	0,0	0,0	NOUN
m-1057	100	13	,	,	PUNCT
m-1057	100	14	,	,	PUNCT
m-1057	100	15	u	u	NOUN
m-1057	100	16	x	x	X
m-1057	100	17	u	u	NOUN
m-1057	100	18	x	x	X
m-1057	100	19	x	x	PUNCT
m-1057	100	20	ω	ω	PROPN
m-1057	100	21	where	where	SCONJ
m-1057	100	22			PROPN
m-1057	100	23	0u	0u	PROPN
m-1057	100	24	x	x	PUNCT
m-1057	100	25	represents	represent	VERB
m-1057	100	26	the	the	DET
m-1057	100	27	state	state	NOUN
m-1057	100	28	of	of	ADP
m-1057	100	29	the	the	DET
m-1057	100	30	system	system	NOUN
m-1057	100	31	at	at	ADP
m-1057	100	32	time	time	NOUN
m-1057	100	33	0	0	NUM
m-1057	100	34	t	t	NOUN
m-1057	100	35			NUM
m-1057	100	36	.	.	PUNCT
m-1057	101	1	5	5	X
m-1057	101	2	.	.	X
m-1057	101	3	semigroup	semigroup	PROPN
m-1057	101	4	representation	representation	NOUN
m-1057	101	5	and	and	CCONJ
m-1057	101	6	solution	solution	NOUN
m-1057	101	7	method	method	VERB
m-1057	101	8	the	the	DET
m-1057	101	9	solution	solution	NOUN
m-1057	101	10	is	be	AUX
m-1057	101	11	sought	seek	VERB
m-1057	101	12	in	in	ADP
m-1057	101	13	the	the	DET
m-1057	101	14	layout	layout	NOUN
m-1057	101	15	of	of	ADP
m-1057	101	16	semigroup	semigroup	PROPN
m-1057	101	17	theory	theory	NOUN
m-1057	101	18	,	,	PUNCT
m-1057	101	19	which	which	PRON
m-1057	101	20	provides	provide	VERB
m-1057	101	21	a	a	DET
m-1057	101	22	powerful	powerful	ADJ
m-1057	101	23	method	method	NOUN
m-1057	101	24	to	to	PART
m-1057	101	25	deal	deal	VERB
m-1057	101	26	with	with	ADP
m-1057	101	27	evolution	evolution	NOUN
m-1057	101	28	equations	equation	NOUN
m-1057	101	29	.	.	PUNCT
m-1057	102	1	we	we	PRON
m-1057	102	2	assume	assume	VERB
m-1057	102	3	that	that	SCONJ
m-1057	102	4	a	a	PRON
m-1057	102	5	generates	generate	VERB
m-1057	102	6	a	a	DET
m-1057	102	7	strongly	strongly	ADV
m-1057	102	8	continuous	continuous	ADJ
m-1057	102	9	semigroup	semigroup	ADJ
m-1057	102	10			NOUN
m-1057	102	11			PROPN
m-1057	102	12	0	0	NUM
m-1057	102	13	t	t	PROPN
m-1057	102	14	t	t	PROPN
m-1057	102	15	t	t	PROPN
m-1057	102	16			NUM
m-1057	102	17	on	on	ADP
m-1057	102	18	a	a	DET
m-1057	102	19	banachspace	banachspace	NOUN
m-1057	102	20	x	x	PUNCT
m-1057	102	21	.	.	PUNCT
m-1057	103	1	the	the	DET
m-1057	103	2	semigroup	semigroup	PROPN
m-1057	103	3	approach	approach	NOUN
m-1057	103	4	allows	allow	VERB
m-1057	103	5	us	we	PRON
m-1057	103	6	to	to	PART
m-1057	103	7	express	express	VERB
m-1057	103	8	the	the	DET
m-1057	103	9	solution	solution	NOUN
m-1057	103	10	in	in	ADP
m-1057	103	11	the	the	DET
m-1057	103	12	form	form	NOUN
m-1057	103	13	of	of	ADP
m-1057	103	14	equation	equation	NOUN
m-1057	103	15			PROPN
m-1057	103	16	5	5	PROPN
m-1057	103	17	.	.	PUNCT
m-1057	104	1	here	here	ADV
m-1057	104	2	,	,	PUNCT
m-1057	104	3	the	the	DET
m-1057	104	4	term	term	NOUN
m-1057	104	5			NOUN
m-1057	104	6			PROPN
m-1057	104	7	0	0	NUM
m-1057	104	8	t	t	NOUN
m-1057	104	9	t	t	NOUN
m-1057	104	10	u	u	NOUN
m-1057	104	11	represents	represent	VERB
m-1057	104	12	the	the	DET
m-1057	104	13	evolution	evolution	NOUN
m-1057	104	14	of	of	ADP
m-1057	104	15	initial	initial	ADJ
m-1057	104	16	condition	condition	NOUN
m-1057	104	17	,	,	PUNCT
m-1057	104	18	and	and	CCONJ
m-1057	104	19	the	the	DET
m-1057	104	20	integral	integral	ADJ
m-1057	104	21	term	term	NOUN
m-1057	104	22	capture	capture	VERB
m-1057	104	23	the	the	DET
m-1057	104	24	influence	influence	NOUN
m-1057	104	25	of	of	ADP
m-1057	104	26	the	the	DET
m-1057	104	27	forcing	force	VERB
m-1057	104	28			NOUN
m-1057	104	29			PUNCT
m-1057	104	30			PROPN
m-1057	104	31			PROPN
m-1057	104	32	,	,	PUNCT
m-1057	104	33	,	,	PUNCT
m-1057	104	34	f	f	PROPN
m-1057	104	35	x	x	X
m-1057	104	36	t	t	PROPN
m-1057	104	37	s	s	PART
m-1057	104	38	x	x	SYM
m-1057	104	39	t	t	ADJ
m-1057	104	40	over	over	ADP
m-1057	104	41	time	time	NOUN
m-1057	104	42	,	,	PUNCT
m-1057	104	43	see	see	VERB
m-1057	104	44	[	[	X
m-1057	104	45	18	18	NUM
m-1057	104	46	,	,	PUNCT
m-1057	104	47	24	24	NUM
m-1057	104	48	]	]	PUNCT
m-1057	104	49	.	.	PUNCT
m-1057	105	1	5.1	5.1	NUM
m-1057	105	2	.	.	PUNCT
m-1057	106	1	well	well	ADJ
m-1057	106	2	-	-	PUNCT
m-1057	106	3	posedness	posedness	NOUN
m-1057	106	4	of	of	ADP
m-1057	106	5	the	the	DET
m-1057	106	6	problem	problem	NOUN
m-1057	106	7	to	to	PART
m-1057	106	8	ensure	ensure	VERB
m-1057	106	9	the	the	DET
m-1057	106	10	problem	problem	NOUN
m-1057	106	11	is	be	AUX
m-1057	106	12	well	well	ADV
m-1057	106	13	-	-	PUNCT
m-1057	106	14	posed	pose	VERB
m-1057	106	15	,	,	PUNCT
m-1057	106	16	we	we	PRON
m-1057	106	17	need	need	VERB
m-1057	106	18	to	to	PART
m-1057	106	19	establish	establish	VERB
m-1057	106	20	that	that	SCONJ
m-1057	106	21	equation	equation	NOUN
m-1057	106	22			PROPN
m-1057	106	23	5	5	PROPN
m-1057	106	24	exists	exist	VERB
m-1057	106	25	,	,	PUNCT
m-1057	106	26	is	be	AUX
m-1057	106	27	unique	unique	ADJ
m-1057	106	28	,	,	PUNCT
m-1057	106	29	and	and	CCONJ
m-1057	106	30	depends	depend	VERB
m-1057	106	31	continuously	continuously	ADV
m-1057	106	32	on	on	ADP
m-1057	106	33	the	the	DET
m-1057	106	34	initial	initial	ADJ
m-1057	106	35	conditions	condition	NOUN
m-1057	106	36	.	.	PUNCT
m-1057	107	1	this	this	PRON
m-1057	107	2	is	be	AUX
m-1057	107	3	done	do	VERB
m-1057	107	4	through	through	ADP
m-1057	107	5	the	the	DET
m-1057	107	6	following	follow	VERB
m-1057	107	7	steps	step	NOUN
m-1057	107	8	:	:	PUNCT
m-1057	107	9			DET
m-1057	107	10	existence	existence	NOUN
m-1057	107	11	:	:	PUNCT
m-1057	107	12	by	by	ADP
m-1057	107	13	the	the	DET
m-1057	107	14	properties	property	NOUN
m-1057	107	15	of	of	ADP
m-1057	107	16	semigroups	semigroup	NOUN
m-1057	107	17	,	,	PUNCT
m-1057	107	18	the	the	DET
m-1057	107	19	integral	integral	ADJ
m-1057	107	20	equation	equation	NOUN
m-1057	107	21	for	for	ADP
m-1057	107	22			NOUN
m-1057	107	23	u	u	PROPN
m-1057	107	24	t	t	PROPN
m-1057	107	25	is	be	AUX
m-1057	107	26	welldefined	welldefine	VERB
m-1057	107	27	and	and	CCONJ
m-1057	107	28	yields	yield	VERB
m-1057	107	29	a	a	DET
m-1057	107	30	solution	solution	NOUN
m-1057	107	31	.	.	PUNCT
m-1057	108	1	the	the	DET
m-1057	108	2	regularity	regularity	NOUN
m-1057	108	3	of	of	ADP
m-1057	108	4			NOUN
m-1057	108	5	,f	,f	NOUN
m-1057	108	6	x	x	PUNCT
m-1057	108	7	t	t	NOUN
m-1057	108	8	and	and	CCONJ
m-1057	108	9			PROPN
m-1057	108	10	,s	,s	X
m-1057	108	11	x	x	PUNCT
m-1057	108	12	t	t	NOUN
m-1057	108	13	ensure	ensure	VERB
m-1057	108	14	that	that	SCONJ
m-1057	108	15	the	the	DET
m-1057	108	16	integral	integral	NOUN
m-1057	108	17	is	be	AUX
m-1057	108	18	finite	finite	ADJ
m-1057	108	19	and	and	CCONJ
m-1057	108	20	the	the	DET
m-1057	108	21	solution	solution	NOUN
m-1057	108	22	ie	ie	ADP
m-1057	108	23	well	well	ADV
m-1057	108	24	-	-	PUNCT
m-1057	108	25	behaved	behave	VERB
m-1057	108	26	.	.	PUNCT
m-1057	109	1			PRON
m-1057	109	2	uniqueness	uniqueness	NOUN
m-1057	109	3	:	:	PUNCT
m-1057	109	4	if	if	SCONJ
m-1057	109	5	two	two	NUM
m-1057	109	6	solutions	solution	NOUN
m-1057	109	7			NOUN
m-1057	109	8	1u	1u	PUNCT
m-1057	109	9	t	t	PROPN
m-1057	109	10	and	and	CCONJ
m-1057	109	11			PROPN
m-1057	109	12	2u	2u	NOUN
m-1057	109	13	t	t	NOUN
m-1057	109	14	exist	exist	VERB
m-1057	109	15	,	,	PUNCT
m-1057	109	16	we	we	PRON
m-1057	109	17	show	show	VERB
m-1057	109	18	that	that	SCONJ
m-1057	109	19			NOUN
m-1057	109	20			SYM
m-1057	109	21			NOUN
m-1057	109	22	1	1	NOUN
m-1057	109	23	2u	2u	PROPN
m-1057	109	24	t	t	PROPN
m-1057	109	25	u	u	X
m-1057	109	26	t	t	PROPN
m-1057	109	27	by	by	ADP
m-1057	109	28	employing	employ	VERB
m-1057	109	29	the	the	DET
m-1057	109	30	banach	banach	ADV
m-1057	109	31	fixed	fix	VERB
m-1057	109	32	-	-	PUNCT
m-1057	109	33	point	point	NOUN
m-1057	109	34	theorem	theorem	NOUN
m-1057	109	35	[	[	X
m-1057	109	36	3	3	NUM
m-1057	109	37	,	,	PUNCT
m-1057	109	38	25	25	NUM
m-1057	109	39	]	]	PUNCT
m-1057	109	40	,	,	PUNCT
m-1057	109	41	this	this	DET
m-1057	109	42	relying	rely	VERB
m-1057	109	43	on	on	ADP
m-1057	109	44	the	the	DET
m-1057	109	45	fact	fact	NOUN
m-1057	109	46	that	that	SCONJ
m-1057	109	47	the	the	DET
m-1057	109	48	operator	operator	NOUN
m-1057	109	49			NOUN
m-1057	109	50	t	t	PROPN
m-1057	109	51	t	t	PROPN
m-1057	109	52	is	be	AUX
m-1057	109	53	strongly	strongly	ADV
m-1057	109	54	continuous	continuous	ADJ
m-1057	109	55	and	and	CCONJ
m-1057	109	56	the	the	DET
m-1057	109	57	forcing	force	VERB
m-1057	109	58	terms	term	NOUN
m-1057	109	59			NOUN
m-1057	109	60	,f	,f	NOUN
m-1057	109	61	x	x	PUNCT
m-1057	109	62	t	t	NOUN
m-1057	109	63	and	and	CCONJ
m-1057	109	64			PROPN
m-1057	109	65	,s	,s	X
m-1057	109	66	x	x	PUNCT
m-1057	109	67	t	t	NOUN
m-1057	109	68	are	be	AUX
m-1057	109	69	assume	assume	VERB
m-1057	109	70	be	be	AUX
m-1057	109	71	identical	identical	ADJ
m-1057	109	72	for	for	ADP
m-1057	109	73	both	both	DET
m-1057	109	74	solutions	solution	NOUN
m-1057	109	75	.	.	PUNCT
m-1057	110	1			X
m-1057	110	2	continuous	continuous	ADJ
m-1057	110	3	dependence	dependence	NOUN
m-1057	110	4	:	:	PUNCT
m-1057	110	5	since	since	SCONJ
m-1057	110	6	the	the	DET
m-1057	110	7	solution	solution	NOUN
m-1057	110	8	depends	depend	VERB
m-1057	110	9	continuously	continuously	ADV
m-1057	110	10	on	on	ADP
m-1057	110	11	the	the	DET
m-1057	110	12	initial	initial	ADJ
m-1057	110	13	condition	condition	NOUN
m-1057	110	14			NOUN
m-1057	111	1	0u	0u	PROPN
m-1057	111	2	x	x	INTJ
m-1057	111	3	,	,	PUNCT
m-1057	111	4	small	small	ADJ
m-1057	111	5	changes	change	NOUN
m-1057	111	6	in	in	ADP
m-1057	111	7	the	the	DET
m-1057	111	8	initial	initial	ADJ
m-1057	111	9	condition	condition	NOUN
m-1057	111	10	lead	lead	NOUN
m-1057	111	11	to	to	ADP
m-1057	111	12	small	small	ADJ
m-1057	111	13	changes	change	NOUN
m-1057	111	14	in	in	ADP
m-1057	111	15	the	the	DET
m-1057	111	16	solution	solution	NOUN
m-1057	111	17	,	,	PUNCT
m-1057	111	18	which	which	PRON
m-1057	111	19	is	be	AUX
m-1057	111	20	a	a	DET
m-1057	111	21	key	key	ADJ
m-1057	111	22	property	property	NOUN
m-1057	111	23	in	in	ADP
m-1057	111	24	proving	prove	VERB
m-1057	111	25	stability	stability	NOUN
m-1057	111	26	.	.	PUNCT
m-1057	112	1	5.2	5.2	NUM
m-1057	112	2	.	.	PUNCT
m-1057	112	3	influence	influence	NOUN
m-1057	112	4	of	of	ADP
m-1057	112	5	the	the	DET
m-1057	112	6	sincfunctionterm	sincfunctionterm	NOUN
m-1057	112	7	a	a	DET
m-1057	112	8	distinctive	distinctive	ADJ
m-1057	112	9	feature	feature	NOUN
m-1057	112	10	of	of	ADP
m-1057	112	11	this	this	DET
m-1057	112	12	research	research	NOUN
m-1057	112	13	is	be	AUX
m-1057	112	14	the	the	DET
m-1057	112	15	inclusion	inclusion	NOUN
m-1057	112	16	of	of	ADP
m-1057	112	17	sinc	sinc	ADJ
m-1057	112	18	function	function	NOUN
m-1057	112	19	in	in	ADP
m-1057	112	20	the	the	DET
m-1057	112	21	forcing	force	VERB
m-1057	112	22	term	term	NOUN
m-1057	112	23	.	.	PUNCT
m-1057	113	1	the	the	DET
m-1057	113	2	sinc	sinc	PROPN
m-1057	113	3	function	function	PROPN
m-1057	113	4	introduce	introduce	VERB
m-1057	113	5	oscillations	oscillation	NOUN
m-1057	113	6	into	into	ADP
m-1057	113	7	the	the	DET
m-1057	113	8	system	system	NOUN
m-1057	113	9	,	,	PUNCT
m-1057	113	10	which	which	PRON
m-1057	113	11	can	can	AUX
m-1057	113	12	affect	affect	VERB
m-1057	113	13	both	both	DET
m-1057	113	14	the	the	DET
m-1057	113	15	regularity	regularity	NOUN
m-1057	113	16	and	and	CCONJ
m-1057	113	17	ijo	ijo	PROPN
m-1057	113	18	journals	journal	NOUN
m-1057	113	19	volume	volume	NOUN
m-1057	113	20	08	08	NUM
m-1057	114	1	|	|	ADV
m-1057	114	2	issue	issue	VERB
m-1057	114	3	04	04	NUM
m-1057	115	1	|	|	CCONJ
m-1057	115	2	april	april	PROPN
m-1057	115	3	2025	2025	NUM
m-1057	115	4	|	|	ADV
m-1057	115	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1057	115	6	27	27	NUM
m-1057	115	7	ijo	ijo	PROPN
m-1057	115	8	international	international	ADJ
m-1057	115	9	journal	journal	PROPN
m-1057	115	10	of	of	ADP
m-1057	115	11	mathematics	mathematics	PROPN
m-1057	115	12	(	(	PUNCT
m-1057	115	13	issn	issn	PROPN
m-1057	115	14	:	:	PUNCT
m-1057	115	15	2992	2992	NUM
m-1057	115	16	-	-	SYM
m-1057	115	17	4421	4421	NUM
m-1057	115	18	)	)	PUNCT
m-1057	115	19	otobong	otobong	PROPN
m-1057	115	20	j.	j.	PROPN
m-1057	115	21	tom1	tom1	PROPN
m-1057	116	1	*	*	PUNCT
m-1057	116	2	https://ijojournals.com/	https://ijojournals.com/	PROPN
m-1057	116	3	volume	volume	NOUN
m-1057	116	4	08	08	NUM
m-1057	116	5	||	||	PROPN
m-1057	116	6	issue	issue	NOUN
m-1057	116	7	04	04	NUM
m-1057	116	8	||	||	NOUN
m-1057	116	9	april	april	PROPN
m-1057	116	10	,	,	PUNCT
m-1057	116	11	2025	2025	NUM
m-1057	116	12	||	||	PUNCT
m-1057	117	1	“	"	PUNCT
m-1057	117	2	semigroup	semigroup	ADJ
m-1057	117	3	approach	approach	NOUN
m-1057	117	4	for	for	ADP
m-1057	117	5	the	the	DET
m-1057	117	6	solution	solution	NOUN
m-1057	117	7	of	of	ADP
m-1057	117	8	boundary	boundary	ADJ
m-1057	117	9	layer	layer	NOUN
m-1057	117	10	equation	equation	NOUN
m-1057	117	11	with	with	ADP
m-1057	117	12	sinc	sinc	ADJ
m-1057	117	13	function	function	NOUN
m-1057	117	14	term	term	NOUN
m-1057	117	15	"	"	PUNCT
m-1057	117	16	stability	stability	NOUN
m-1057	117	17	of	of	ADP
m-1057	117	18	the	the	DET
m-1057	117	19	solution	solution	NOUN
m-1057	117	20	.	.	PUNCT
m-1057	118	1	in	in	ADP
m-1057	118	2	the	the	DET
m-1057	118	3	context	context	NOUN
m-1057	118	4	of	of	ADP
m-1057	118	5	boundary	boundary	ADJ
m-1057	118	6	layers	layer	NOUN
m-1057	118	7	,	,	PUNCT
m-1057	118	8	the	the	DET
m-1057	118	9	sinc	sinc	PROPN
m-1057	118	10	function	function	NOUN
m-1057	118	11	term	term	NOUN
m-1057	118	12	might	might	AUX
m-1057	118	13	represent	represent	VERB
m-1057	118	14	oscillatory	oscillatory	ADJ
m-1057	118	15	external	external	ADJ
m-1057	118	16	forces	force	NOUN
m-1057	118	17	or	or	CCONJ
m-1057	118	18	disturbances	disturbance	NOUN
m-1057	118	19	that	that	PRON
m-1057	118	20	interact	interact	VERB
m-1057	118	21	with	with	ADP
m-1057	118	22	the	the	DET
m-1057	118	23	boundary	boundary	ADJ
m-1057	118	24	layer	layer	NOUN
m-1057	118	25	dynamics	dynamic	NOUN
m-1057	118	26	.	.	PUNCT
m-1057	119	1			X
m-1057	119	2	oscillatory	oscillatory	ADJ
m-1057	119	3	behavior	behavior	NOUN
m-1057	119	4	:	:	PUNCT
m-1057	119	5	the	the	DET
m-1057	119	6	sinc	sinc	PROPN
m-1057	119	7	function	function	PROPN
m-1057	119	8	’s	’s	PART
m-1057	119	9	oscillations	oscillation	NOUN
m-1057	119	10	may	may	AUX
m-1057	119	11	induce	induce	VERB
m-1057	119	12	transient	transient	ADJ
m-1057	119	13	effects	effect	NOUN
m-1057	119	14	in	in	ADP
m-1057	119	15	the	the	DET
m-1057	119	16	system	system	NOUN
m-1057	119	17	,	,	PUNCT
m-1057	119	18	but	but	CCONJ
m-1057	119	19	under	under	ADP
m-1057	119	20	suitable	suitable	ADJ
m-1057	119	21	condition	condition	NOUN
m-1057	119	22	(	(	PUNCT
m-1057	119	23	e.g.	e.g.	ADV
m-1057	119	24	,	,	PUNCT
m-1057	119	25	decaying	decay	VERB
m-1057	119	26	forcing	force	VERB
m-1057	119	27	terms	term	NOUN
m-1057	119	28	)	)	PUNCT
m-1057	119	29	,	,	PUNCT
m-1057	119	30	these	these	DET
m-1057	119	31	oscillations	oscillation	NOUN
m-1057	119	32	do	do	AUX
m-1057	119	33	not	not	PART
m-1057	119	34	lead	lead	VERB
m-1057	119	35	to	to	ADP
m-1057	119	36	unbounded	unbounded	ADJ
m-1057	119	37	growth	growth	NOUN
m-1057	119	38	of	of	ADP
m-1057	119	39	the	the	DET
m-1057	119	40	solution	solution	NOUN
m-1057	119	41	.	.	PUNCT
m-1057	120	1			X
m-1057	120	2	damping	damp	VERB
m-1057	120	3	effects	effect	NOUN
m-1057	120	4	:	:	PUNCT
m-1057	120	5	the	the	DET
m-1057	120	6	decay	decay	NOUN
m-1057	120	7	of	of	ADP
m-1057	120	8	the	the	DET
m-1057	120	9	sinc	sinc	PROPN
m-1057	120	10	function	function	NOUN
m-1057	120	11	ensures	ensure	VERB
m-1057	120	12	that	that	SCONJ
m-1057	120	13	its	its	PRON
m-1057	120	14	influence	influence	NOUN
m-1057	120	15	fades	fade	VERB
m-1057	120	16	over	over	ADP
m-1057	120	17	time	time	NOUN
m-1057	120	18	,	,	PUNCT
m-1057	120	19	which	which	PRON
m-1057	120	20	implies	imply	VERB
m-1057	120	21	that	that	SCONJ
m-1057	120	22	the	the	DET
m-1057	120	23	system	system	NOUN
m-1057	120	24	will	will	AUX
m-1057	120	25	eventually	eventually	ADV
m-1057	120	26	settle	settle	VERB
m-1057	120	27	to	to	ADP
m-1057	120	28	a	a	DET
m-1057	120	29	steady	steady	ADJ
m-1057	120	30	state	state	NOUN
m-1057	120	31	,	,	PUNCT
m-1057	120	32	as	as	SCONJ
m-1057	120	33	shown	show	VERB
m-1057	120	34	by	by	ADP
m-1057	120	35	the	the	DET
m-1057	120	36	exponential	exponential	ADJ
m-1057	120	37	decay	decay	NOUN
m-1057	120	38	established	establish	VERB
m-1057	120	39	earlier	early	ADV
m-1057	120	40	.	.	PUNCT
m-1057	121	1	5.3	5.3	NUM
m-1057	121	2	.	.	PUNCT
m-1057	121	3	regularity	regularity	NOUN
m-1057	121	4	of	of	ADP
m-1057	121	5	solutions	solution	NOUN
m-1057	121	6	this	this	PRON
m-1057	121	7	is	be	AUX
m-1057	121	8	another	another	DET
m-1057	121	9	crucial	crucial	ADJ
m-1057	121	10	aspect	aspect	NOUN
m-1057	121	11	of	of	ADP
m-1057	121	12	the	the	DET
m-1057	121	13	research	research	NOUN
m-1057	121	14	.	.	PUNCT
m-1057	122	1	regularity	regularity	NOUN
m-1057	122	2	refers	refer	VERB
m-1057	122	3	to	to	ADP
m-1057	122	4	the	the	DET
m-1057	122	5	smoothness	smoothness	NOUN
m-1057	122	6	of	of	ADP
m-1057	122	7	the	the	DET
m-1057	122	8	solution	solution	NOUN
m-1057	122	9	.	.	PUNCT
m-1057	123	1	if	if	SCONJ
m-1057	123	2			PROPN
m-1057	123	3	u	u	PROPN
m-1057	123	4	t	t	PROPN
m-1057	123	5	belongs	belong	VERB
m-1057	123	6	to	to	ADP
m-1057	123	7	a	a	DET
m-1057	123	8	function	function	NOUN
m-1057	123	9	space	space	NOUN
m-1057	123	10	with	with	ADP
m-1057	123	11	sufficient	sufficient	ADJ
m-1057	123	12	differentiability	differentiability	NOUN
m-1057	123	13	(	(	PUNCT
m-1057	123	14	e.g.	e.g.	ADJ
m-1057	123	15	,	,	PUNCT
m-1057	123	16	1	1	NUM
m-1057	123	17	2	2	NUM
m-1057	123	18	,	,	PUNCT
m-1057	123	19	,	,	PUNCT
m-1057	123	20	c	c	NOUN
m-1057	123	21	l	l	NOUN
m-1057	123	22	etc	etc	X
m-1057	123	23	.	.	X
m-1057	123	24	)	)	PUNCT
m-1057	123	25	,	,	PUNCT
m-1057	123	26	it	it	PRON
m-1057	123	27	is	be	AUX
m-1057	123	28	said	say	VERB
m-1057	123	29	to	to	PART
m-1057	123	30	be	be	AUX
m-1057	123	31	regular	regular	ADJ
m-1057	123	32	.	.	PUNCT
m-1057	124	1	the	the	PRON
m-1057	124	2	higher	high	ADJ
m-1057	124	3	the	the	DET
m-1057	124	4	regularity	regularity	NOUN
m-1057	124	5	the	the	PRON
m-1057	124	6	smoother	smooth	ADJ
m-1057	124	7	the	the	DET
m-1057	124	8	solution	solution	NOUN
m-1057	124	9	,	,	PUNCT
m-1057	124	10	and	and	CCONJ
m-1057	124	11	this	this	DET
m-1057	124	12	property	property	NOUN
m-1057	124	13	often	often	ADV
m-1057	124	14	plays	play	VERB
m-1057	124	15	a	a	DET
m-1057	124	16	crucial	crucial	ADJ
m-1057	124	17	role	role	NOUN
m-1057	124	18	in	in	ADP
m-1057	124	19	the	the	DET
m-1057	124	20	stability	stability	NOUN
m-1057	124	21	and	and	CCONJ
m-1057	124	22	long	long	ADJ
m-1057	124	23	-	-	PUNCT
m-1057	124	24	term	term	NOUN
m-1057	124	25	behavior	behavior	NOUN
m-1057	124	26	of	of	ADP
m-1057	124	27	solutions	solution	NOUN
m-1057	124	28	.	.	PUNCT
m-1057	125	1	the	the	DET
m-1057	125	2	solution	solution	NOUN
m-1057	125	3			PROPN
m-1057	125	4	u	u	PROPN
m-1057	125	5	t	t	PROPN
m-1057	125	6	is	be	AUX
m-1057	125	7	shown	show	VERB
m-1057	125	8	to	to	PART
m-1057	125	9	belong	belong	VERB
m-1057	125	10	to	to	ADP
m-1057	125	11	the	the	DET
m-1057	125	12	class	class	NOUN
m-1057	125	13	of	of	ADP
m-1057	125	14	1c	1c	NOUN
m-1057	125	15	under	under	ADP
m-1057	125	16	suitable	suitable	ADJ
m-1057	125	17	regularity	regularity	NOUN
m-1057	125	18	assumptions	assumption	NOUN
m-1057	125	19	on	on	ADP
m-1057	125	20	the	the	DET
m-1057	125	21	initial	initial	ADJ
m-1057	125	22	data	datum	NOUN
m-1057	125	23	0u	0u	ADJ
m-1057	125	24	and	and	CCONJ
m-1057	125	25	the	the	DET
m-1057	125	26	forcing	force	VERB
m-1057	125	27	term	term	NOUN
m-1057	125	28			NOUN
m-1057	125	29			PUNCT
m-1057	125	30			PROPN
m-1057	125	31			PROPN
m-1057	125	32	,	,	PUNCT
m-1057	125	33	,	,	PUNCT
m-1057	126	1	f	f	PROPN
m-1057	126	2	x	x	X
m-1057	126	3	t	t	PROPN
m-1057	126	4	s	s	PART
m-1057	126	5	x	x	SYM
m-1057	126	6	t	t	PROPN
m-1057	126	7	.	.	PUNCT
m-1057	127	1	higher	high	ADJ
m-1057	127	2	regularity	regularity	NOUN
m-1057	127	3	ensures	ensure	VERB
m-1057	127	4	that	that	SCONJ
m-1057	127	5	the	the	DET
m-1057	127	6	solution	solution	NOUN
m-1057	127	7	behaves	behave	VERB
m-1057	127	8	smoothly	smoothly	ADV
m-1057	127	9	over	over	ADP
m-1057	127	10	times	time	NOUN
m-1057	127	11	and	and	CCONJ
m-1057	127	12	that	that	SCONJ
m-1057	127	13	its	its	PRON
m-1057	127	14	derivatives	derivative	NOUN
m-1057	127	15	exist	exist	VERB
m-1057	127	16	and	and	CCONJ
m-1057	127	17	are	be	AUX
m-1057	127	18	continuous	continuous	ADJ
m-1057	127	19	.	.	PUNCT
m-1057	128	1	by	by	ADP
m-1057	128	2	applying	apply	VERB
m-1057	128	3	standard	standard	ADJ
m-1057	128	4	semigroup	semigroup	PROPN
m-1057	128	5	theory	theory	NOUN
m-1057	128	6	,	,	PUNCT
m-1057	128	7	we	we	PRON
m-1057	128	8	can	can	AUX
m-1057	128	9	also	also	ADV
m-1057	128	10	show	show	VERB
m-1057	128	11	that	that	SCONJ
m-1057	128	12	higher	high	ADJ
m-1057	128	13	derivatives	derivative	NOUN
m-1057	128	14	of	of	ADP
m-1057	128	15			NOUN
m-1057	128	16	u	u	PROPN
m-1057	128	17	t	t	PROPN
m-1057	128	18	exist	exist	VERB
m-1057	128	19	and	and	CCONJ
m-1057	128	20	are	be	AUX
m-1057	128	21	bounded	bound	VERB
m-1057	128	22	,	,	PUNCT
m-1057	128	23	which	which	PRON
m-1057	128	24	is	be	AUX
m-1057	128	25	important	important	ADJ
m-1057	128	26	for	for	ADP
m-1057	128	27	numerical	numerical	ADJ
m-1057	128	28	simulations	simulation	NOUN
m-1057	128	29	and	and	CCONJ
m-1057	128	30	further	further	ADJ
m-1057	128	31	theoretical	theoretical	ADJ
m-1057	128	32	analysis	analysis	NOUN
m-1057	128	33	,	,	PUNCT
m-1057	128	34	see	see	VERB
m-1057	128	35	[	[	X
m-1057	128	36	18	18	NUM
m-1057	128	37	,	,	PUNCT
m-1057	128	38	19	19	NUM
m-1057	128	39	,	,	PUNCT
m-1057	128	40	22	22	NUM
m-1057	128	41	]	]	PUNCT
m-1057	128	42	.	.	PUNCT
m-1057	129	1	6	6	X
m-1057	129	2	.	.	X
m-1057	129	3	results	result	VERB
m-1057	129	4	well	well	ADV
m-1057	129	5	-	-	PUNCT
m-1057	129	6	posedness	posedness	NOUN
m-1057	129	7	of	of	ADP
m-1057	129	8	boundary	boundary	ADJ
m-1057	129	9	layer	layer	NOUN
m-1057	129	10	equation	equation	NOUN
m-1057	129	11	:	:	PUNCT
m-1057	129	12	we	we	PRON
m-1057	129	13	consider	consider	VERB
m-1057	129	14	the	the	DET
m-1057	129	15	initial	initial	ADJ
m-1057	129	16	-	-	PUNCT
m-1057	129	17	boundary	boundary	NOUN
m-1057	129	18	value	value	NOUN
m-1057	129	19	problem	problem	NOUN
m-1057	129	20	:	:	PUNCT
m-1057	129	21			NOUN
m-1057	130	1			SYM
m-1057	130	2			NOUN
m-1057	130	3			SYM
m-1057	130	4			NOUN
m-1057	130	5			SYM
m-1057	130	6			NOUN
m-1057	130	7			SYM
m-1057	130	8			NOUN
m-1057	130	9			PROPN
m-1057	130	10	0	0	NUM
m-1057	130	11	,	,	PUNCT
m-1057	130	12	,	,	PUNCT
m-1057	130	13	,	,	PUNCT
m-1057	130	14	,	,	PUNCT
m-1057	130	15	0	0	NUM
m-1057	130	16	7	7	NUM
m-1057	130	17	,	,	PUNCT
m-1057	130	18	0	0	NUM
m-1057	130	19	,	,	PUNCT
m-1057	130	20	u	u	PROPN
m-1057	130	21	au	au	PROPN
m-1057	130	22	f	f	PROPN
m-1057	130	23	x	x	X
m-1057	130	24	t	t	PROPN
m-1057	130	25	s	s	X
m-1057	130	26	x	x	X
m-1057	130	27	t	t	X
m-1057	130	28	x	x	SYM
m-1057	130	29	t	t	PROPN
m-1057	130	30	t	t	X
m-1057	130	31	u	u	X
m-1057	130	32	x	x	PROPN
m-1057	130	33	u	u	NOUN
m-1057	130	34	x	x	X
m-1057	130	35	x	x	SYM
m-1057	130	36			PROPN
m-1057	130	37			PROPN
m-1057	130	38			PROPN
m-1057	130	39			PUNCT
m-1057	130	40			NOUN
m-1057	130	41			VERB
m-1057	130	42			PROPN
m-1057	131	1			PROPN
m-1057	131	2			PROPN
m-1057	131	3	ω	ω	PROPN
m-1057	131	4	ω	ω	NUM
m-1057	131	5	where	where	SCONJ
m-1057	131	6	a	a	PRON
m-1057	131	7	is	be	AUX
m-1057	131	8	as	as	SCONJ
m-1057	131	9	assumed	assume	VERB
m-1057	131	10	in	in	ADP
m-1057	131	11	section	section	NOUN
m-1057	131	12	4	4	NUM
m-1057	131	13	.	.	PUNCT
m-1057	131	14	ijo	ijo	PROPN
m-1057	131	15	journals	journal	NOUN
m-1057	131	16	volume	volume	NOUN
m-1057	131	17	08	08	NUM
m-1057	132	1	|	|	ADV
m-1057	132	2	issue	issue	VERB
m-1057	132	3	04	04	NUM
m-1057	133	1	|	|	CCONJ
m-1057	133	2	april	april	PROPN
m-1057	133	3	2025	2025	NUM
m-1057	133	4	|	|	ADV
m-1057	133	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	PROPN
m-1057	133	6	28	28	NUM
m-1057	133	7	ijo	ijo	PROPN
m-1057	133	8	international	international	PROPN
m-1057	133	9	journal	journal	PROPN
m-1057	133	10	of	of	ADP
m-1057	133	11	mathematics	mathematics	PROPN
m-1057	133	12	(	(	PUNCT
m-1057	133	13	issn	issn	PROPN
m-1057	133	14	:	:	PUNCT
m-1057	133	15	2992	2992	NUM
m-1057	133	16	-	-	SYM
m-1057	133	17	4421	4421	NUM
m-1057	133	18	)	)	PUNCT
m-1057	134	1	otobong	otobong	PROPN
m-1057	134	2	j.	j.	PROPN
m-1057	134	3	tom1	tom1	PROPN
m-1057	134	4	*	*	PUNCT
m-1057	135	1	https://ijojournals.com/	https://ijojournals.com/	PROPN
m-1057	135	2	volume	volume	NOUN
m-1057	135	3	08	08	NUM
m-1057	135	4	||	||	PROPN
m-1057	135	5	issue	issue	NOUN
m-1057	135	6	04	04	NUM
m-1057	135	7	||	||	NOUN
m-1057	135	8	april	april	PROPN
m-1057	135	9	,	,	PUNCT
m-1057	135	10	2025	2025	NUM
m-1057	135	11	||	||	PUNCT
m-1057	136	1	“	"	PUNCT
m-1057	136	2	semigroup	semigroup	ADJ
m-1057	136	3	approach	approach	NOUN
m-1057	136	4	for	for	ADP
m-1057	136	5	the	the	DET
m-1057	136	6	solution	solution	NOUN
m-1057	136	7	of	of	ADP
m-1057	136	8	boundary	boundary	ADJ
m-1057	136	9	layer	layer	NOUN
m-1057	136	10	equation	equation	NOUN
m-1057	136	11	with	with	ADP
m-1057	136	12	sinc	sinc	ADJ
m-1057	136	13	function	function	NOUN
m-1057	136	14	term	term	NOUN
m-1057	136	15	"	"	PUNCT
m-1057	136	16	theorem	theorem	VERB
m-1057	136	17	5.1	5.1	NUM
m-1057	136	18	(	(	PUNCT
m-1057	136	19	existence	existence	NOUN
m-1057	136	20	and	and	CCONJ
m-1057	136	21	uniqueness	uniqueness	NOUN
m-1057	136	22	of	of	ADP
m-1057	136	23	mild	mild	ADJ
m-1057	136	24	solution	solution	NOUN
m-1057	136	25	):	):	PUNCT
m-1057	136	26	if	if	SCONJ
m-1057	136	27	a	a	PRON
m-1057	136	28	is	be	AUX
m-1057	136	29	as	as	SCONJ
m-1057	136	30	assumed	assume	VERB
m-1057	136	31	in	in	ADP
m-1057	136	32	section	section	NOUN
m-1057	136	33	5	5	NUM
m-1057	136	34	,	,	PUNCT
m-1057	136	35	and	and	CCONJ
m-1057	136	36	if	if	SCONJ
m-1057	136	37			NOUN
m-1057	136	38	,f	,f	NOUN
m-1057	136	39	x	x	PUNCT
m-1057	136	40	t	t	NOUN
m-1057	136	41	and	and	CCONJ
m-1057	136	42			PROPN
m-1057	136	43	,s	,s	X
m-1057	136	44	x	x	PUNCT
m-1057	137	1	t	t	NOUN
m-1057	137	2	satisfy	satisfy	VERB
m-1057	137	3	suitable	suitable	ADJ
m-1057	137	4	regularity	regularity	NOUN
m-1057	137	5	conditions	condition	NOUN
m-1057	137	6	,	,	PUNCT
m-1057	137	7	then	then	ADV
m-1057	137	8	equation	equation	NOUN
m-1057	137	9			PROPN
m-1057	137	10	7	7	NOUN
m-1057	137	11	has	have	VERB
m-1057	137	12	a	a	DET
m-1057	137	13	unique	unique	ADJ
m-1057	137	14	mild	mild	ADJ
m-1057	137	15	solution	solution	NOUN
m-1057	137	16	given	give	VERB
m-1057	137	17	by	by	ADP
m-1057	137	18	equation	equation	NOUN
m-1057	137	19			PROPN
m-1057	137	20	5	5	PROPN
m-1057	137	21	.	.	PUNCT
m-1057	138	1	proof	proof	NOUN
m-1057	138	2	:	:	PUNCT
m-1057	138	3	we	we	PRON
m-1057	138	4	apply	apply	VERB
m-1057	138	5	duhamel	duhamel	PROPN
m-1057	138	6	’s	’s	PART
m-1057	138	7	formula	formula	NOUN
m-1057	139	1	[	[	X
m-1057	139	2	3	3	NUM
m-1057	139	3	,	,	PUNCT
m-1057	139	4	15	15	NUM
m-1057	139	5	]	]	PUNCT
m-1057	139	6	to	to	PART
m-1057	139	7	construct	construct	VERB
m-1057	139	8	a	a	DET
m-1057	139	9	mild	mild	ADJ
m-1057	139	10	solution	solution	NOUN
m-1057	139	11	of	of	ADP
m-1057	139	12	equation	equation	NOUN
m-1057	139	13			PROPN
m-1057	139	14	5	5	PROPN
m-1057	139	15	.	.	PUNCT
m-1057	140	1	since	since	SCONJ
m-1057	140	2	the	the	DET
m-1057	140	3	assumption	assumption	NOUN
m-1057	140	4	of	of	ADP
m-1057	140	5	section	section	NOUN
m-1057	140	6	5	5	NUM
m-1057	140	7	holds	hold	VERB
m-1057	140	8	,	,	PUNCT
m-1057	140	9	it	it	PRON
m-1057	140	10	satisfies	satisfy	VERB
m-1057	140	11	;	;	PUNCT
m-1057	140	12			NOUN
m-1057	140	13			NOUN
m-1057	141	1	0	0	INTJ
m-1057	141	2	,	,	PUNCT
m-1057	141	3	t	t	PROPN
m-1057	141	4	i	i	PROPN
m-1057	141	5			NOUN
m-1057	141	6			NOUN
m-1057	141	7			SYM
m-1057	141	8			NOUN
m-1057	141	9			SYM
m-1057	141	10			NOUN
m-1057	141	11	t	t	NOUN
m-1057	141	12	t	t	PROPN
m-1057	141	13	s	s	PROPN
m-1057	141	14	t	t	PROPN
m-1057	141	15	t	t	PROPN
m-1057	141	16	t	t	PROPN
m-1057	141	17	s	s	PROPN
m-1057	141	18			NUM
m-1057	141	19			NOUN
m-1057	141	20			NOUN
m-1057	141	21			PROPN
m-1057	141	22	tt	tt	PROPN
m-1057	141	23	t	t	PROPN
m-1057	141	24	me	me	PROPN
m-1057	141	25	for	for	ADP
m-1057	141	26	some	some	PRON
m-1057	141	27	,	,	PUNCT
m-1057	141	28	0	0	NUM
m-1057	141	29	m	m	NOUN
m-1057	141	30			PROPN
m-1057	141	31			NUM
m-1057	141	32	the	the	DET
m-1057	141	33	existence	existence	NOUN
m-1057	141	34	of	of	ADP
m-1057	141	35	the	the	DET
m-1057	141	36	integral	integral	ADJ
m-1057	141	37	form	form	NOUN
m-1057	141	38	follows	follow	VERB
m-1057	141	39	from	from	ADP
m-1057	141	40	the	the	DET
m-1057	141	41	properties	property	NOUN
m-1057	141	42	of	of	ADP
m-1057	141	43	semigroups	semigroup	NOUN
m-1057	141	44	and	and	CCONJ
m-1057	141	45	the	the	DET
m-1057	141	46	assumed	assumed	ADJ
m-1057	141	47	regularity	regularity	NOUN
m-1057	141	48	of	of	ADP
m-1057	141	49			NOUN
m-1057	141	50	,f	,f	NOUN
m-1057	141	51	x	x	PUNCT
m-1057	141	52	t	t	NOUN
m-1057	141	53	and	and	CCONJ
m-1057	141	54			PROPN
m-1057	141	55	,s	,s	X
m-1057	141	56	x	x	SYM
m-1057	141	57	t	t	NOUN
m-1057	141	58	,	,	PUNCT
m-1057	141	59	ensuring	ensure	VERB
m-1057	141	60	that	that	SCONJ
m-1057	141	61	the	the	DET
m-1057	141	62	function	function	NOUN
m-1057	141	63	inside	inside	ADP
m-1057	141	64	the	the	DET
m-1057	141	65	integral	integral	ADJ
m-1057	141	66	is	be	AUX
m-1057	141	67	welldefined	welldefine	VERB
m-1057	141	68	.	.	PUNCT
m-1057	142	1	next	next	ADV
m-1057	142	2	,	,	PUNCT
m-1057	142	3	we	we	PRON
m-1057	142	4	prove	prove	VERB
m-1057	142	5	the	the	DET
m-1057	142	6	uniqueness	uniqueness	NOUN
m-1057	142	7	of	of	ADP
m-1057	142	8	the	the	DET
m-1057	142	9	solution	solution	NOUN
m-1057	142	10	.	.	PUNCT
m-1057	143	1	assume	assume	VERB
m-1057	143	2	there	there	PRON
m-1057	143	3	exist	exist	VERB
m-1057	143	4	two	two	NUM
m-1057	143	5	solutions	solution	NOUN
m-1057	143	6			NOUN
m-1057	143	7	1u	1u	PUNCT
m-1057	143	8	t	t	PROPN
m-1057	143	9	and	and	CCONJ
m-1057	143	10			PROPN
m-1057	143	11	2u	2u	NOUN
m-1057	144	1	t	t	X
m-1057	144	2	satisfying	satisfy	VERB
m-1057	144	3	the	the	DET
m-1057	144	4	integral	integral	ADJ
m-1057	144	5	equation	equation	NOUN
m-1057	144	6			NOUN
m-1057	145	1			SYM
m-1057	145	2			NOUN
m-1057	145	3			SYM
m-1057	145	4			NOUN
m-1057	145	5			SYM
m-1057	145	6			NOUN
m-1057	145	7			PUNCT
m-1057	145	8			NOUN
m-1057	146	1			NOUN
m-1057	147	1			PUNCT
m-1057	147	2			NOUN
m-1057	147	3			SYM
m-1057	147	4			NOUN
m-1057	147	5			SYM
m-1057	147	6			NOUN
m-1057	147	7			SYM
m-1057	147	8			NOUN
m-1057	147	9			PUNCT
m-1057	147	10			NOUN
m-1057	148	1			NOUN
m-1057	148	2	1	1	NOUN
m-1057	148	3	2	2	NUM
m-1057	148	4	1	1	NUM
m-1057	148	5	2	2	NUM
m-1057	148	6	1	1	NUM
m-1057	148	7	2	2	NUM
m-1057	148	8	1	1	NUM
m-1057	148	9	20	20	NUM
m-1057	148	10	0	0	NUM
m-1057	148	11	0	0	NUM
m-1057	149	1	t	t	NOUN
m-1057	149	2	u	u	NOUN
m-1057	149	3	t	t	PROPN
m-1057	149	4	u	u	NOUN
m-1057	149	5	t	t	PROPN
m-1057	149	6	t	t	PROPN
m-1057	149	7	t	t	X
m-1057	149	8	u	u	X
m-1057	149	9	u	u	X
m-1057	149	10	t	t	NOUN
m-1057	149	11	t	t	NOUN
m-1057	149	12	s	s	X
m-1057	149	13	f	f	PROPN
m-1057	149	14	s	s	PROPN
m-1057	149	15	f	f	X
m-1057	149	16	s	s	X
m-1057	149	17	s	s	X
m-1057	149	18	s	s	X
m-1057	149	19	s	s	X
m-1057	149	20	s	s	X
m-1057	149	21	ds	ds	PROPN
m-1057	149	22			PROPN
m-1057	149	23			PROPN
m-1057	149	24			PUNCT
m-1057	149	25			PROPN
m-1057	149	26			PROPN
m-1057	149	27			VERB
m-1057	149	28			NOUN
m-1057	149	29	if	if	SCONJ
m-1057	149	30			PROPN
m-1057	149	31			SYM
m-1057	149	32			NOUN
m-1057	149	33	1	1	VERB
m-1057	149	34	20	20	NUM
m-1057	149	35	0u	0u	ADJ
m-1057	149	36	u	u	X
m-1057	149	37	and	and	CCONJ
m-1057	149	38	1	1	NUM
m-1057	149	39	2	2	NUM
m-1057	149	40	1	1	NUM
m-1057	149	41	2,f	2,f	NUM
m-1057	149	42	f	f	NOUN
m-1057	149	43	s	s	X
m-1057	149	44	s	s	NOUN
m-1057	149	45			ADJ
m-1057	149	46	,	,	PUNCT
m-1057	149	47	then	then	ADV
m-1057	149	48			NOUN
m-1057	149	49			SYM
m-1057	149	50			NOUN
m-1057	149	51			PUNCT
m-1057	149	52			NOUN
m-1057	149	53			PUNCT
m-1057	149	54	1	1	NUM
m-1057	149	55	2	2	NUM
m-1057	149	56	0	0	NUM
m-1057	149	57	0	0	NUM
m-1057	149	58	0	0	NUM
m-1057	150	1	t	t	NOUN
m-1057	150	2	t	t	NOUN
m-1057	150	3	s	s	X
m-1057	150	4	u	u	NOUN
m-1057	150	5	t	t	X
m-1057	150	6	u	u	NOUN
m-1057	150	7	t	t	PROPN
m-1057	150	8	m	m	NOUN
m-1057	150	9	e	e	NOUN
m-1057	150	10	ds	ds	X
m-1057	150	11			PROPN
m-1057	150	12			PROPN
m-1057	150	13			PROPN
m-1057	150	14			NOUN
m-1057	150	15			PROPN
m-1057	150	16	thus	thus	ADV
m-1057	150	17	,	,	PUNCT
m-1057	150	18	1	1	NUM
m-1057	150	19	2u	2u	PROPN
m-1057	150	20	u	u	X
m-1057	150	21	,	,	PUNCT
m-1057	150	22	proving	prove	VERB
m-1057	150	23	the	the	DET
m-1057	150	24	uniqueness	uniqueness	NOUN
m-1057	150	25	.	.	PUNCT
m-1057	151	1	finally	finally	ADV
m-1057	151	2	,	,	PUNCT
m-1057	151	3	we	we	PRON
m-1057	151	4	prove	prove	VERB
m-1057	151	5	the	the	DET
m-1057	151	6	continuity	continuity	NOUN
m-1057	151	7	of	of	ADP
m-1057	151	8	the	the	DET
m-1057	151	9	solution	solution	NOUN
m-1057	151	10	.	.	PUNCT
m-1057	152	1	by	by	ADP
m-1057	152	2	the	the	DET
m-1057	152	3	strong	strong	ADJ
m-1057	152	4	continuity	continuity	NOUN
m-1057	152	5	of	of	ADP
m-1057	152	6			NOUN
m-1057	152	7	t	t	PROPN
m-1057	152	8	t	t	PROPN
m-1057	152	9	,	,	PUNCT
m-1057	152	10	we	we	PRON
m-1057	152	11	can	can	AUX
m-1057	152	12	show	show	VERB
m-1057	152	13	that	that	SCONJ
m-1057	152	14			NOUN
m-1057	152	15	u	u	PROPN
m-1057	152	16	t	t	PROPN
m-1057	152	17	is	be	AUX
m-1057	152	18	continuous	continuous	ADJ
m-1057	152	19	in	in	ADP
m-1057	152	20	x	x	PUNCT
m-1057	152	21	as	as	SCONJ
m-1057	152	22	follows	follow	VERB
m-1057	152	23	:	:	PUNCT
m-1057	152	24	by	by	ADP
m-1057	152	25	assumption	assumption	NOUN
m-1057	152	26	,	,	PUNCT
m-1057	152	27			PROPN
m-1057	152	28	t	t	PROPN
m-1057	152	29	t	t	PROPN
m-1057	152	30	is	be	AUX
m-1057	152	31	strongly	strongly	ADV
m-1057	152	32	continuous	continuous	ADJ
m-1057	152	33	semigroup	semigroup	NOUN
m-1057	152	34	,	,	PUNCT
m-1057	152	35	meaning	mean	VERB
m-1057	152	36	that	that	SCONJ
m-1057	152	37	for	for	ADP
m-1057	152	38	all	all	DET
m-1057	152	39	0	0	NUM
m-1057	152	40	,	,	PUNCT
m-1057	152	41	u	u	PROPN
m-1057	152	42	x	x	PROPN
m-1057	152	43	ijo	ijo	PROPN
m-1057	152	44	journals	journals	PROPN
m-1057	152	45	volume	volume	NOUN
m-1057	152	46	08	08	NUM
m-1057	153	1	|	|	ADV
m-1057	153	2	issue	issue	VERB
m-1057	153	3	04	04	NUM
m-1057	154	1	|	|	CCONJ
m-1057	154	2	april	april	PROPN
m-1057	154	3	2025	2025	NUM
m-1057	154	4	|	|	ADV
m-1057	154	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1057	154	6	29	29	NUM
m-1057	154	7	ijo	ijo	PROPN
m-1057	154	8	international	international	PROPN
m-1057	154	9	journal	journal	PROPN
m-1057	154	10	of	of	ADP
m-1057	154	11	mathematics	mathematics	PROPN
m-1057	154	12	(	(	PUNCT
m-1057	154	13	issn	issn	PROPN
m-1057	154	14	:	:	PUNCT
m-1057	154	15	2992	2992	NUM
m-1057	154	16	-	-	SYM
m-1057	154	17	4421	4421	NUM
m-1057	154	18	)	)	PUNCT
m-1057	155	1	otobong	otobong	PROPN
m-1057	155	2	j.	j.	PROPN
m-1057	155	3	tom1	tom1	PROPN
m-1057	155	4	*	*	PUNCT
m-1057	156	1	https://ijojournals.com/	https://ijojournals.com/	PROPN
m-1057	156	2	volume	volume	NOUN
m-1057	156	3	08	08	NUM
m-1057	156	4	||	||	PROPN
m-1057	156	5	issue	issue	NOUN
m-1057	156	6	04	04	NUM
m-1057	156	7	||	||	NOUN
m-1057	156	8	april	april	PROPN
m-1057	156	9	,	,	PUNCT
m-1057	156	10	2025	2025	NUM
m-1057	156	11	||	||	PUNCT
m-1057	157	1	“	"	PUNCT
m-1057	157	2	semigroup	semigroup	ADJ
m-1057	157	3	approach	approach	NOUN
m-1057	157	4	for	for	ADP
m-1057	157	5	the	the	DET
m-1057	157	6	solution	solution	NOUN
m-1057	157	7	of	of	ADP
m-1057	157	8	boundary	boundary	ADJ
m-1057	157	9	layer	layer	NOUN
m-1057	157	10	equation	equation	NOUN
m-1057	157	11	with	with	ADP
m-1057	157	12	sinc	sinc	ADJ
m-1057	157	13	function	function	NOUN
m-1057	157	14	term	term	NOUN
m-1057	157	15	"	"	PUNCT
m-1057	157	16			NOUN
m-1057	157	17			PROPN
m-1057	157	18	0	0	SYM
m-1057	157	19	0	0	NUM
m-1057	157	20	0	0	NUM
m-1057	158	1	lim	lim	NOUN
m-1057	158	2	x	x	PROPN
m-1057	158	3	t	t	PROPN
m-1057	158	4	t	t	X
m-1057	158	5	u	u	X
m-1057	158	6	u	u	PROPN
m-1057	158	7	x	x	X
m-1057	158	8			NUM
m-1057	158	9			PROPN
m-1057	158	10			NOUN
m-1057	158	11	this	this	PRON
m-1057	158	12	directly	directly	ADV
m-1057	158	13	implies	imply	VERB
m-1057	158	14	that	that	SCONJ
m-1057	158	15			NOUN
m-1057	158	16			PROPN
m-1057	158	17	0	0	NUM
m-1057	158	18	t	t	NOUN
m-1057	158	19	t	t	NOUN
m-1057	158	20	u	u	NOUN
m-1057	158	21	is	be	AUX
m-1057	158	22	continuous	continuous	ADJ
m-1057	158	23	as	as	ADP
m-1057	158	24	function	function	NOUN
m-1057	158	25	of	of	ADP
m-1057	158	26	t	t	PROPN
m-1057	158	27	x	x	PROPN
m-1057	158	28	.	.	PUNCT
m-1057	159	1	now	now	ADV
m-1057	159	2	,	,	PUNCT
m-1057	159	3	we	we	PRON
m-1057	159	4	need	need	VERB
m-1057	159	5	to	to	PART
m-1057	159	6	prove	prove	VERB
m-1057	159	7	the	the	DET
m-1057	159	8	continuity	continuity	NOUN
m-1057	159	9	of	of	ADP
m-1057	159	10	integral	integral	ADJ
m-1057	159	11	term	term	NOUN
m-1057	159	12	by	by	ADP
m-1057	159	13	analyzing	analyze	VERB
m-1057	159	14	the	the	DET
m-1057	159	15	integral	integral	ADJ
m-1057	159	16	term	term	NOUN
m-1057	159	17	:	:	PUNCT
m-1057	159	18			NOUN
m-1057	159	19			SYM
m-1057	159	20			NOUN
m-1057	159	21			SYM
m-1057	159	22			NOUN
m-1057	159	23			PUNCT
m-1057	159	24			NOUN
m-1057	159	25			NOUN
m-1057	160	1			PROPN
m-1057	160	2	0	0	PUNCT
m-1057	161	1	t	t	NOUN
m-1057	162	1	i	i	PRON
m-1057	162	2	t	t	PROPN
m-1057	162	3	t	t	PROPN
m-1057	162	4	t	t	PROPN
m-1057	162	5	s	s	PART
m-1057	162	6	f	f	PROPN
m-1057	162	7	s	s	X
m-1057	162	8	s	s	X
m-1057	162	9	s	s	X
m-1057	162	10	ds	ds	PROPN
m-1057	162	11			NOUN
m-1057	162	12			NOUN
m-1057	162	13	to	to	PART
m-1057	162	14	prove	prove	VERB
m-1057	162	15	that	that	SCONJ
m-1057	162	16			NOUN
m-1057	162	17	i	i	PROPN
m-1057	162	18	t	t	PROPN
m-1057	162	19	is	be	AUX
m-1057	162	20	continuous	continuous	ADJ
m-1057	162	21	in	in	ADP
m-1057	162	22	x	x	SYM
m-1057	162	23	,	,	PUNCT
m-1057	162	24	we	we	PRON
m-1057	162	25	consider	consider	VERB
m-1057	162	26	a	a	DET
m-1057	162	27	small	small	ADJ
m-1057	162	28	perturbation	perturbation	NOUN
m-1057	162	29	h	h	NOUN
m-1057	162	30	in	in	ADP
m-1057	162	31	time	time	NOUN
m-1057	162	32	and	and	CCONJ
m-1057	162	33	examine	examine	VERB
m-1057	162	34	the	the	DET
m-1057	162	35	difference	difference	NOUN
m-1057	162	36	:	:	PUNCT
m-1057	162	37			NOUN
m-1057	162	38			SYM
m-1057	162	39			NOUN
m-1057	162	40			SYM
m-1057	162	41			NOUN
m-1057	162	42			SYM
m-1057	162	43			NOUN
m-1057	162	44			PUNCT
m-1057	162	45			NOUN
m-1057	163	1			NOUN
m-1057	164	1			PUNCT
m-1057	164	2			NOUN
m-1057	164	3			SYM
m-1057	164	4			NOUN
m-1057	164	5			PUNCT
m-1057	164	6			NOUN
m-1057	164	7			NOUN
m-1057	165	1			PROPN
m-1057	165	2	0	0	SYM
m-1057	165	3	0	0	NUM
m-1057	166	1	t	t	NOUN
m-1057	167	1	h	h	NOUN
m-1057	168	1	t	t	NOUN
m-1057	169	1	i	i	PRON
m-1057	169	2	t	t	PROPN
m-1057	170	1	h	h	NOUN
m-1057	171	1	i	i	PRON
m-1057	171	2	t	t	PROPN
m-1057	171	3	t	t	PROPN
m-1057	171	4	t	t	PROPN
m-1057	171	5	h	h	PROPN
m-1057	171	6	s	s	PART
m-1057	171	7	f	f	PROPN
m-1057	171	8	s	s	X
m-1057	171	9	s	s	X
m-1057	171	10	s	s	X
m-1057	171	11	ds	ds	ADP
m-1057	171	12	t	t	PROPN
m-1057	171	13	t	t	PROPN
m-1057	171	14	s	s	PART
m-1057	171	15	f	f	PROPN
m-1057	171	16	s	s	X
m-1057	171	17	s	s	X
m-1057	171	18	s	s	X
m-1057	171	19	ds	ds	PROPN
m-1057	171	20			ADV
m-1057	171	21			VERB
m-1057	171	22			PROPN
m-1057	171	23			PROPN
m-1057	171	24			ADV
m-1057	171	25			PROPN
m-1057	171	26			VERB
m-1057	171	27			PROPN
m-1057	171	28			PROPN
m-1057	171	29			NUM
m-1057	171	30			PUNCT
m-1057	171	31	splitting	split	VERB
m-1057	171	32	the	the	DET
m-1057	171	33	difference	difference	NOUN
m-1057	171	34	,	,	PUNCT
m-1057	171	35	we	we	PRON
m-1057	171	36	get	get	VERB
m-1057	171	37			NOUN
m-1057	171	38			PUNCT
m-1057	171	39			NOUN
m-1057	171	40			SYM
m-1057	171	41			NOUN
m-1057	171	42			PUNCT
m-1057	171	43			NOUN
m-1057	172	1			NOUN
m-1057	173	1			PUNCT
m-1057	173	2			NOUN
m-1057	173	3			PUNCT
m-1057	173	4			NOUN
m-1057	173	5			NOUN
m-1057	174	1			PROPN
m-1057	174	2	0	0	PUNCT
m-1057	175	1	t	t	NOUN
m-1057	176	1	i	i	PRON
m-1057	176	2	t	t	NOUN
m-1057	177	1	h	h	NOUN
m-1057	178	1	i	i	PRON
m-1057	178	2	t	t	PROPN
m-1057	178	3	t	t	PROPN
m-1057	178	4	t	t	PROPN
m-1057	178	5	h	h	PROPN
m-1057	178	6	s	s	PROPN
m-1057	178	7	t	t	PROPN
m-1057	178	8	t	t	PROPN
m-1057	178	9	s	s	X
m-1057	178	10	f	f	PROPN
m-1057	178	11	s	s	X
m-1057	178	12	s	s	NOUN
m-1057	178	13	s	s	PROPN
m-1057	178	14	ds	ds	PROPN
m-1057	178	15			PROPN
m-1057	178	16			PROPN
m-1057	178	17			PUNCT
m-1057	178	18			PROPN
m-1057	178	19			PROPN
m-1057	178	20			PROPN
m-1057	178	21			PART
m-1057	178	22			NUM
m-1057	178	23			NOUN
m-1057	178	24			SYM
m-1057	178	25			NOUN
m-1057	178	26			PUNCT
m-1057	178	27			NOUN
m-1057	179	1			NOUN
m-1057	180	1			PROPN
m-1057	181	1	t	t	PROPN
m-1057	182	1	h	h	NOUN
m-1057	183	1	t	t	PROPN
m-1057	183	2	t	t	PROPN
m-1057	183	3	t	t	PROPN
m-1057	183	4	h	h	PROPN
m-1057	183	5	s	s	PART
m-1057	183	6	f	f	PROPN
m-1057	183	7	s	s	X
m-1057	183	8	s	s	X
m-1057	183	9	s	s	X
m-1057	183	10	ds	ds	PROPN
m-1057	183	11			VERB
m-1057	183	12			PUNCT
m-1057	183	13			PROPN
m-1057	183	14			NUM
m-1057	183	15	for	for	ADP
m-1057	183	16	the	the	DET
m-1057	183	17	first	first	ADJ
m-1057	183	18	term	term	NOUN
m-1057	183	19	:	:	PUNCT
m-1057	183	20			NOUN
m-1057	183	21			PUNCT
m-1057	183	22			NOUN
m-1057	184	1			NOUN
m-1057	185	1			PUNCT
m-1057	185	2			NOUN
m-1057	185	3			PUNCT
m-1057	185	4			NOUN
m-1057	185	5			NOUN
m-1057	186	1			PROPN
m-1057	186	2	0	0	PUNCT
m-1057	186	3	t	t	PROPN
m-1057	186	4	t	t	PROPN
m-1057	186	5	t	t	PROPN
m-1057	186	6	h	h	PROPN
m-1057	186	7	s	s	PROPN
m-1057	186	8	t	t	PROPN
m-1057	186	9	t	t	PROPN
m-1057	186	10	s	s	X
m-1057	186	11	f	f	PROPN
m-1057	186	12	s	s	X
m-1057	186	13	s	s	NOUN
m-1057	186	14	s	s	PROPN
m-1057	186	15	ds	ds	PROPN
m-1057	186	16			PROPN
m-1057	186	17			PROPN
m-1057	186	18			PROPN
m-1057	186	19			NUM
m-1057	186	20	since	since	SCONJ
m-1057	186	21			NOUN
m-1057	186	22	t	t	PROPN
m-1057	186	23	t	t	PROPN
m-1057	186	24	is	be	AUX
m-1057	186	25	strongly	strongly	ADV
m-1057	186	26	continuous	continuous	ADJ
m-1057	186	27	,	,	PUNCT
m-1057	186	28	for	for	ADP
m-1057	186	29	each	each	DET
m-1057	186	30	fixed	fix	VERB
m-1057	186	31	s	s	NOUN
m-1057	186	32	,	,	PUNCT
m-1057	186	33			PROPN
m-1057	186	34			SYM
m-1057	186	35			NOUN
m-1057	186	36			PROPN
m-1057	186	37	0	0	PUNCT
m-1057	187	1	lim	lim	PROPN
m-1057	187	2	h	h	PROPN
m-1057	187	3	t	t	PROPN
m-1057	187	4	t	t	PROPN
m-1057	187	5	h	h	PROPN
m-1057	187	6	s	s	PROPN
m-1057	187	7	t	t	PROPN
m-1057	187	8	t	t	PROPN
m-1057	187	9	s	s	PART
m-1057	187	10			NOUN
m-1057	187	11			VERB
m-1057	187	12			PROPN
m-1057	187	13			PRON
m-1057	187	14			PROPN
m-1057	187	15	in	in	ADP
m-1057	187	16	x	x	X
m-1057	187	17	.	.	PUNCT
m-1057	188	1	since	since	SCONJ
m-1057	188	2			NOUN
m-1057	188	3			SYM
m-1057	188	4			NOUN
m-1057	189	1	f	f	ADP
m-1057	190	1	s	s	PART
m-1057	190	2	s	s	NOUN
m-1057	190	3	s	s	NOUN
m-1057	190	4	is	be	AUX
m-1057	190	5	integrable	integrable	ADJ
m-1057	190	6	,	,	PUNCT
m-1057	190	7	we	we	PRON
m-1057	190	8	can	can	AUX
m-1057	190	9	use	use	VERB
m-1057	190	10	the	the	DET
m-1057	190	11	lebesgue	lebesgue	NOUN
m-1057	190	12	dominated	dominate	VERB
m-1057	190	13	convergence	convergence	NOUN
m-1057	190	14	theorem	theorem	VERB
m-1057	190	15	[	[	X
m-1057	190	16	16	16	NUM
m-1057	190	17	,	,	PUNCT
m-1057	190	18	17	17	NUM
m-1057	190	19	]	]	PUNCT
m-1057	190	20	to	to	PART
m-1057	190	21	conclude	conclude	VERB
m-1057	190	22	that	that	PRON
m-1057	190	23	:	:	PUNCT
m-1057	191	1			NOUN
m-1057	191	2			PUNCT
m-1057	191	3			PROPN
m-1057	191	4			NOUN
m-1057	192	1			PUNCT
m-1057	192	2			NOUN
m-1057	192	3			PUNCT
m-1057	192	4			NOUN
m-1057	192	5			NOUN
m-1057	193	1			PROPN
m-1057	193	2	00	00	PUNCT
m-1057	194	1	lim	lim	PROPN
m-1057	194	2	0	0	PROPN
m-1057	194	3	.	.	PUNCT
m-1057	195	1	t	t	PROPN
m-1057	195	2	h	h	PROPN
m-1057	195	3	t	t	PROPN
m-1057	195	4	t	t	PROPN
m-1057	195	5	h	h	PROPN
m-1057	195	6	s	s	PROPN
m-1057	195	7	t	t	PROPN
m-1057	195	8	t	t	PROPN
m-1057	195	9	s	s	X
m-1057	195	10	f	f	PROPN
m-1057	195	11	s	s	X
m-1057	195	12	s	s	NOUN
m-1057	195	13	s	s	X
m-1057	195	14	ds	ds	ADJ
m-1057	195	15			NOUN
m-1057	195	16			VERB
m-1057	195	17			PROPN
m-1057	195	18			PROPN
m-1057	195	19			PROPN
m-1057	195	20			NUM
m-1057	195	21			PROPN
m-1057	195	22	ijo	ijo	PROPN
m-1057	195	23	journals	journal	NOUN
m-1057	195	24	volume	volume	NOUN
m-1057	195	25	08	08	NUM
m-1057	196	1	|	|	ADV
m-1057	196	2	issue	issue	VERB
m-1057	196	3	04	04	NUM
m-1057	197	1	|	|	CCONJ
m-1057	197	2	april	april	PROPN
m-1057	197	3	2025	2025	NUM
m-1057	197	4	|	|	ADV
m-1057	197	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1057	197	6	30	30	NUM
m-1057	197	7	ijo	ijo	PROPN
m-1057	197	8	international	international	PROPN
m-1057	197	9	journal	journal	PROPN
m-1057	197	10	of	of	ADP
m-1057	197	11	mathematics	mathematics	PROPN
m-1057	197	12	(	(	PUNCT
m-1057	197	13	issn	issn	PROPN
m-1057	197	14	:	:	PUNCT
m-1057	197	15	2992	2992	NUM
m-1057	197	16	-	-	SYM
m-1057	197	17	4421	4421	NUM
m-1057	197	18	)	)	PUNCT
m-1057	197	19	otobong	otobong	PROPN
m-1057	197	20	j.	j.	PROPN
m-1057	197	21	tom1	tom1	PROPN
m-1057	198	1	*	*	PUNCT
m-1057	198	2	https://ijojournals.com/	https://ijojournals.com/	PROPN
m-1057	198	3	volume	volume	NOUN
m-1057	198	4	08	08	NUM
m-1057	198	5	||	||	PROPN
m-1057	198	6	issue	issue	NOUN
m-1057	198	7	04	04	NUM
m-1057	198	8	||	||	NOUN
m-1057	198	9	april	april	PROPN
m-1057	198	10	,	,	PUNCT
m-1057	198	11	2025	2025	NUM
m-1057	198	12	||	||	PUNCT
m-1057	199	1	“	"	PUNCT
m-1057	199	2	semigroup	semigroup	ADJ
m-1057	199	3	approach	approach	NOUN
m-1057	199	4	for	for	ADP
m-1057	199	5	the	the	DET
m-1057	199	6	solution	solution	NOUN
m-1057	199	7	of	of	ADP
m-1057	199	8	boundary	boundary	ADJ
m-1057	199	9	layer	layer	NOUN
m-1057	199	10	equation	equation	NOUN
m-1057	199	11	with	with	ADP
m-1057	199	12	sinc	sinc	ADJ
m-1057	199	13	function	function	NOUN
m-1057	199	14	term	term	NOUN
m-1057	199	15	"	"	PUNCT
m-1057	199	16	for	for	ADP
m-1057	199	17	the	the	DET
m-1057	199	18	second	second	ADJ
m-1057	199	19	term	term	NOUN
m-1057	199	20	.	.	PUNCT
m-1057	200	1			NOUN
m-1057	200	2			PUNCT
m-1057	200	3			NOUN
m-1057	200	4			PUNCT
m-1057	200	5			NOUN
m-1057	200	6			NOUN
m-1057	201	1			PROPN
m-1057	201	2	0	0	PUNCT
m-1057	202	1	lim	lim	PROPN
m-1057	202	2	t	t	PROPN
m-1057	202	3	h	h	NOUN
m-1057	202	4	th	th	X
m-1057	202	5	t	t	PROPN
m-1057	202	6	t	t	PROPN
m-1057	202	7	h	h	PROPN
m-1057	202	8	s	s	PART
m-1057	202	9	f	f	PROPN
m-1057	202	10	s	s	X
m-1057	202	11	s	s	X
m-1057	202	12	s	s	X
m-1057	202	13	ds	ds	ADJ
m-1057	202	14			X
m-1057	202	15			NOUN
m-1057	202	16			VERB
m-1057	202	17			PROPN
m-1057	202	18			NOUN
m-1057	202	19	as	as	ADP
m-1057	202	20	0h	0h	NOUN
m-1057	202	21	,	,	PUNCT
m-1057	202	22	the	the	DET
m-1057	202	23	interval	interval	NOUN
m-1057	202	24			PROPN
m-1057	202	25	,t	,t	PROPN
m-1057	202	26	t	t	PROPN
m-1057	202	27	h	h	PROPN
m-1057	202	28	shrinks	shrink	VERB
m-1057	202	29	to	to	ADP
m-1057	202	30	zero	zero	NUM
m-1057	202	31	,	,	PUNCT
m-1057	202	32	and	and	CCONJ
m-1057	203	1	since	since	SCONJ
m-1057	203	2			NOUN
m-1057	203	3			SYM
m-1057	203	4			NOUN
m-1057	204	1	f	f	ADP
m-1057	205	1	s	s	PART
m-1057	205	2	s	s	NOUN
m-1057	205	3	s	s	NOUN
m-1057	205	4	is	be	AUX
m-1057	205	5	integrable	integrable	ADJ
m-1057	205	6	,	,	PUNCT
m-1057	205	7	this	this	DET
m-1057	205	8	integral	integral	NOUN
m-1057	205	9	also	also	ADV
m-1057	205	10	vanishes	vanish	VERB
m-1057	205	11	.	.	PUNCT
m-1057	206	1	finally	finally	ADV
m-1057	206	2	,	,	PUNCT
m-1057	206	3	since	since	SCONJ
m-1057	206	4	both	both	DET
m-1057	206	5	terms	term	NOUN
m-1057	206	6	vanish	vanish	VERB
m-1057	206	7	as	as	ADP
m-1057	206	8	0h	0h	NOUN
m-1057	206	9	,	,	PUNCT
m-1057	206	10	we	we	PRON
m-1057	206	11	have	have	VERB
m-1057	206	12			NOUN
m-1057	206	13			SYM
m-1057	206	14			NOUN
m-1057	206	15			PROPN
m-1057	206	16	0	0	PUNCT
m-1057	207	1	lim	lim	PROPN
m-1057	207	2	0	0	NUM
m-1057	208	1	h	h	NOUN
m-1057	209	1	i	i	PRON
m-1057	209	2	t	t	NOUN
m-1057	210	1	h	h	NOUN
m-1057	210	2	i	i	PRON
m-1057	210	3	t	t	PROPN
m-1057	210	4			NOUN
m-1057	210	5			VERB
m-1057	210	6			PROPN
m-1057	210	7			PROPN
m-1057	210	8	thus	thus	ADV
m-1057	210	9	,	,	PUNCT
m-1057	210	10			PROPN
m-1057	210	11	i	i	PROPN
m-1057	210	12	t	t	PROPN
m-1057	210	13	is	be	AUX
m-1057	210	14	continuous	continuous	ADJ
m-1057	210	15	in	in	ADP
m-1057	210	16	x	x	X
m-1057	210	17	,	,	PUNCT
m-1057	210	18	and	and	CCONJ
m-1057	210	19	their	their	PRON
m-1057	210	20	sum	sum	NOUN
m-1057	210	21			PROPN
m-1057	210	22	u	u	PROPN
m-1057	210	23	t	t	PROPN
m-1057	210	24	is	be	AUX
m-1057	210	25	also	also	ADV
m-1057	210	26	continuous	continuous	ADJ
m-1057	210	27	in	in	ADP
m-1057	210	28	x	x	X
m-1057	210	29	.	.	PUNCT
m-1057	211	1	therefore	therefore	ADV
m-1057	211	2	,	,	PUNCT
m-1057	211	3	the	the	DET
m-1057	211	4	mild	mild	ADJ
m-1057	211	5	solution	solution	NOUN
m-1057	211	6			NOUN
m-1057	211	7	u	u	PROPN
m-1057	211	8	t	t	PROPN
m-1057	211	9	in	in	ADP
m-1057	211	10	equation	equation	NOUN
m-1057	211	11			PROPN
m-1057	211	12	5	5	PROPN
m-1057	211	13	is	be	AUX
m-1057	211	14	continuous	continuous	ADJ
m-1057	211	15	in	in	ADP
m-1057	211	16	x	x	X
m-1057	211	17	.	.	PUNCT
m-1057	212	1	proposition	proposition	NOUN
m-1057	212	2	5.2	5.2	NUM
m-1057	212	3	.	.	PUNCT
m-1057	213	1	(	(	PUNCT
m-1057	213	2	decay	decay	NOUN
m-1057	213	3	rate	rate	NOUN
m-1057	213	4	of	of	ADP
m-1057	213	5	solution	solution	NOUN
m-1057	213	6	):	):	PUNCT
m-1057	213	7	if	if	SCONJ
m-1057	213	8			NOUN
m-1057	213	9	,f	,f	NOUN
m-1057	213	10	x	x	PUNCT
m-1057	213	11	t	t	NOUN
m-1057	213	12	and	and	CCONJ
m-1057	213	13			PROPN
m-1057	213	14	,s	,s	X
m-1057	213	15	x	x	PUNCT
m-1057	214	1	t	t	NOUN
m-1057	214	2	vanishes	vanish	VERB
m-1057	214	3	as	as	ADP
m-1057	214	4	,	,	PUNCT
m-1057	214	5	t	t	PROPN
m-1057	214	6	then	then	ADV
m-1057	214	7			PROPN
m-1057	214	8			PROPN
m-1057	214	9	0u	0u	ADJ
m-1057	214	10	t	t	PROPN
m-1057	214	11			PUNCT
m-1057	214	12	exponentially	exponentially	ADV
m-1057	214	13	fast	fast	ADV
m-1057	214	14	.	.	PUNCT
m-1057	215	1	proof	proof	NOUN
m-1057	215	2	:	:	PUNCT
m-1057	215	3	since	since	SCONJ
m-1057	215	4			PROPN
m-1057	215	5	,f	,f	NOUN
m-1057	215	6	x	x	PUNCT
m-1057	215	7	t	t	NOUN
m-1057	215	8	and	and	CCONJ
m-1057	215	9			PROPN
m-1057	215	10	,s	,s	X
m-1057	215	11	x	x	PUNCT
m-1057	215	12	t	t	NOUN
m-1057	215	13	tend	tend	VERB
m-1057	215	14	to	to	PART
m-1057	215	15	zero	zero	NUM
m-1057	215	16	,	,	PUNCT
m-1057	215	17	the	the	DET
m-1057	215	18	integral	integral	ADJ
m-1057	215	19	term	term	NOUN
m-1057	215	20	in	in	ADP
m-1057	215	21			NOUN
m-1057	216	1			SYM
m-1057	216	2			NOUN
m-1057	216	3			SYM
m-1057	216	4			NOUN
m-1057	216	5			SYM
m-1057	216	6			NOUN
m-1057	217	1	0	0	NOUN
m-1057	217	2	0	0	NUM
m-1057	218	1	t	t	NOUN
m-1057	218	2	t	t	PROPN
m-1057	218	3	stu	stu	PROPN
m-1057	218	4	t	t	PROPN
m-1057	218	5	me	i	PRON
m-1057	218	6	u	u	NOUN
m-1057	218	7	m	m	NOUN
m-1057	218	8	e	e	X
m-1057	218	9	f	f	PROPN
m-1057	218	10	s	s	PROPN
m-1057	218	11	s	s	X
m-1057	218	12	s	s	NOUN
m-1057	218	13	ds	ds	ADJ
m-1057	218	14			ADJ
m-1057	218	15			NOUN
m-1057	218	16			NOUN
m-1057	218	17			X
m-1057	218	18			NUM
m-1057	218	19	vanishes	vanish	VERB
m-1057	218	20	as	as	ADP
m-1057	218	21	t	t	PROPN
m-1057	218	22	.	.	PUNCT
m-1057	219	1	thus	thus	ADV
m-1057	219	2	,	,	PUNCT
m-1057	219	3			PROPN
m-1057	219	4			PROPN
m-1057	219	5	0	0	NUM
m-1057	219	6	0tu	0tu	PROPN
m-1057	219	7	t	t	PROPN
m-1057	219	8	me	i	PRON
m-1057	219	9	u	u	PROPN
m-1057	219	10			NOUN
m-1057	220	1	this	this	PRON
m-1057	220	2	shows	show	VERB
m-1057	220	3	exponential	exponential	ADJ
m-1057	220	4	decay	decay	NOUN
m-1057	220	5	of	of	ADP
m-1057	220	6	solution	solution	NOUN
m-1057	220	7	.	.	PUNCT
m-1057	221	1	theorem	theorem	VERB
m-1057	221	2	6.4	6.4	NUM
m-1057	221	3	.	.	PUNCT
m-1057	222	1	(	(	PUNCT
m-1057	222	2	higher	high	ADJ
m-1057	222	3	regularity	regularity	NOUN
m-1057	222	4	of	of	ADP
m-1057	222	5	solutions	solution	NOUN
m-1057	222	6	):	):	PUNCT
m-1057	222	7	if	if	SCONJ
m-1057	222	8			PROPN
m-1057	222	9	0u	0u	PROPN
m-1057	223	1	d	d	X
m-1057	223	2	a	a	PROPN
m-1057	223	3	,	,	PUNCT
m-1057	223	4	and	and	CCONJ
m-1057	223	5			NOUN
m-1057	223	6			PROPN
m-1057	223	7			PROPN
m-1057	223	8			PROPN
m-1057	223	9	,	,	PUNCT
m-1057	223	10	,	,	PUNCT
m-1057	223	11	f	f	PROPN
m-1057	223	12	x	x	X
m-1057	223	13	t	t	PROPN
m-1057	223	14	s	s	PART
m-1057	223	15	x	x	SYM
m-1057	223	16	t	t	PROPN
m-1057	223	17	are	be	AUX
m-1057	223	18	sufficiently	sufficiently	ADV
m-1057	223	19	smooth	smooth	ADJ
m-1057	223	20	,	,	PUNCT
m-1057	223	21	then	then	ADV
m-1057	223	22	the	the	DET
m-1057	223	23	solution	solution	NOUN
m-1057	223	24	satisfies	satisfy	VERB
m-1057	223	25	ijo	ijo	PROPN
m-1057	223	26	journals	journal	NOUN
m-1057	223	27	volume	volume	NOUN
m-1057	223	28	08	08	NUM
m-1057	224	1	|	|	ADV
m-1057	224	2	issue	issue	VERB
m-1057	224	3	04	04	NUM
m-1057	225	1	|	|	CCONJ
m-1057	225	2	april	april	PROPN
m-1057	225	3	2025	2025	NUM
m-1057	225	4	|	|	ADV
m-1057	225	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	PROPN
m-1057	225	6	31	31	NUM
m-1057	225	7	ijo	ijo	PROPN
m-1057	225	8	international	international	PROPN
m-1057	225	9	journal	journal	PROPN
m-1057	225	10	of	of	ADP
m-1057	225	11	mathematics	mathematics	PROPN
m-1057	225	12	(	(	PUNCT
m-1057	225	13	issn	issn	PROPN
m-1057	225	14	:	:	PUNCT
m-1057	225	15	2992	2992	NUM
m-1057	225	16	-	-	SYM
m-1057	225	17	4421	4421	NUM
m-1057	225	18	)	)	PUNCT
m-1057	226	1	otobong	otobong	PROPN
m-1057	226	2	j.	j.	PROPN
m-1057	226	3	tom1	tom1	PROPN
m-1057	226	4	*	*	PUNCT
m-1057	227	1	https://ijojournals.com/	https://ijojournals.com/	PROPN
m-1057	227	2	volume	volume	NOUN
m-1057	227	3	08	08	NUM
m-1057	227	4	||	||	PROPN
m-1057	227	5	issue	issue	NOUN
m-1057	227	6	04	04	NUM
m-1057	227	7	||	||	NOUN
m-1057	227	8	april	april	PROPN
m-1057	227	9	,	,	PUNCT
m-1057	227	10	2025	2025	NUM
m-1057	227	11	||	||	PUNCT
m-1057	228	1	“	"	PUNCT
m-1057	228	2	semigroup	semigroup	ADJ
m-1057	228	3	approach	approach	NOUN
m-1057	228	4	for	for	ADP
m-1057	228	5	the	the	DET
m-1057	228	6	solution	solution	NOUN
m-1057	228	7	of	of	ADP
m-1057	228	8	boundary	boundary	ADJ
m-1057	228	9	layer	layer	NOUN
m-1057	228	10	equation	equation	NOUN
m-1057	228	11	with	with	ADP
m-1057	228	12	sinc	sinc	ADJ
m-1057	228	13	function	function	NOUN
m-1057	228	14	term	term	NOUN
m-1057	228	15	"	"	PUNCT
m-1057	228	16			PROPN
m-1057	228	17			PROPN
m-1057	228	18	1	1	PROPN
m-1057	228	19	,	,	PUNCT
m-1057	228	20	0	0	NUM
m-1057	228	21	,	,	PUNCT
m-1057	228	22	,	,	PUNCT
m-1057	228	23	du	du	PROPN
m-1057	228	24	au	au	PROPN
m-1057	228	25	f	f	PROPN
m-1057	228	26	s	s	PROPN
m-1057	228	27	u	u	NOUN
m-1057	228	28	c	c	NOUN
m-1057	228	29	t	t	NOUN
m-1057	228	30	x	x	PUNCT
m-1057	228	31	dt	dt	X
m-1057	228	32			PROPN
m-1057	228	33			PROPN
m-1057	228	34			ADJ
m-1057	228	35			NOUN
m-1057	228	36	.	.	PUNCT
m-1057	229	1	proof	proof	NOUN
m-1057	229	2	:	:	PUNCT
m-1057	229	3	first	first	X
m-1057	229	4	,	,	PUNCT
m-1057	229	5	since	since	SCONJ
m-1057	229	6			PROPN
m-1057	229	7	0u	0u	PROPN
m-1057	230	1	d	d	INTJ
m-1057	230	2	a	a	PROPN
m-1057	230	3	,	,	PUNCT
m-1057	230	4	we	we	PRON
m-1057	230	5	apply	apply	VERB
m-1057	230	6	a	a	PRON
m-1057	230	7	to	to	ADP
m-1057	230	8	the	the	DET
m-1057	230	9	mild	mild	ADJ
m-1057	230	10	solution	solution	NOUN
m-1057	230	11	formula	formula	NOUN
m-1057	230	12			NOUN
m-1057	230	13			SYM
m-1057	230	14			NOUN
m-1057	230	15			SYM
m-1057	230	16			NOUN
m-1057	230	17			PUNCT
m-1057	230	18			NOUN
m-1057	231	1			NOUN
m-1057	232	1			PUNCT
m-1057	232	2			NOUN
m-1057	232	3	0	0	NOUN
m-1057	232	4	0	0	NUM
m-1057	232	5	tdu	tdu	NOUN
m-1057	232	6	at	at	ADP
m-1057	232	7	t	t	PROPN
m-1057	232	8	u	u	PROPN
m-1057	232	9	a	a	DET
m-1057	232	10	t	t	NOUN
m-1057	232	11	t	t	X
m-1057	232	12	s	s	X
m-1057	232	13	f	f	PROPN
m-1057	232	14	s	s	X
m-1057	232	15	s	s	X
m-1057	232	16	s	s	X
m-1057	232	17	ds	ds	PRON
m-1057	232	18	f	f	PROPN
m-1057	232	19	s	s	PROPN
m-1057	232	20	dt	dt	X
m-1057	232	21			PROPN
m-1057	232	22			ADJ
m-1057	232	23			PROPN
m-1057	232	24			ADV
m-1057	232	25			PUNCT
m-1057	232	26			NUM
m-1057	232	27	using	use	VERB
m-1057	232	28	the	the	DET
m-1057	232	29	properties	property	NOUN
m-1057	232	30	of	of	ADP
m-1057	232	31	semigroups	semigroup	NOUN
m-1057	232	32	[	[	X
m-1057	232	33	3	3	NUM
m-1057	232	34	,	,	PUNCT
m-1057	232	35	19	19	NUM
m-1057	232	36	]	]	PUNCT
m-1057	232	37	,	,	PUNCT
m-1057	232	38			PROPN
m-1057	232	39			SYM
m-1057	232	40			NOUN
m-1057	232	41	at	at	NOUN
m-1057	232	42	t	t	PROPN
m-1057	232	43	t	t	PROPN
m-1057	232	44	t	t	PROPN
m-1057	232	45	a	a	NOUN
m-1057	232	46	,	,	PUNCT
m-1057	232	47	we	we	PRON
m-1057	232	48	write	write	VERB
m-1057	232	49	du	du	PROPN
m-1057	232	50	au	au	PROPN
m-1057	232	51	f	f	PROPN
m-1057	232	52	s	s	PROPN
m-1057	232	53	dt	dt	X
m-1057	232	54			PROPN
m-1057	232	55			ADV
m-1057	232	56			PUNCT
m-1057	232	57	this	this	PRON
m-1057	232	58	implies	imply	VERB
m-1057	232	59	that	that	SCONJ
m-1057	232	60	u	u	NOUN
m-1057	232	61	is	be	AUX
m-1057	232	62	differentiable	differentiable	ADJ
m-1057	232	63	with	with	ADP
m-1057	232	64	the	the	DET
m-1057	232	65	stated	stated	ADJ
m-1057	232	66	regularity[6	regularity[6	PROPN
m-1057	232	67	]	]	PUNCT
m-1057	232	68	.	.	PUNCT
m-1057	233	1	example	example	NOUN
m-1057	233	2	6.1	6.1	NUM
m-1057	233	3	.	.	PUNCT
m-1057	234	1	consider	consider	VERB
m-1057	234	2	the	the	DET
m-1057	234	3	boundary	boundary	ADJ
m-1057	234	4	value	value	NOUN
m-1057	234	5	problem	problem	NOUN
m-1057	234	6	:	:	PUNCT
m-1057	234	7			NOUN
m-1057	234	8			SYM
m-1057	234	9			NOUN
m-1057	235	1			SYM
m-1057	235	2			NOUN
m-1057	235	3			SYM
m-1057	235	4			NOUN
m-1057	235	5			SYM
m-1057	235	6			NOUN
m-1057	235	7			SYM
m-1057	235	8			NOUN
m-1057	235	9			PUNCT
m-1057	235	10			NOUN
m-1057	235	11			NOUN
m-1057	235	12	2	2	NUM
m-1057	235	13	2	2	NUM
m-1057	235	14	0	0	NUM
m-1057	235	15	sinc	sinc	PROPN
m-1057	235	16	,	,	PUNCT
m-1057	235	17	0,1	0,1	NUM
m-1057	235	18	,	,	PUNCT
m-1057	235	19	0	0	NUM
m-1057	235	20	,	,	PUNCT
m-1057	235	21	0	0	NUM
m-1057	235	22	,	,	PUNCT
m-1057	235	23	1	1	NUM
m-1057	235	24	0	0	NUM
m-1057	235	25	,	,	PUNCT
m-1057	235	26	0	0	NUM
m-1057	235	27	0	0	NUM
m-1057	235	28	,	,	PUNCT
m-1057	235	29	sin	sin	NOUN
m-1057	235	30	.	.	PUNCT
m-1057	236	1	u	u	PRON
m-1057	236	2	u	u	X
m-1057	236	3	t	t	PROPN
m-1057	236	4	x	x	PROPN
m-1057	236	5	t	t	PROPN
m-1057	236	6	t	t	PROPN
m-1057	236	7	x	x	PUNCT
m-1057	236	8	u	u	NOUN
m-1057	236	9	t	t	PROPN
m-1057	236	10	u	u	NOUN
m-1057	236	11	t	t	PROPN
m-1057	236	12	t	t	X
m-1057	236	13	u	u	X
m-1057	236	14	x	x	PROPN
m-1057	236	15	u	u	PROPN
m-1057	236	16	x	x	X
m-1057	236	17	x	x	PROPN
m-1057	236	18			ADP
m-1057	236	19			PROPN
m-1057	236	20			PROPN
m-1057	236	21			PROPN
m-1057	236	22			ADJ
m-1057	236	23			NOUN
m-1057	236	24			ADP
m-1057	236	25			PROPN
m-1057	236	26			PROPN
m-1057	236	27			NUM
m-1057	236	28			PROPN
m-1057	236	29			NOUN
m-1057	237	1			NUM
m-1057	237	2			NOUN
m-1057	237	3			PROPN
m-1057	237	4			NUM
m-1057	237	5			NOUN
m-1057	237	6	v	v	ADP
m-1057	237	7	this	this	PRON
m-1057	237	8	is	be	AUX
m-1057	237	9	a	a	DET
m-1057	237	10	linear	linear	ADJ
m-1057	237	11	boundary	boundary	ADJ
m-1057	237	12	layer	layer	NOUN
m-1057	237	13	equation	equation	NOUN
m-1057	237	14	with	with	ADP
m-1057	237	15	sinc	sinc	ADJ
m-1057	237	16	forcing	forcing	NOUN
m-1057	237	17	.	.	PUNCT
m-1057	238	1	we	we	PRON
m-1057	238	2	interpret	interpret	VERB
m-1057	238	3	the	the	DET
m-1057	238	4	sinc	sinc	PROPN
m-1057	238	5	term	term	NOUN
m-1057	238	6	as	as	ADP
m-1057	238	7	an	an	DET
m-1057	238	8	external	external	ADJ
m-1057	238	9	time	time	NOUN
m-1057	238	10	-	-	PUNCT
m-1057	238	11	dependent	dependent	ADJ
m-1057	238	12	forcing	forcing	NOUN
m-1057	238	13	that	that	PRON
m-1057	238	14	is	be	AUX
m-1057	238	15	spartially	spartially	ADV
m-1057	238	16	uniform	uniform	ADJ
m-1057	238	17	(	(	PUNCT
m-1057	238	18	i.e.	i.e.	X
m-1057	238	19	,	,	PUNCT
m-1057	238	20	acts	act	VERB
m-1057	238	21	identically	identically	ADV
m-1057	238	22	across	across	ADP
m-1057	238	23	all	all	DET
m-1057	238	24	spatial	spatial	ADJ
m-1057	238	25	points	point	NOUN
m-1057	238	26	)	)	PUNCT
m-1057	238	27	.	.	PUNCT
m-1057	239	1	let	let	VERB
m-1057	239	2	2	2	NUM
m-1057	239	3	2	2	NUM
m-1057	239	4	d	d	NOUN
m-1057	239	5	a	a	DET
m-1057	239	6	dx	dx	PROPN
m-1057	239	7	v	v	PROPN
m-1057	239	8	with	with	ADP
m-1057	239	9	domain	domain	NOUN
m-1057	239	10			NOUN
m-1057	239	11			SYM
m-1057	239	12			NOUN
m-1057	239	13			SYM
m-1057	239	14			NOUN
m-1057	239	15	2	2	NOUN
m-1057	239	16	1	1	NUM
m-1057	239	17	00,1	00,1	NOUN
m-1057	239	18	0,1d	0,1d	NOUN
m-1057	240	1	a	a	DET
m-1057	240	2	u	u	NOUN
m-1057	240	3	h	h	NOUN
m-1057	240	4	h	h	NOUN
m-1057	240	5			NOUN
m-1057	240	6			PUNCT
m-1057	240	7	.	.	PUNCT
m-1057	241	1	then	then	ADV
m-1057	241	2	a	a	DET
m-1057	241	3	generates	generate	VERB
m-1057	241	4	a	a	DET
m-1057	241	5	strongly	strongly	ADV
m-1057	241	6	continuous	continuous	ADJ
m-1057	241	7	analytic	analytic	ADJ
m-1057	241	8	semigroup	semigroup	NOUN
m-1057	241	9			NOUN
m-1057	241	10			PROPN
m-1057	241	11	tat	tat	NOUN
m-1057	241	12	t	t	PROPN
m-1057	241	13	e	e	PROPN
m-1057	241	14	.	.	PUNCT
m-1057	242	1	the	the	DET
m-1057	242	2	mild	mild	ADJ
m-1057	242	3	solution	solution	NOUN
m-1057	242	4	is	be	AUX
m-1057	242	5	given	give	VERB
m-1057	242	6	by	by	ADP
m-1057	242	7	:	:	PUNCT
m-1057	242	8	ijo	ijo	PROPN
m-1057	242	9	journals	journal	NOUN
m-1057	242	10	volume	volume	NOUN
m-1057	242	11	08	08	NUM
m-1057	242	12	|	|	ADV
m-1057	242	13	issue	issue	VERB
m-1057	242	14	04	04	NUM
m-1057	243	1	|	|	CCONJ
m-1057	243	2	april	april	PROPN
m-1057	243	3	2025	2025	NUM
m-1057	243	4	|	|	ADV
m-1057	243	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	PROPN
m-1057	243	6	32	32	NUM
m-1057	243	7	ijo	ijo	PROPN
m-1057	243	8	international	international	PROPN
m-1057	243	9	journal	journal	PROPN
m-1057	243	10	of	of	ADP
m-1057	243	11	mathematics	mathematics	PROPN
m-1057	243	12	(	(	PUNCT
m-1057	243	13	issn	issn	PROPN
m-1057	243	14	:	:	PUNCT
m-1057	243	15	2992	2992	NUM
m-1057	243	16	-	-	SYM
m-1057	243	17	4421	4421	NUM
m-1057	243	18	)	)	PUNCT
m-1057	243	19	otobong	otobong	PROPN
m-1057	243	20	j.	j.	PROPN
m-1057	243	21	tom1	tom1	PROPN
m-1057	244	1	*	*	PUNCT
m-1057	244	2	https://ijojournals.com/	https://ijojournals.com/	PROPN
m-1057	244	3	volume	volume	NOUN
m-1057	244	4	08	08	NUM
m-1057	244	5	||	||	PROPN
m-1057	244	6	issue	issue	NOUN
m-1057	244	7	04	04	NUM
m-1057	244	8	||	||	NOUN
m-1057	244	9	april	april	PROPN
m-1057	244	10	,	,	PUNCT
m-1057	244	11	2025	2025	NUM
m-1057	244	12	||	||	PUNCT
m-1057	245	1	“	"	PUNCT
m-1057	245	2	semigroup	semigroup	ADJ
m-1057	245	3	approach	approach	NOUN
m-1057	245	4	for	for	ADP
m-1057	245	5	the	the	DET
m-1057	245	6	solution	solution	NOUN
m-1057	245	7	of	of	ADP
m-1057	245	8	boundary	boundary	ADJ
m-1057	245	9	layer	layer	NOUN
m-1057	245	10	equation	equation	NOUN
m-1057	245	11	with	with	ADP
m-1057	245	12	sinc	sinc	ADJ
m-1057	245	13	function	function	NOUN
m-1057	245	14	term	term	NOUN
m-1057	245	15	"	"	PUNCT
m-1057	245	16			NOUN
m-1057	245	17			PROPN
m-1057	245	18			NOUN
m-1057	245	19			SYM
m-1057	245	20			NOUN
m-1057	245	21			SYM
m-1057	245	22			NOUN
m-1057	245	23	0	0	NOUN
m-1057	245	24	0	0	PUNCT
m-1057	245	25	t	t	NOUN
m-1057	245	26	u	u	NOUN
m-1057	245	27	t	t	PROPN
m-1057	245	28	t	t	PROPN
m-1057	245	29	t	t	PROPN
m-1057	245	30	u	u	PROPN
m-1057	245	31	t	t	PROPN
m-1057	245	32	t	t	PROPN
m-1057	245	33	s	s	X
m-1057	245	34	f	f	PROPN
m-1057	245	35	s	s	PROPN
m-1057	245	36	ds	ds	PROPN
m-1057	245	37			ADJ
m-1057	245	38			NOUN
m-1057	245	39	.	.	PUNCT
m-1057	246	1	the	the	DET
m-1057	246	2	eigenfunctions	eigenfunction	NOUN
m-1057	246	3	of	of	ADP
m-1057	246	4	a	a	PRON
m-1057	246	5	are	be	AUX
m-1057	246	6	:	:	PUNCT
m-1057	246	7			NOUN
m-1057	246	8			SYM
m-1057	246	9			NOUN
m-1057	246	10			SYM
m-1057	246	11			NOUN
m-1057	246	12			PROPN
m-1057	246	13	2	2	NUM
m-1057	246	14	2sin	2sin	NUM
m-1057	246	15	,	,	PUNCT
m-1057	246	16	n	n	X
m-1057	246	17	ne	ne	X
m-1057	246	18	x	x	SYM
m-1057	246	19	n	n	PROPN
m-1057	246	20	x	x	X
m-1057	246	21	n	n	NOUN
m-1057	246	22			NOUN
m-1057	246	23			NOUN
m-1057	246	24	vλ	vλ	PUNCT
m-1057	246	25	.	.	PUNCT
m-1057	247	1	so	so	ADV
m-1057	247	2	the	the	DET
m-1057	247	3	semigroup	semigroup	PROPN
m-1057	247	4	acts	act	VERB
m-1057	247	5	as	as	ADP
m-1057	247	6	:	:	PUNCT
m-1057	247	7			NOUN
m-1057	247	8			SYM
m-1057	247	9			NOUN
m-1057	248	1	0	0	NOUN
m-1057	248	2	01	01	NUM
m-1057	248	3	,	,	PUNCT
m-1057	248	4	nt	not	PART
m-1057	248	5	n	n	ADV
m-1057	248	6	nn	nn	PROPN
m-1057	248	7	t	t	PROPN
m-1057	248	8	t	t	X
m-1057	248	9	u	u	X
m-1057	248	10	e	e	X
m-1057	248	11	u	u	NOUN
m-1057	248	12	e	e	X
m-1057	248	13	e	e	X
m-1057	248	14	x	x	PART
m-1057	248	15			VERB
m-1057	248	16			NUM
m-1057	248	17			PROPN
m-1057	248	18	λ	λ	X
m-1057	248	19	.	.	PUNCT
m-1057	249	1	since	since	SCONJ
m-1057	249	2			NOUN
m-1057	249	3			SYM
m-1057	249	4			NOUN
m-1057	249	5			SYM
m-1057	249	6			NOUN
m-1057	250	1	0	0	NOUN
m-1057	250	2	1	1	NUM
m-1057	250	3	2	2	NUM
m-1057	250	4	sin	sin	NOUN
m-1057	250	5	2	2	NUM
m-1057	250	6	u	u	NOUN
m-1057	250	7	x	x	NOUN
m-1057	250	8	x	x	X
m-1057	250	9	e	e	X
m-1057	250	10	x	x	PROPN
m-1057	250	11			NUM
m-1057	250	12	,	,	PUNCT
m-1057	250	13	only	only	ADV
m-1057	250	14	the	the	DET
m-1057	250	15	first	first	ADJ
m-1057	250	16	mode	mode	NOUN
m-1057	250	17	is	be	AUX
m-1057	250	18	nonzero	nonzero	NOUN
m-1057	250	19	:	:	PUNCT
m-1057	250	20			NOUN
m-1057	250	21			SYM
m-1057	250	22			NOUN
m-1057	250	23			NOUN
m-1057	250	24	2	2	NUM
m-1057	250	25	1	1	NUM
m-1057	250	26	2	2	NUM
m-1057	250	27	2	2	NUM
m-1057	250	28	t	t	NOUN
m-1057	250	29	t	t	NOUN
m-1057	250	30	e	e	X
m-1057	250	31	e	e	PROPN
m-1057	250	32	x	x	PRON
m-1057	250	33	v	v	NOUN
m-1057	250	34	.	.	PUNCT
m-1057	251	1	now	now	ADV
m-1057	251	2	consider	consider	VERB
m-1057	251	3	:	:	PUNCT
m-1057	252	1			NOUN
m-1057	252	2			SYM
m-1057	252	3			NOUN
m-1057	252	4			SYM
m-1057	252	5			NOUN
m-1057	252	6			SYM
m-1057	252	7			NOUN
m-1057	252	8			PUNCT
m-1057	252	9			NOUN
m-1057	252	10			PUNCT
m-1057	252	11	1	1	NUM
m-1057	252	12	1	1	NUM
m-1057	252	13	0	0	NUM
m-1057	252	14	,	,	PUNCT
m-1057	252	15	sinc	sinc	PROPN
m-1057	252	16	1	1	NUM
m-1057	252	17	sinc	sinc	PROPN
m-1057	252	18	1	1	NUM
m-1057	252	19	,	,	PUNCT
m-1057	252	20	,	,	PUNCT
m-1057	252	21	2	2	NUM
m-1057	252	22	2	2	NUM
m-1057	252	23	,	,	PUNCT
m-1057	252	24	odd	odd	ADJ
m-1057	252	25	,	,	PUNCT
m-1057	252	26	1	1	NUM
m-1057	252	27	,	,	PUNCT
m-1057	252	28	2	2	NUM
m-1057	252	29	sin	sin	NOUN
m-1057	252	30	0	0	NUM
m-1057	252	31	,	,	PUNCT
m-1057	252	32	even	even	ADV
m-1057	252	33	.	.	PUNCT
m-1057	253	1	n	n	CCONJ
m-1057	253	2	nn	nn	PROPN
m-1057	254	1	n	n	ADV
m-1057	254	2	f	f	PROPN
m-1057	254	3	s	s	AUX
m-1057	254	4	x	x	X
m-1057	254	5	s	s	X
m-1057	254	6	s	s	X
m-1057	254	7	e	e	X
m-1057	254	8	e	e	X
m-1057	254	9	x	x	X
m-1057	254	10	n	n	PROPN
m-1057	254	11	e	e	X
m-1057	254	12	n	n	PROPN
m-1057	254	13	x	x	PROPN
m-1057	254	14	dx	dx	PROPN
m-1057	254	15	n	n	CCONJ
m-1057	254	16	n	n	PROPN
m-1057	254	17			ADJ
m-1057	254	18			NOUN
m-1057	254	19			NOUN
m-1057	254	20			NOUN
m-1057	254	21			PROPN
m-1057	254	22			NUM
m-1057	254	23			NOUN
m-1057	254	24			NOUN
m-1057	255	1			NUM
m-1057	256	1			NOUN
m-1057	256	2			NOUN
m-1057	256	3			NUM
m-1057	256	4			NUM
m-1057	256	5			PROPN
m-1057	256	6			X
m-1057	256	7			PUNCT
m-1057	257	1	hence	hence	ADV
m-1057	257	2	:	:	PUNCT
m-1057	258	1			NOUN
m-1057	258	2			SYM
m-1057	258	3			NOUN
m-1057	258	4			SYM
m-1057	258	5			NOUN
m-1057	258	6			SYM
m-1057	258	7			NOUN
m-1057	258	8			SYM
m-1057	258	9			PROPN
m-1057	258	10	sinc	sinc	NOUN
m-1057	258	11	1	1	NUM
m-1057	258	12	odd	odd	ADJ
m-1057	258	13	2	2	NUM
m-1057	258	14	2	2	NUM
m-1057	258	15	n	n	ADP
m-1057	258	16	t	t	NOUN
m-1057	258	17	s	s	NOUN
m-1057	258	18	s	s	NOUN
m-1057	258	19	n	n	CCONJ
m-1057	258	20	n	n	CCONJ
m-1057	258	21	n	n	CCONJ
m-1057	258	22	n	n	NOUN
m-1057	258	23	t	t	NOUN
m-1057	258	24	t	t	X
m-1057	258	25	s	s	X
m-1057	258	26	f	f	PROPN
m-1057	258	27	s	s	PROPN
m-1057	258	28	e	e	NOUN
m-1057	258	29	e	e	X
m-1057	258	30	e	e	AUX
m-1057	258	31	n	n	VERB
m-1057	258	32			PROPN
m-1057	258	33			PROPN
m-1057	258	34			PROPN
m-1057	258	35			X
m-1057	258	36			PROPN
m-1057	258	37			SYM
m-1057	258	38	λ	λ	X
m-1057	258	39	.	.	PUNCT
m-1057	259	1	integrating	integrating	NOUN
m-1057	259	2	:	:	PUNCT
m-1057	259	3			NOUN
m-1057	259	4			SYM
m-1057	259	5			NOUN
m-1057	259	6			SYM
m-1057	259	7			NOUN
m-1057	259	8			SYM
m-1057	259	9			NOUN
m-1057	259	10			SYM
m-1057	259	11			NOUN
m-1057	260	1	1	1	ADJ
m-1057	260	2	0	0	NUM
m-1057	260	3	0	0	NUM
m-1057	260	4	odd	odd	ADJ
m-1057	260	5	2	2	NUM
m-1057	260	6	2	2	NUM
m-1057	260	7	sincn	sincn	NOUN
m-1057	260	8	t	t	PROPN
m-1057	260	9	t	t	PROPN
m-1057	260	10	t	t	PROPN
m-1057	260	11	s	s	AUX
m-1057	260	12	n	n	CCONJ
m-1057	260	13	n	n	CCONJ
m-1057	260	14	n	n	NOUN
m-1057	260	15	t	t	NOUN
m-1057	260	16	t	t	X
m-1057	260	17	s	s	X
m-1057	260	18	f	f	X
m-1057	260	19	s	s	X
m-1057	260	20	ds	ds	NOUN
m-1057	260	21	e	e	X
m-1057	260	22	s	s	NOUN
m-1057	260	23	ds	ds	ADJ
m-1057	260	24	e	e	NOUN
m-1057	260	25	x	x	PART
m-1057	260	26	n	n	PRON
m-1057	260	27			PROPN
m-1057	260	28			NUM
m-1057	260	29			PROPN
m-1057	261	1			PROPN
m-1057	261	2			PROPN
m-1057	261	3			PROPN
m-1057	261	4			PROPN
m-1057	261	5			NOUN
m-1057	261	6			ADJ
m-1057	261	7			NOUN
m-1057	261	8			PUNCT
m-1057	262	1	λ	λ	X
m-1057	262	2	.	.	PUNCT
m-1057	263	1	combining	combine	VERB
m-1057	263	2	,	,	PUNCT
m-1057	263	3	we	we	PRON
m-1057	263	4	have	have	VERB
m-1057	263	5	the	the	DET
m-1057	263	6	mild	mild	ADJ
m-1057	263	7	solution	solution	NOUN
m-1057	263	8	:	:	PUNCT
m-1057	263	9	ijo	ijo	PROPN
m-1057	263	10	journals	journal	NOUN
m-1057	263	11	volume	volume	NOUN
m-1057	263	12	08	08	NUM
m-1057	264	1	|	|	ADV
m-1057	264	2	issue	issue	VERB
m-1057	264	3	04	04	NUM
m-1057	265	1	|	|	CCONJ
m-1057	265	2	april	april	PROPN
m-1057	265	3	2025	2025	NUM
m-1057	265	4	|	|	ADV
m-1057	265	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1057	265	6	33	33	NUM
m-1057	265	7	ijo	ijo	PROPN
m-1057	265	8	international	international	PROPN
m-1057	265	9	journal	journal	PROPN
m-1057	265	10	of	of	ADP
m-1057	265	11	mathematics	mathematics	PROPN
m-1057	265	12	(	(	PUNCT
m-1057	265	13	issn	issn	PROPN
m-1057	265	14	:	:	PUNCT
m-1057	265	15	2992	2992	NUM
m-1057	265	16	-	-	SYM
m-1057	265	17	4421	4421	NUM
m-1057	265	18	)	)	PUNCT
m-1057	265	19	otobong	otobong	PROPN
m-1057	265	20	j.	j.	PROPN
m-1057	265	21	tom1	tom1	PROPN
m-1057	266	1	*	*	PUNCT
m-1057	266	2	https://ijojournals.com/	https://ijojournals.com/	PROPN
m-1057	266	3	volume	volume	NOUN
m-1057	266	4	08	08	NUM
m-1057	266	5	||	||	PROPN
m-1057	266	6	issue	issue	NOUN
m-1057	266	7	04	04	NUM
m-1057	266	8	||	||	NOUN
m-1057	266	9	april	april	PROPN
m-1057	266	10	,	,	PUNCT
m-1057	266	11	2025	2025	NUM
m-1057	266	12	||	||	PUNCT
m-1057	267	1	“	"	PUNCT
m-1057	267	2	semigroup	semigroup	ADJ
m-1057	267	3	approach	approach	NOUN
m-1057	267	4	for	for	ADP
m-1057	267	5	the	the	DET
m-1057	267	6	solution	solution	NOUN
m-1057	267	7	of	of	ADP
m-1057	267	8	boundary	boundary	ADJ
m-1057	267	9	layer	layer	NOUN
m-1057	267	10	equation	equation	NOUN
m-1057	267	11	with	with	ADP
m-1057	267	12	sinc	sinc	ADJ
m-1057	267	13	function	function	NOUN
m-1057	267	14	term	term	NOUN
m-1057	267	15	"	"	PUNCT
m-1057	267	16			NOUN
m-1057	267	17			PROPN
m-1057	267	18			NOUN
m-1057	267	19			SYM
m-1057	267	20			NOUN
m-1057	267	21			SYM
m-1057	267	22			NOUN
m-1057	267	23			SYM
m-1057	267	24			NOUN
m-1057	267	25			PUNCT
m-1057	267	26			NOUN
m-1057	267	27			PROPN
m-1057	267	28	22	22	NUM
m-1057	267	29	11	11	NUM
m-1057	267	30	0	0	NUM
m-1057	267	31	odd	odd	ADJ
m-1057	267	32	2	2	NUM
m-1057	267	33	2	2	NUM
m-1057	267	34	2	2	NUM
m-1057	267	35	,	,	PUNCT
m-1057	267	36	sinc	sinc	NOUN
m-1057	267	37	2	2	NUM
m-1057	267	38	t	t	PROPN
m-1057	267	39	n	n	ADP
m-1057	267	40	t	t	PROPN
m-1057	267	41	st	st	PROPN
m-1057	267	42	n	n	PROPN
m-1057	267	43	n	n	CCONJ
m-1057	267	44	n	n	CCONJ
m-1057	267	45	u	u	NOUN
m-1057	267	46	t	t	NOUN
m-1057	267	47	x	x	PUNCT
m-1057	267	48	e	e	NOUN
m-1057	267	49	e	e	X
m-1057	267	50	x	x	X
m-1057	267	51	e	e	NOUN
m-1057	267	52	s	s	PRON
m-1057	267	53	ds	ds	ADJ
m-1057	267	54	e	e	NOUN
m-1057	267	55	x	x	PROPN
m-1057	267	56	n	n	CCONJ
m-1057	267	57			PROPN
m-1057	267	58			ADJ
m-1057	267	59			NOUN
m-1057	267	60			NUM
m-1057	267	61			NUM
m-1057	267	62			PROPN
m-1057	267	63			PROPN
m-1057	267	64			ADV
m-1057	267	65			NUM
m-1057	267	66			PROPN
m-1057	267	67			PROPN
m-1057	267	68			NOUN
m-1057	267	69			X
m-1057	267	70			X
m-1057	267	71			PUNCT
m-1057	267	72	vv	vv	INTJ
m-1057	267	73	.	.	PUNCT
m-1057	268	1	truncating	truncate	VERB
m-1057	268	2	to	to	ADP
m-1057	268	3	first	first	ADJ
m-1057	268	4	odd	odd	ADJ
m-1057	268	5	mode	mode	NOUN
m-1057	268	6			NOUN
m-1057	269	1	1n	1n	PROPN
m-1057	270	1			NUM
m-1057	270	2	,	,	PUNCT
m-1057	270	3	we	we	PRON
m-1057	270	4	have	have	VERB
m-1057	270	5	:	:	PUNCT
m-1057	270	6			NOUN
m-1057	270	7			PROPN
m-1057	270	8			NOUN
m-1057	270	9			SYM
m-1057	270	10			NOUN
m-1057	270	11			PUNCT
m-1057	270	12			NOUN
m-1057	270	13			PROPN
m-1057	270	14	22	22	NUM
m-1057	270	15	0	0	NUM
m-1057	270	16	2	2	NUM
m-1057	270	17	2	2	NUM
m-1057	270	18	2	2	NUM
m-1057	270	19	,	,	PUNCT
m-1057	270	20	sinc	sinc	X
m-1057	270	21	sin	sin	NOUN
m-1057	270	22	2	2	NUM
m-1057	270	23	t	t	NOUN
m-1057	270	24	t	t	PROPN
m-1057	270	25	stu	stu	PROPN
m-1057	270	26	t	t	PROPN
m-1057	270	27	x	x	PUNCT
m-1057	270	28	e	e	X
m-1057	270	29	e	e	NOUN
m-1057	270	30	s	s	VERB
m-1057	270	31	ds	ds	ADJ
m-1057	270	32	x	x	INTJ
m-1057	270	33			PROPN
m-1057	270	34			ADJ
m-1057	270	35			ADJ
m-1057	270	36			NOUN
m-1057	270	37			PUNCT
m-1057	270	38			PROPN
m-1057	270	39			NOUN
m-1057	270	40			X
m-1057	270	41			ADJ
m-1057	270	42			NOUN
m-1057	270	43			NOUN
m-1057	270	44			PROPN
m-1057	270	45			ADP
m-1057	270	46	vv	vv	INTJ
m-1057	270	47	.	.	PUNCT
m-1057	271	1	this	this	PRON
m-1057	271	2	is	be	AUX
m-1057	271	3	a	a	DET
m-1057	271	4	practical	practical	ADJ
m-1057	271	5	,	,	PUNCT
m-1057	271	6	computable	computable	ADJ
m-1057	271	7	low	low	ADJ
m-1057	271	8	-	-	PUNCT
m-1057	271	9	mode	mode	NOUN
m-1057	271	10	mild	mild	ADJ
m-1057	271	11	solution	solution	NOUN
m-1057	271	12	.	.	PUNCT
m-1057	272	1	example	example	NOUN
m-1057	273	1	6.2	6.2	NUM
m-1057	273	2	.	.	PUNCT
m-1057	274	1	consideranother	consideranother	ADJ
m-1057	274	2	case	case	NOUN
m-1057	274	3	given	give	VERB
m-1057	274	4	by	by	ADP
m-1057	274	5	:	:	PUNCT
m-1057	274	6			PROPN
m-1057	275	1			PROPN
m-1057	275	2			NOUN
m-1057	275	3			SYM
m-1057	275	4			NOUN
m-1057	275	5			SYM
m-1057	275	6			NOUN
m-1057	275	7			SYM
m-1057	275	8			NOUN
m-1057	275	9			SYM
m-1057	275	10			NOUN
m-1057	275	11			SYM
m-1057	275	12			NOUN
m-1057	275	13			PUNCT
m-1057	275	14			NOUN
m-1057	275	15			PROPN
m-1057	275	16	2	2	NUM
m-1057	275	17	2	2	NUM
m-1057	275	18	sinc	sinc	NOUN
m-1057	275	19	,	,	PUNCT
m-1057	275	20	,	,	PUNCT
m-1057	275	21	0	0	NUM
m-1057	275	22	,	,	PUNCT
m-1057	275	23	1	1	NUM
m-1057	275	24	0	0	NUM
m-1057	275	25	,	,	PUNCT
m-1057	275	26	0	0	NUM
m-1057	275	27	,	,	PUNCT
m-1057	275	28	sin	sin	NOUN
m-1057	275	29	,	,	PUNCT
m-1057	275	30	1	1	X
m-1057	275	31	.	.	PUNCT
m-1057	276	1	u	u	PRON
m-1057	276	2	u	u	X
m-1057	276	3	u	u	X
m-1057	276	4	u	u	X
m-1057	276	5	x	x	PROPN
m-1057	276	6	t	t	NOUN
m-1057	276	7	t	t	NOUN
m-1057	276	8	x	x	PUNCT
m-1057	276	9	x	x	PUNCT
m-1057	276	10	u	u	NOUN
m-1057	276	11	t	t	X
m-1057	276	12	u	u	NOUN
m-1057	276	13	t	t	PROPN
m-1057	276	14	u	u	NOUN
m-1057	276	15	x	x	NOUN
m-1057	276	16	x	x	PUNCT
m-1057	276	17	x	x	SYM
m-1057	276	18	x	x	SYM
m-1057	276	19	x	x	SYM
m-1057	276	20			NOUN
m-1057	276	21			ADJ
m-1057	276	22			NOUN
m-1057	276	23			ADP
m-1057	276	24			ADJ
m-1057	276	25			ADJ
m-1057	276	26			ADJ
m-1057	276	27			PROPN
m-1057	276	28			PROPN
m-1057	276	29			VERB
m-1057	276	30			PROPN
m-1057	276	31			PROPN
m-1057	276	32			PROPN
m-1057	276	33			PROPN
m-1057	276	34			PROPN
m-1057	276	35			PROPN
m-1057	276	36			NUM
m-1057	276	37			PROPN
m-1057	276	38			PROPN
m-1057	276	39			NUM
m-1057	276	40			NOUN
m-1057	276	41	v	v	ADP
m-1057	276	42	this	this	PRON
m-1057	276	43	is	be	AUX
m-1057	276	44	a	a	DET
m-1057	276	45	semilinear	semilinear	ADJ
m-1057	276	46	case	case	NOUN
m-1057	276	47	with	with	ADP
m-1057	276	48	sinc	sinc	ADJ
m-1057	276	49	forcing	forcing	NOUN
m-1057	276	50	.	.	PUNCT
m-1057	277	1	in	in	ADP
m-1057	277	2	this	this	DET
m-1057	277	3	case	case	NOUN
m-1057	277	4	,	,	PUNCT
m-1057	277	5	the	the	DET
m-1057	277	6	mild	mild	ADJ
m-1057	277	7	solution	solution	NOUN
m-1057	277	8	is	be	AUX
m-1057	277	9	obtained	obtain	VERB
m-1057	277	10	as	as	ADP
m-1057	277	11	follows	follow	VERB
m-1057	277	12	:	:	PUNCT
m-1057	277	13	let	let	VERB
m-1057	277	14			NOUN
m-1057	277	15			PROPN
m-1057	277	16			PROPN
m-1057	277	17			NOUN
m-1057	277	18			SYM
m-1057	277	19			NOUN
m-1057	277	20			PUNCT
m-1057	277	21			NOUN
m-1057	277	22	sincxf	sincxf	PUNCT
m-1057	277	23	u	u	NOUN
m-1057	277	24	s	s	PART
m-1057	277	25	u	u	NOUN
m-1057	277	26	s	s	PROPN
m-1057	277	27	u	u	NOUN
m-1057	277	28	s	s	NOUN
m-1057	277	29	s	s	PROPN
m-1057	277	30			PROPN
m-1057	277	31			PROPN
m-1057	277	32			ADV
m-1057	277	33	,	,	PUNCT
m-1057	277	34	then	then	ADV
m-1057	277	35	:	:	PUNCT
m-1057	277	36			NOUN
m-1057	278	1			SYM
m-1057	278	2			NOUN
m-1057	278	3			SYM
m-1057	278	4			NOUN
m-1057	278	5			PUNCT
m-1057	278	6			NOUN
m-1057	279	1			NOUN
m-1057	280	1	0	0	INTJ
m-1057	280	2	0	0	NUM
m-1057	280	3	t	t	NOUN
m-1057	280	4	u	u	NOUN
m-1057	280	5	t	t	PROPN
m-1057	280	6	t	t	PROPN
m-1057	280	7	t	t	PROPN
m-1057	280	8	u	u	PROPN
m-1057	280	9	t	t	PROPN
m-1057	280	10	t	t	PROPN
m-1057	280	11	s	s	PART
m-1057	280	12	f	f	PROPN
m-1057	280	13	u	u	PROPN
m-1057	280	14	s	s	PROPN
m-1057	280	15	ds	ds	NOUN
m-1057	280	16			ADJ
m-1057	280	17			NOUN
m-1057	280	18	.	.	PUNCT
m-1057	281	1	as	as	SCONJ
m-1057	281	2	in	in	ADP
m-1057	281	3	example	example	NOUN
m-1057	281	4	5.1	5.1	NUM
m-1057	281	5	,	,	PUNCT
m-1057	281	6			NOUN
m-1057	281	7			SYM
m-1057	281	8			NOUN
m-1057	281	9			NUM
m-1057	281	10	2	2	NUM
m-1057	281	11	0	0	NUM
m-1057	281	12	2	2	NUM
m-1057	281	13	sin	sin	NOUN
m-1057	281	14	2	2	NUM
m-1057	281	15	tt	tt	PROPN
m-1057	281	16	t	t	NOUN
m-1057	281	17	u	u	PROPN
m-1057	281	18	e	e	PROPN
m-1057	281	19	x	x	PROPN
m-1057	281	20			VERB
m-1057	281	21	v	v	NOUN
m-1057	281	22	.	.	PUNCT
m-1057	282	1	for	for	ADP
m-1057	282	2	the	the	DET
m-1057	282	3	nonlinear	nonlinear	ADJ
m-1057	282	4	term	term	NOUN
m-1057	282	5	assume	assume	VERB
m-1057	282	6			NOUN
m-1057	282	7			SYM
m-1057	282	8			NOUN
m-1057	282	9			PUNCT
m-1057	282	10			PROPN
m-1057	282	11			PROPN
m-1057	282	12	,	,	PUNCT
m-1057	282	13	sinu	sinu	NOUN
m-1057	282	14	t	t	PROPN
m-1057	282	15	x	x	PROPN
m-1057	282	16	t	t	PROPN
m-1057	282	17	x	x	PROPN
m-1057	282	18			PROPN
m-1057	282	19	.	.	PUNCT
m-1057	283	1	then	then	ADV
m-1057	283	2	:	:	PUNCT
m-1057	283	3			PRON
m-1057	283	4			NOUN
m-1057	283	5			SYM
m-1057	283	6			PROPN
m-1057	284	1	cosxu	cosxu	PROPN
m-1057	284	2	t	t	PROPN
m-1057	284	3	x	x	PROPN
m-1057	285	1			PROPN
m-1057	285	2			NOUN
m-1057	285	3			NOUN
m-1057	285	4			NOUN
m-1057	285	5			NOUN
m-1057	285	6			SYM
m-1057	285	7			NOUN
m-1057	285	8			SYM
m-1057	285	9			PROPN
m-1057	285	10	2	2	NOUN
m-1057	285	11	sin	sin	NOUN
m-1057	285	12	cosxu	cosxu	VERB
m-1057	285	13	u	u	PROPN
m-1057	285	14	t	t	PROPN
m-1057	285	15	x	x	PROPN
m-1057	285	16	x	x	PROPN
m-1057	285	17			PROPN
m-1057	285	18			PROPN
m-1057	285	19			NOUN
m-1057	285	20			NOUN
m-1057	285	21	.	.	PUNCT
m-1057	286	1	ijo	ijo	PROPN
m-1057	286	2	journals	journal	NOUN
m-1057	286	3	volume	volume	NOUN
m-1057	286	4	08	08	NUM
m-1057	287	1	|	|	ADV
m-1057	287	2	issue	issue	VERB
m-1057	287	3	04	04	NUM
m-1057	288	1	|	|	CCONJ
m-1057	288	2	april	april	PROPN
m-1057	288	3	2025	2025	NUM
m-1057	288	4	|	|	ADV
m-1057	288	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	PROPN
m-1057	288	6	34	34	NUM
m-1057	288	7	ijo	ijo	PROPN
m-1057	288	8	international	international	PROPN
m-1057	288	9	journal	journal	PROPN
m-1057	288	10	of	of	ADP
m-1057	288	11	mathematics	mathematics	PROPN
m-1057	288	12	(	(	PUNCT
m-1057	288	13	issn	issn	PROPN
m-1057	288	14	:	:	PUNCT
m-1057	288	15	2992	2992	NUM
m-1057	288	16	-	-	SYM
m-1057	288	17	4421	4421	NUM
m-1057	288	18	)	)	PUNCT
m-1057	289	1	otobong	otobong	PROPN
m-1057	289	2	j.	j.	PROPN
m-1057	289	3	tom1	tom1	PROPN
m-1057	289	4	*	*	PUNCT
m-1057	290	1	https://ijojournals.com/	https://ijojournals.com/	PROPN
m-1057	290	2	volume	volume	NOUN
m-1057	290	3	08	08	NUM
m-1057	290	4	||	||	PROPN
m-1057	290	5	issue	issue	NOUN
m-1057	290	6	04	04	NUM
m-1057	290	7	||	||	NOUN
m-1057	290	8	april	april	PROPN
m-1057	290	9	,	,	PUNCT
m-1057	290	10	2025	2025	NUM
m-1057	290	11	||	||	PUNCT
m-1057	291	1	“	"	PUNCT
m-1057	291	2	semigroup	semigroup	ADJ
m-1057	291	3	approach	approach	NOUN
m-1057	291	4	for	for	ADP
m-1057	291	5	the	the	DET
m-1057	291	6	solution	solution	NOUN
m-1057	291	7	of	of	ADP
m-1057	291	8	boundary	boundary	ADJ
m-1057	291	9	layer	layer	NOUN
m-1057	291	10	equation	equation	NOUN
m-1057	291	11	with	with	ADP
m-1057	291	12	sinc	sinc	ADJ
m-1057	291	13	function	function	NOUN
m-1057	291	14	term	term	NOUN
m-1057	291	15	"	"	PUNCT
m-1057	291	16	we	we	PRON
m-1057	291	17	project	project	VERB
m-1057	291	18	xu	xu	PROPN
m-1057	291	19	u	u	PROPN
m-1057	291	20	onto	onto	ADP
m-1057	291	21			NOUN
m-1057	291	22			PROPN
m-1057	291	23			NOUN
m-1057	291	24	1	1	VERB
m-1057	291	25	2	2	NUM
m-1057	291	26	sine	sine	NOUN
m-1057	291	27	x	x	X
m-1057	291	28	x	x	PROPN
m-1057	291	29	;	;	PUNCT
m-1057	291	30			PROPN
m-1057	291	31			PROPN
m-1057	291	32			NOUN
m-1057	291	33			PUNCT
m-1057	291	34			NOUN
m-1057	291	35			NOUN
m-1057	291	36	1	1	NUM
m-1057	291	37	2	2	NUM
m-1057	291	38	2	2	NUM
m-1057	291	39	1	1	NUM
m-1057	291	40	0	0	NUM
m-1057	291	41	,	,	PUNCT
m-1057	291	42	2	2	NUM
m-1057	291	43	sin	sin	NOUN
m-1057	291	44	cosxu	cosxu	VERB
m-1057	291	45	u	u	PROPN
m-1057	291	46	e	e	PROPN
m-1057	291	47	t	t	NOUN
m-1057	291	48	x	x	X
m-1057	291	49	x	x	X
m-1057	291	50	dx	dx	X
m-1057	291	51			PROPN
m-1057	291	52			ADJ
m-1057	291	53			NOUN
m-1057	291	54			NOUN
m-1057	291	55			X
m-1057	291	56			NOUN
m-1057	291	57			SYM
m-1057	291	58			NOUN
m-1057	291	59			PUNCT
m-1057	291	60	1	1	NUM
m-1057	291	61	2	2	NUM
m-1057	291	62	0	0	NUM
m-1057	291	63	1	1	NUM
m-1057	291	64	1	1	NUM
m-1057	291	65	1	1	NUM
m-1057	291	66	sin	sin	NOUN
m-1057	291	67	cos	cos	ADP
m-1057	291	68	2	2	NUM
m-1057	291	69	2	2	NUM
m-1057	291	70	x	x	SYM
m-1057	291	71	x	x	X
m-1057	291	72	dx	dx	X
m-1057	291	73			ADJ
m-1057	291	74			PROPN
m-1057	291	75			ADJ
m-1057	291	76			ADJ
m-1057	291	77			PROPN
m-1057	291	78			NOUN
m-1057	291	79			PROPN
m-1057	291	80	so	so	ADV
m-1057	291	81	:	:	PUNCT
m-1057	291	82			NOUN
m-1057	291	83			SYM
m-1057	291	84			NOUN
m-1057	291	85	2	2	ADJ
m-1057	291	86	2	2	NUM
m-1057	291	87	1	1	NUM
m-1057	291	88	1	1	NUM
m-1057	291	89	2	2	NUM
m-1057	291	90	,	,	PUNCT
m-1057	291	91	2	2	NUM
m-1057	291	92	2	2	NUM
m-1057	291	93	2	2	NUM
m-1057	291	94	xu	xu	NUM
m-1057	291	95	u	u	NOUN
m-1057	291	96	e	e	PROPN
m-1057	291	97	t	t	PROPN
m-1057	291	98	t	t	PROPN
m-1057	291	99			PROPN
m-1057	291	100			X
m-1057	291	101			PROPN
m-1057	291	102			ADJ
m-1057	291	103			PROPN
m-1057	291	104			NUM
m-1057	291	105			NOUN
m-1057	291	106	.	.	PUNCT
m-1057	292	1	projection	projection	NOUN
m-1057	292	2	of	of	ADP
m-1057	292	3	forcing	force	VERB
m-1057	292	4	term	term	NOUN
m-1057	292	5	:	:	PUNCT
m-1057	292	6			NOUN
m-1057	293	1			SYM
m-1057	293	2			NOUN
m-1057	293	3			NOUN
m-1057	293	4	1	1	NUM
m-1057	293	5	1	1	NUM
m-1057	293	6	30	30	NUM
m-1057	293	7	4	4	NUM
m-1057	293	8	,	,	PUNCT
m-1057	293	9	2	2	NUM
m-1057	293	10	1	1	NUM
m-1057	293	11	sin	sin	NOUN
m-1057	293	12	2e	2e	NOUN
m-1057	293	13	x	x	PUNCT
m-1057	293	14	x	x	PUNCT
m-1057	293	15	x	x	X
m-1057	293	16	dx	dx	PROPN
m-1057	293	17			PROPN
m-1057	293	18			PROPN
m-1057	293	19			PROPN
m-1057	293	20			NOUN
m-1057	293	21			NUM
m-1057	293	22			PROPN
m-1057	293	23	.	.	PUNCT
m-1057	294	1	putting	put	VERB
m-1057	294	2	everything	everything	PRON
m-1057	294	3	together	together	ADV
m-1057	294	4	,	,	PUNCT
m-1057	294	5	the	the	DET
m-1057	294	6	scalar	scalar	ADJ
m-1057	294	7	integral	integral	ADJ
m-1057	294	8	equation	equation	NOUN
m-1057	294	9	for	for	ADP
m-1057	294	10			NOUN
m-1057	294	11	t	t	PUNCT
m-1057	294	12	is	be	AUX
m-1057	294	13	:	:	PUNCT
m-1057	294	14			NOUN
m-1057	294	15			SYM
m-1057	294	16			NOUN
m-1057	294	17			SYM
m-1057	294	18			NOUN
m-1057	294	19			PUNCT
m-1057	294	20			NOUN
m-1057	294	21			NOUN
m-1057	294	22	22	22	NUM
m-1057	294	23	2	2	NUM
m-1057	294	24	30	30	NUM
m-1057	294	25	2	2	NUM
m-1057	294	26	2	2	NUM
m-1057	294	27	4	4	NUM
m-1057	294	28	2	2	NUM
m-1057	294	29	sinc	sinc	NOUN
m-1057	294	30	2	2	NUM
m-1057	294	31	2	2	NUM
m-1057	294	32	t	t	PROPN
m-1057	294	33	st	st	PROPN
m-1057	294	34	t	t	PROPN
m-1057	294	35	t	t	X
m-1057	294	36	e	e	X
m-1057	294	37	e	e	X
m-1057	294	38	s	s	X
m-1057	294	39	s	s	X
m-1057	294	40	ds	ds	ADJ
m-1057	294	41			NOUN
m-1057	294	42			NOUN
m-1057	294	43			X
m-1057	294	44			PROPN
m-1057	294	45			NOUN
m-1057	294	46			PUNCT
m-1057	294	47			PROPN
m-1057	294	48			ADJ
m-1057	294	49			PROPN
m-1057	294	50			PUNCT
m-1057	294	51			PROPN
m-1057	294	52			PROPN
m-1057	294	53			NOUN
m-1057	294	54			NOUN
m-1057	294	55			PROPN
m-1057	294	56			ADP
m-1057	294	57	vv	vv	INTJ
m-1057	294	58	.	.	PUNCT
m-1057	295	1	this	this	DET
m-1057	295	2	a	a	DET
m-1057	295	3	nonlinearvolterra	nonlinearvolterra	ADJ
m-1057	295	4	equation	equation	NOUN
m-1057	295	5	of	of	ADP
m-1057	295	6	the	the	DET
m-1057	295	7	second	second	ADJ
m-1057	295	8	kind	kind	NOUN
m-1057	295	9	.	.	PUNCT
m-1057	296	1	remark	remark	VERB
m-1057	296	2	:	:	PUNCT
m-1057	296	3			PRON
m-1057	296	4	the	the	DET
m-1057	296	5	nonlinear	nonlinear	ADJ
m-1057	296	6	term	term	NOUN
m-1057	296	7	creates	create	VERB
m-1057	296	8	a	a	DET
m-1057	296	9	coupling	coupling	NOUN
m-1057	296	10	effect	effect	NOUN
m-1057	296	11	where	where	SCONJ
m-1057	296	12	past	past	ADJ
m-1057	296	13	values	value	NOUN
m-1057	296	14	of	of	ADP
m-1057	296	15			PROPN
m-1057	296	16	s	s	PUNCT
m-1057	296	17	impact	impact	VERB
m-1057	296	18	present	present	ADJ
m-1057	296	19			NOUN
m-1057	296	20	t	t	NUM
m-1057	296	21	.	.	PUNCT
m-1057	297	1			PUNCT
m-1057	298	1	the	the	DET
m-1057	298	2	integral	integral	ADJ
m-1057	298	3	equation	equation	NOUN
m-1057	298	4	can	can	AUX
m-1057	298	5	be	be	AUX
m-1057	298	6	approximated	approximate	VERB
m-1057	298	7	numerically	numerically	ADV
m-1057	298	8	(	(	PUNCT
m-1057	298	9	e.g.	e.g.	ADJ
m-1057	298	10	,	,	PUNCT
m-1057	298	11	trapezoidal	trapezoidal	ADJ
m-1057	298	12	rule	rule	NOUN
m-1057	298	13	or	or	CCONJ
m-1057	298	14	fixed	fix	VERB
m-1057	298	15	point	point	NOUN
m-1057	298	16	iteration	iteration	NOUN
m-1057	298	17	)	)	PUNCT
m-1057	298	18	.	.	PUNCT
m-1057	299	1			PUNCT
m-1057	300	1	the	the	DET
m-1057	300	2	result	result	NOUN
m-1057	300	3	is	be	AUX
m-1057	300	4	a	a	DET
m-1057	300	5	reduced	reduce	VERB
m-1057	300	6	-	-	PUNCT
m-1057	300	7	order	order	NOUN
m-1057	300	8	approximation	approximation	NOUN
m-1057	300	9	to	to	ADP
m-1057	300	10	the	the	DET
m-1057	300	11	original	original	ADJ
m-1057	300	12	pde	pde	NOUN
m-1057	300	13	using	use	VERB
m-1057	300	14	the	the	DET
m-1057	300	15	semigroup	semigroup	ADJ
m-1057	300	16	eigenfunction	eigenfunction	NOUN
m-1057	300	17	method	method	NOUN
m-1057	300	18	.	.	PUNCT
m-1057	301	1	ijo	ijo	PROPN
m-1057	301	2	journals	journal	NOUN
m-1057	301	3	volume	volume	NOUN
m-1057	301	4	08	08	NUM
m-1057	302	1	|	|	ADV
m-1057	302	2	issue	issue	VERB
m-1057	302	3	04	04	NUM
m-1057	303	1	|	|	CCONJ
m-1057	303	2	april	april	PROPN
m-1057	303	3	2025	2025	NUM
m-1057	303	4	|	|	ADV
m-1057	303	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1057	303	6	35	35	NUM
m-1057	303	7	ijo	ijo	PROPN
m-1057	303	8	international	international	ADJ
m-1057	303	9	journal	journal	PROPN
m-1057	303	10	of	of	ADP
m-1057	303	11	mathematics	mathematics	PROPN
m-1057	303	12	(	(	PUNCT
m-1057	303	13	issn	issn	PROPN
m-1057	303	14	:	:	PUNCT
m-1057	303	15	2992	2992	NUM
m-1057	303	16	-	-	SYM
m-1057	303	17	4421	4421	NUM
m-1057	303	18	)	)	PUNCT
m-1057	303	19	otobong	otobong	PROPN
m-1057	303	20	j.	j.	PROPN
m-1057	303	21	tom1	tom1	PROPN
m-1057	304	1	*	*	PUNCT
m-1057	304	2	https://ijojournals.com/	https://ijojournals.com/	PROPN
m-1057	304	3	volume	volume	NOUN
m-1057	304	4	08	08	NUM
m-1057	304	5	||	||	PROPN
m-1057	304	6	issue	issue	NOUN
m-1057	304	7	04	04	NUM
m-1057	304	8	||	||	NOUN
m-1057	304	9	april	april	PROPN
m-1057	304	10	,	,	PUNCT
m-1057	304	11	2025	2025	NUM
m-1057	304	12	||	||	PUNCT
m-1057	305	1	“	"	PUNCT
m-1057	305	2	semigroup	semigroup	ADJ
m-1057	305	3	approach	approach	NOUN
m-1057	305	4	for	for	ADP
m-1057	305	5	the	the	DET
m-1057	305	6	solution	solution	NOUN
m-1057	305	7	of	of	ADP
m-1057	305	8	boundary	boundary	ADJ
m-1057	305	9	layer	layer	NOUN
m-1057	305	10	equation	equation	NOUN
m-1057	305	11	with	with	ADP
m-1057	305	12	sinc	sinc	ADJ
m-1057	305	13	function	function	NOUN
m-1057	305	14	term	term	NOUN
m-1057	305	15	"	"	PUNCT
m-1057	305	16	7	7	NUM
m-1057	305	17	.	.	PUNCT
m-1057	305	18	conclusion	conclusion	NOUN
m-1057	305	19	we	we	PRON
m-1057	305	20	have	have	AUX
m-1057	305	21	successfully	successfully	ADV
m-1057	305	22	establish	establish	VERB
m-1057	305	23	a	a	DET
m-1057	305	24	pattern	pattern	NOUN
m-1057	305	25	for	for	ADP
m-1057	305	26	solving	solve	VERB
m-1057	305	27	boundary	boundary	ADJ
m-1057	305	28	layer	layer	NOUN
m-1057	305	29	equations	equation	NOUN
m-1057	305	30	incoperatingsinc	incoperatingsinc	VERB
m-1057	305	31	function	function	VERB
m-1057	305	32	in	in	ADP
m-1057	305	33	the	the	DET
m-1057	305	34	forcing	force	VERB
m-1057	305	35	term	term	NOUN
m-1057	305	36	using	use	VERB
m-1057	305	37	semigroup	semigroup	PROPN
m-1057	305	38	theory	theory	NOUN
m-1057	305	39	.	.	PUNCT
m-1057	306	1	the	the	DET
m-1057	306	2	major	major	ADJ
m-1057	306	3	results	result	NOUN
m-1057	306	4	include	include	VERB
m-1057	306	5	the	the	DET
m-1057	306	6	wellposedness	wellposedness	NOUN
m-1057	306	7	,	,	PUNCT
m-1057	306	8	regularity	regularity	NOUN
m-1057	306	9	and	and	CCONJ
m-1057	306	10	the	the	DET
m-1057	306	11	decay	decay	NOUN
m-1057	306	12	rate	rate	NOUN
m-1057	306	13	of	of	ADP
m-1057	306	14	the	the	DET
m-1057	306	15	solutions	solution	NOUN
m-1057	306	16	,	,	PUNCT
m-1057	306	17	along	along	ADP
m-1057	306	18	with	with	ADP
m-1057	306	19	detailed	detailed	ADJ
m-1057	306	20	analysis	analysis	NOUN
m-1057	306	21	of	of	ADP
m-1057	306	22	the	the	DET
m-1057	306	23	role	role	NOUN
m-1057	306	24	of	of	ADP
m-1057	306	25	the	the	DET
m-1057	306	26	sinc	sinc	PROPN
m-1057	306	27	function	function	NOUN
m-1057	306	28	term	term	NOUN
m-1057	306	29	in	in	ADP
m-1057	306	30	these	these	DET
m-1057	306	31	equations	equation	NOUN
m-1057	306	32	.	.	PUNCT
m-1057	307	1	this	this	DET
m-1057	307	2	layout	layout	NOUN
m-1057	307	3	paves	pave	VERB
m-1057	307	4	way	way	NOUN
m-1057	307	5	for	for	ADP
m-1057	307	6	further	further	ADJ
m-1057	307	7	exploration	exploration	NOUN
m-1057	307	8	into	into	ADP
m-1057	307	9	numerical	numerical	ADJ
m-1057	307	10	methods	method	NOUN
m-1057	307	11	,	,	PUNCT
m-1057	307	12	such	such	ADJ
m-1057	307	13	as	as	ADP
m-1057	307	14	the	the	DET
m-1057	307	15	use	use	NOUN
m-1057	307	16	of	of	ADP
m-1057	307	17	sinc	sinc	NOUN
m-1057	307	18	functions	function	NOUN
m-1057	307	19	in	in	ADP
m-1057	307	20	discretization	discretization	NOUN
m-1057	307	21	schemes	scheme	NOUN
m-1057	307	22	,	,	PUNCT
m-1057	307	23	and	and	CCONJ
m-1057	307	24	also	also	ADV
m-1057	307	25	have	have	VERB
m-1057	307	26	applications	application	NOUN
m-1057	307	27	in	in	ADP
m-1057	307	28	modeling	model	VERB
m-1057	307	29	physical	physical	ADJ
m-1057	307	30	systems	system	NOUN
m-1057	307	31	with	with	ADP
m-1057	307	32	oscillatory	oscillatory	ADJ
m-1057	307	33	boundary	boundary	ADJ
m-1057	307	34	conditions	condition	NOUN
m-1057	307	35	.	.	PUNCT
m-1057	308	1	illustrative	illustrative	ADJ
m-1057	308	2	examples	example	NOUN
m-1057	308	3	have	have	AUX
m-1057	308	4	been	be	AUX
m-1057	308	5	shown	show	VERB
m-1057	308	6	to	to	PART
m-1057	308	7	validate	validate	VERB
m-1057	308	8	the	the	DET
m-1057	308	9	approach	approach	NOUN
m-1057	308	10	and	and	CCONJ
m-1057	308	11	applicability	applicability	NOUN
m-1057	308	12	.	.	PUNCT
m-1057	309	1	references	reference	NOUN
m-1057	309	2	[	[	X
m-1057	309	3	1	1	NUM
m-1057	309	4	]	]	PUNCT
m-1057	309	5	prandtl	prandtl	NOUN
m-1057	309	6	,	,	PUNCT
m-1057	309	7	l.	l.	PROPN
m-1057	309	8	on	on	ADP
m-1057	309	9	the	the	DET
m-1057	309	10	motion	motion	NOUN
m-1057	309	11	of	of	ADP
m-1057	309	12	fluids	fluid	NOUN
m-1057	309	13	with	with	ADP
m-1057	309	14	very	very	ADV
m-1057	309	15	little	little	ADJ
m-1057	309	16	viscosity	viscosity	NOUN
m-1057	309	17	,	,	PUNCT
m-1057	309	18	in	in	ADP
m-1057	309	19	proceedings	proceeding	NOUN
m-1057	309	20	of	of	ADP
m-1057	309	21	the	the	DET
m-1057	309	22	third	third	ADJ
m-1057	309	23	international	international	PROPN
m-1057	309	24	congress	congress	PROPN
m-1057	309	25	of	of	ADP
m-1057	309	26	mathematicians	mathematician	NOUN
m-1057	309	27	,	,	PUNCT
m-1057	309	28	heidelberg	heidelberg	PROPN
m-1057	309	29	,	,	PUNCT
m-1057	309	30	germany	germany	PROPN
m-1057	309	31	,	,	PUNCT
m-1057	309	32	(	(	PUNCT
m-1057	309	33	1964	1964	NUM
m-1057	309	34	)	)	PUNCT
m-1057	309	35	,	,	PUNCT
m-1057	309	36	484	484	NUM
m-1057	309	37	-	-	SYM
m-1057	309	38	491	491	NUM
m-1057	309	39	.	.	PUNCT
m-1057	310	1	[	[	X
m-1057	310	2	2	2	NUM
m-1057	310	3	]	]	PUNCT
m-1057	310	4	hille	hille	PROPN
m-1057	310	5	,	,	PUNCT
m-1057	310	6	e.	e.	PROPN
m-1057	310	7	and	and	CCONJ
m-1057	310	8	phillips	phillips	PROPN
m-1057	310	9	,	,	PUNCT
m-1057	310	10	r.	r.	PROPN
m-1057	310	11	s	s	PROPN
m-1057	310	12	,	,	PUNCT
m-1057	310	13	functional	functional	ADJ
m-1057	310	14	analysis	analysis	NOUN
m-1057	310	15	analysis	analysis	NOUN
m-1057	310	16	and	and	CCONJ
m-1057	310	17	semi	semi	NOUN
m-1057	310	18	-	-	NOUN
m-1057	310	19	groups	group	NOUN
m-1057	310	20	.	.	PUNCT
m-1057	311	1	ams	am	NOUN
m-1057	311	2	colloquium	colloquium	NOUN
m-1057	311	3	publication	publication	NOUN
m-1057	311	4	,	,	PUNCT
m-1057	311	5	vol	vol	NOUN
m-1057	311	6	.	.	PROPN
m-1057	311	7	32	32	NUM
m-1057	311	8	(	(	PUNCT
m-1057	311	9	1957	1957	NUM
m-1057	311	10	)	)	PUNCT
m-1057	311	11	.	.	PUNCT
m-1057	312	1	[	[	X
m-1057	312	2	3	3	X
m-1057	312	3	]	]	X
m-1057	312	4	pazy	pazy	NOUN
m-1057	312	5	a.	a.	NOUN
m-1057	312	6	,	,	PUNCT
m-1057	312	7	semigroups	semigroup	NOUN
m-1057	312	8	of	of	ADP
m-1057	312	9	linear	linear	PROPN
m-1057	312	10	operators	operator	NOUN
m-1057	312	11	and	and	CCONJ
m-1057	312	12	applications	application	NOUN
m-1057	312	13	to	to	ADP
m-1057	312	14	partial	partial	ADJ
m-1057	312	15	differential	differential	NOUN
m-1057	312	16	equations	equation	NOUN
m-1057	312	17	,	,	PUNCT
m-1057	312	18	springer	springer	NOUN
m-1057	312	19	-	-	PUNCT
m-1057	312	20	verlag	verlag	PROPN
m-1057	312	21	,	,	PUNCT
m-1057	312	22	applied	apply	VERB
m-1057	312	23	math	math	NOUN
m-1057	312	24	.	.	PUNCT
m-1057	313	1	sciences	science	NOUN
m-1057	313	2	,	,	PUNCT
m-1057	313	3	vol	vol	NOUN
m-1057	313	4	.	.	PROPN
m-1057	313	5	44	44	NUM
m-1057	313	6	,	,	PUNCT
m-1057	313	7	1983	1983	NUM
m-1057	313	8	.	.	PUNCT
m-1057	314	1	[	[	X
m-1057	314	2	4	4	NUM
m-1057	314	3	]	]	X
m-1057	314	4	temam	temam	NOUN
m-1057	314	5	,	,	PUNCT
m-1057	314	6	r.	r.	PROPN
m-1057	314	7	,	,	PUNCT
m-1057	314	8	infinite	infinite	ADJ
m-1057	314	9	-	-	PUNCT
m-1057	314	10	dimensional	dimensional	ADJ
m-1057	314	11	dynamical	dynamical	ADJ
m-1057	314	12	system	system	NOUN
m-1057	314	13	in	in	ADP
m-1057	314	14	mechanics	mechanic	NOUN
m-1057	314	15	and	and	CCONJ
m-1057	314	16	physics	physics	PROPN
m-1057	314	17	.	.	PUNCT
m-1057	314	18	springerverlag	springerverlag	PROPN
m-1057	314	19	1997	1997	NUM
m-1057	314	20	.	.	PUNCT
m-1057	315	1	[	[	X
m-1057	315	2	5	5	X
m-1057	315	3	]	]	PUNCT
m-1057	315	4	l.	l.	PROPN
m-1057	315	5	c.	c.	PROPN
m-1057	315	6	evans	evans	PROPN
m-1057	315	7	,	,	PUNCT
m-1057	315	8	partial	partial	ADJ
m-1057	315	9	differential	differential	NOUN
m-1057	315	10	equations	equation	NOUN
m-1057	315	11	,	,	PUNCT
m-1057	315	12	graduate	graduate	NOUN
m-1057	315	13	studies	study	NOUN
m-1057	315	14	in	in	ADP
m-1057	315	15	mathematics	mathematic	NOUN
m-1057	315	16	,	,	PUNCT
m-1057	315	17	vol	vol	NOUN
m-1057	315	18	.	.	PROPN
m-1057	315	19	19	19	NUM
m-1057	315	20	,	,	PUNCT
m-1057	315	21	ams	am	NOUN
m-1057	315	22	,	,	PUNCT
m-1057	315	23	providence	providence	NOUN
m-1057	315	24	,	,	PUNCT
m-1057	315	25	rhode	rhode	NOUN
m-1057	315	26	island	island	NOUN
m-1057	315	27	,	,	PUNCT
m-1057	315	28	2002	2002	NUM
m-1057	315	29	.	.	PUNCT
m-1057	316	1	[	[	X
m-1057	316	2	6	6	NUM
m-1057	316	3	]	]	X
m-1057	316	4	henry	henry	PROPN
m-1057	316	5	,	,	PUNCT
m-1057	316	6	d.	d.	PROPN
m-1057	316	7	,	,	PUNCT
m-1057	316	8	geometric	geometric	ADJ
m-1057	316	9	theory	theory	NOUN
m-1057	316	10	of	of	ADP
m-1057	316	11	semilinear	semilinear	PROPN
m-1057	316	12	parabolic	parabolic	PROPN
m-1057	316	13	equations	equation	NOUN
m-1057	316	14	.	.	PUNCT
m-1057	317	1	lecture	lecture	NOUN
m-1057	317	2	notes	note	NOUN
m-1057	317	3	in	in	ADP
m-1057	317	4	mathematics	mathematic	NOUN
m-1057	317	5	vol	vol	NOUN
m-1057	317	6	.	.	PUNCT
m-1057	318	1	840	840	NUM
m-1057	318	2	,	,	PUNCT
m-1057	318	3	pringer	pringer	NOUN
m-1057	318	4	-	-	PUNCT
m-1057	318	5	verlag	verlag	NOUN
m-1057	318	6	,	,	PUNCT
m-1057	318	7	1981	1981	NUM
m-1057	318	8	.	.	PUNCT
m-1057	319	1	[	[	X
m-1057	319	2	7	7	X
m-1057	319	3	]	]	X
m-1057	319	4	pr	pr	PROPN
m-1057	319	5	�	�	PROPN
m-1057	319	6	̈ss	̈ss	PROPN
m-1057	319	7	,	,	PUNCT
m-1057	319	8	j.	j.	PROPN
m-1057	319	9	,	,	PUNCT
m-1057	319	10	evolutional	evolutional	ADJ
m-1057	319	11	integral	integral	ADJ
m-1057	319	12	equations	equation	NOUN
m-1057	319	13	and	and	CCONJ
m-1057	319	14	applications	application	NOUN
m-1057	319	15	.	.	PUNCT
m-1057	320	1	birkhauser	birkhauser	PROPN
m-1057	320	2	,	,	PUNCT
m-1057	320	3	(	(	PUNCT
m-1057	320	4	2015	2015	NUM
m-1057	320	5	)	)	PUNCT
m-1057	320	6	.	.	PUNCT
m-1057	321	1	[	[	X
m-1057	321	2	8	8	NUM
m-1057	321	3	]	]	X
m-1057	321	4	hussain	hussain	PROPN
m-1057	321	5	,	,	PUNCT
m-1057	321	6	s.	s.	PROPN
m-1057	321	7	,	,	PUNCT
m-1057	321	8	and	and	CCONJ
m-1057	321	9	kato	kato	PROPN
m-1057	321	10	,	,	PUNCT
m-1057	321	11	d.	d.	PROPN
m-1057	321	12	,	,	PUNCT
m-1057	321	13	semigroup	semigroup	PROPN
m-1057	321	14	-	-	PUNCT
m-1057	321	15	based	base	VERB
m-1057	321	16	numerical	numerical	ADJ
m-1057	321	17	approximations	approximation	NOUN
m-1057	321	18	for	for	ADP
m-1057	321	19	boundary	boundary	ADJ
m-1057	321	20	layer	layer	NOUN
m-1057	321	21	equations	equation	NOUN
m-1057	321	22	.	.	PUNCT
m-1057	322	1	journal	journal	NOUN
m-1057	322	2	of	of	ADP
m-1057	322	3	computational	computational	ADJ
m-1057	322	4	fluid	fluid	ADJ
m-1057	322	5	dynamics	dynamic	NOUN
m-1057	322	6	,	,	PUNCT
m-1057	322	7	40(3	40(3	NUM
m-1057	322	8	)	)	PUNCT
m-1057	322	9	(	(	PUNCT
m-1057	322	10	2022	2022	NUM
m-1057	322	11	)	)	PUNCT
m-1057	322	12	785	785	NUM
m-1057	322	13	-	-	SYM
m-1057	322	14	810	810	NUM
m-1057	322	15	.	.	PUNCT
m-1057	323	1	[	[	X
m-1057	323	2	10	10	NUM
m-1057	323	3	]	]	X
m-1057	323	4	lund	lund	PROPN
m-1057	323	5	,	,	PUNCT
m-1057	323	6	j.	j.	PROPN
m-1057	323	7	,	,	PUNCT
m-1057	323	8	and	and	CCONJ
m-1057	323	9	bowers	bower	NOUN
m-1057	323	10	,	,	PUNCT
m-1057	323	11	d.	d.	PROPN
m-1057	323	12	,sinc	,sinc	PUNCT
m-1057	323	13	method	method	NOUN
m-1057	323	14	for	for	ADP
m-1057	323	15	quadrature	quadrature	NOUN
m-1057	323	16	and	and	CCONJ
m-1057	323	17	differential	differential	ADJ
m-1057	323	18	equations	equation	NOUN
m-1057	323	19	.	.	PUNCT
m-1057	324	1	siam	siam	PROPN
m-1057	324	2	(	(	PUNCT
m-1057	324	3	1992	1992	NUM
m-1057	324	4	)	)	PUNCT
m-1057	324	5	.	.	PUNCT
m-1057	325	1	[	[	X
m-1057	325	2	11	11	NUM
m-1057	325	3	]	]	SYM
m-1057	325	4	stenger	stenger	PROPN
m-1057	325	5	,	,	PUNCT
m-1057	325	6	f.	f.	PROPN
m-1057	325	7	numerical	numerical	PROPN
m-1057	325	8	methods	method	NOUN
m-1057	325	9	based	base	VERB
m-1057	325	10	on	on	ADP
m-1057	325	11	sinc	sinc	ADJ
m-1057	325	12	and	and	CCONJ
m-1057	325	13	analytic	analytic	ADJ
m-1057	325	14	functions	function	NOUN
m-1057	325	15	.	.	PUNCT
m-1057	326	1	springer	springer	NOUN
m-1057	326	2	,	,	PUNCT
m-1057	326	3	berlin	berlin	PROPN
m-1057	326	4	,	,	PUNCT
m-1057	326	5	new	new	PROPN
m-1057	326	6	york	york	PROPN
m-1057	326	7	,	,	PUNCT
m-1057	326	8	(	(	PUNCT
m-1057	326	9	1993	1993	NUM
m-1057	326	10	)	)	PUNCT
m-1057	326	11	.	.	PUNCT
m-1057	327	1	[	[	X
m-1057	327	2	12	12	NUM
m-1057	327	3	]	]	X
m-1057	327	4	john	john	PROPN
m-1057	327	5	,	,	PUNCT
m-1057	327	6	e.	e.	PROPN
m-1057	327	7	d.	d.	PROPN
m-1057	327	8	&	&	CCONJ
m-1057	327	9	ogbonna	ogbonna	PROPN
m-1057	327	10	,	,	PUNCT
m-1057	327	11	n.	n.	PROPN
m-1057	327	12	a	a	DET
m-1057	327	13	double	double	ADJ
m-1057	327	14	exponential	exponential	NOUN
m-1057	327	15	sinc	sinc	NOUN
m-1057	327	16	collocation	collocation	NOUN
m-1057	327	17	method	method	NOUN
m-1057	327	18	for	for	ADP
m-1057	327	19	volterrafredholm	volterrafredholm	ADJ
m-1057	327	20	integral	integral	ADJ
m-1057	327	21	equations	equation	NOUN
m-1057	327	22	of	of	ADP
m-1057	327	23	the	the	DET
m-1057	327	24	second	second	ADJ
m-1057	327	25	kind	kind	NOUN
m-1057	327	26	,	,	PUNCT
m-1057	327	27	j.	j.	PROPN
m-1057	327	28	math	math	PROPN
m-1057	327	29	.	.	PUNCT
m-1057	328	1	soc	soc	PROPN
m-1057	328	2	.	.	PUNCT
m-1057	329	1	35	35	NUM
m-1057	329	2	(	(	PUNCT
m-1057	329	3	2016	2016	NUM
m-1057	329	4	)	)	PUNCT
m-1057	329	5	408	408	NUM
m-1057	329	6	-	-	SYM
m-1057	329	7	423	423	NUM
m-1057	329	8	.	.	PUNCT
m-1057	330	1	[	[	X
m-1057	330	2	13	13	NUM
m-1057	330	3	]	]	PUNCT
m-1057	330	4	s.	s.	PROPN
m-1057	330	5	kesavan	kesavan	PROPN
m-1057	330	6	,	,	PUNCT
m-1057	330	7	topics	topic	NOUN
m-1057	330	8	in	in	ADP
m-1057	330	9	functional	functional	ADJ
m-1057	330	10	analysis	analysis	NOUN
m-1057	330	11	and	and	CCONJ
m-1057	330	12	applications	application	NOUN
m-1057	330	13	,	,	PUNCT
m-1057	330	14	new	new	ADJ
m-1057	330	15	age	age	NOUN
m-1057	330	16	international	international	ADJ
m-1057	330	17	(	(	PUNCT
m-1057	330	18	p	p	NOUN
m-1057	330	19	)	)	PUNCT
m-1057	330	20	limited	limited	ADJ
m-1057	330	21	,	,	PUNCT
m-1057	330	22	new	new	ADJ
m-1057	330	23	delhi	delhi	PROPN
m-1057	330	24	,	,	PUNCT
m-1057	330	25	(	(	PUNCT
m-1057	330	26	2003	2003	NUM
m-1057	330	27	)	)	PUNCT
m-1057	330	28	.	.	PUNCT
m-1057	331	1	[	[	X
m-1057	331	2	14	14	NUM
m-1057	331	3	]	]	PUNCT
m-1057	331	4	haim	haim	PROPN
m-1057	331	5	brezis	brezis	NOUN
m-1057	331	6	,	,	PUNCT
m-1057	331	7	functional	functional	ADJ
m-1057	331	8	analysis	analysis	NOUN
m-1057	331	9	,	,	PUNCT
m-1057	331	10	sobolev	sobolev	NOUN
m-1057	331	11	spaces	space	NOUN
m-1057	331	12	and	and	CCONJ
m-1057	331	13	partial	partial	ADJ
m-1057	331	14	differential	differential	NOUN
m-1057	331	15	equations	equation	NOUN
m-1057	331	16	,	,	PUNCT
m-1057	331	17	universitext	universitext	PROPN
m-1057	331	18	.	.	PUNCT
m-1057	331	19	springer	springer	PROPN
m-1057	331	20	,	,	PUNCT
m-1057	331	21	new	new	PROPN
m-1057	331	22	york	york	PROPN
m-1057	331	23	,	,	PUNCT
m-1057	331	24	(	(	PUNCT
m-1057	331	25	2011	2011	NUM
m-1057	331	26	)	)	PUNCT
m-1057	331	27	.	.	PUNCT
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m-1057	332	3	volume	volume	NOUN
m-1057	332	4	08	08	NUM
m-1057	333	1	|	|	ADV
m-1057	333	2	issue	issue	VERB
m-1057	333	3	04	04	NUM
m-1057	334	1	|	|	CCONJ
m-1057	334	2	april	april	PROPN
m-1057	334	3	2025	2025	NUM
m-1057	334	4	|	|	ADV
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m-1057	334	6	36	36	NUM
m-1057	334	7	ijo	ijo	PROPN
m-1057	334	8	international	international	PROPN
m-1057	334	9	journal	journal	PROPN
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m-1057	334	11	mathematics	mathematics	PROPN
m-1057	334	12	(	(	PUNCT
m-1057	334	13	issn	issn	PROPN
m-1057	334	14	:	:	PUNCT
m-1057	334	15	2992	2992	NUM
m-1057	334	16	-	-	SYM
m-1057	334	17	4421	4421	NUM
m-1057	334	18	)	)	PUNCT
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m-1057	334	20	j.	j.	PROPN
m-1057	334	21	tom1	tom1	PROPN
m-1057	335	1	*	*	PUNCT
m-1057	335	2	https://ijojournals.com/	https://ijojournals.com/	PROPN
m-1057	335	3	volume	volume	NOUN
m-1057	335	4	08	08	NUM
m-1057	335	5	||	||	PROPN
m-1057	335	6	issue	issue	NOUN
m-1057	335	7	04	04	NUM
m-1057	335	8	||	||	NOUN
m-1057	335	9	april	april	PROPN
m-1057	335	10	,	,	PUNCT
m-1057	335	11	2025	2025	NUM
m-1057	335	12	||	||	PUNCT
m-1057	336	1	“	"	PUNCT
m-1057	336	2	semigroup	semigroup	ADJ
m-1057	336	3	approach	approach	NOUN
m-1057	336	4	for	for	ADP
m-1057	336	5	the	the	DET
m-1057	336	6	solution	solution	NOUN
m-1057	336	7	of	of	ADP
m-1057	336	8	boundary	boundary	ADJ
m-1057	336	9	layer	layer	NOUN
m-1057	336	10	equation	equation	NOUN
m-1057	336	11	with	with	ADP
m-1057	336	12	sinc	sinc	ADJ
m-1057	336	13	function	function	NOUN
m-1057	336	14	term	term	NOUN
m-1057	336	15	"	"	PUNCT
m-1057	336	16	[	[	X
m-1057	336	17	15	15	NUM
m-1057	336	18	]	]	X
m-1057	336	19	michal	michal	PROPN
m-1057	336	20	rozanski	rozanski	PROPN
m-1057	336	21	,	,	PUNCT
m-1057	336	22	beatasikora	beatasikora	NOUN
m-1057	336	23	,	,	PUNCT
m-1057	336	24	andriansmuda	andriansmuda	NOUN
m-1057	336	25	,	,	PUNCT
m-1057	336	26	and	and	CCONJ
m-1057	336	27	roman	roman	ADJ
m-1057	336	28	witula	witula	NOUN
m-1057	336	29	.	.	PUNCT
m-1057	337	1	on	on	ADP
m-1057	337	2	theoretical	theoretical	ADJ
m-1057	337	3	and	and	CCONJ
m-1057	337	4	practical	practical	ADJ
m-1057	337	5	aspect	aspect	NOUN
m-1057	337	6	of	of	ADP
m-1057	337	7	duhamel	duhamel	PROPN
m-1057	337	8	’s	’s	PART
m-1057	337	9	integral	integral	ADJ
m-1057	337	10	.	.	PUNCT
m-1057	337	11	archives	archive	NOUN
m-1057	337	12	of	of	ADP
m-1057	337	13	control	control	NOUN
m-1057	337	14	sciences	sciences	PROPN
m-1057	337	15	,	,	PUNCT
m-1057	337	16	vol	vol	NOUN
m-1057	337	17	.	.	PUNCT
m-1057	338	1	31(lxvii	31(lxvii	NUM
m-1057	338	2	)	)	PUNCT
m-1057	338	3	,	,	PUNCT
m-1057	339	1	no	no	INTJ
m-1057	339	2	.	.	NOUN
m-1057	339	3	4	4	NUM
m-1057	339	4	,	,	PUNCT
m-1057	339	5	(	(	PUNCT
m-1057	339	6	2021	2021	NUM
m-1057	339	7	)	)	PUNCT
m-1057	339	8	815	815	NUM
m-1057	339	9	-	-	SYM
m-1057	339	10	847	847	NUM
m-1057	339	11	.	.	PUNCT
m-1057	340	1	[	[	X
m-1057	340	2	16	16	NUM
m-1057	340	3	]	]	X
m-1057	340	4	duchesne	duchesne	NOUN
m-1057	340	5	,	,	PUNCT
m-1057	340	6	g.	g.	PROPN
m-1057	340	7	w.	w.	PROPN
m-1057	340	8	,	,	PUNCT
m-1057	340	9	lessard	lessard	PROPN
m-1057	340	10	,	,	PUNCT
m-1057	340	11	jp	jp	NOUN
m-1057	340	12	.	.	PROPN
m-1057	340	13	&	&	CCONJ
m-1057	340	14	takayasu	takayasu	PROPN
m-1057	340	15	.	.	PUNCT
m-1057	341	1	a.	a.	NOUN
m-1057	342	1	a	a	DET
m-1057	342	2	rigorous	rigorous	ADJ
m-1057	342	3	integrator	integrator	NOUN
m-1057	342	4	and	and	CCONJ
m-1057	342	5	global	global	ADJ
m-1057	342	6	existence	existence	NOUN
m-1057	342	7	for	for	ADP
m-1057	342	8	higher	higher	ADV
m-1057	342	9	-	-	PUNCT
m-1057	342	10	dimensional	dimensional	ADJ
m-1057	342	11	semilinear	semilinear	ADJ
m-1057	342	12	parabolic	parabolic	NOUN
m-1057	342	13	pdes	pde	NOUN
m-1057	342	14	via	via	ADP
m-1057	342	15	semigroup	semigroup	PROPN
m-1057	342	16	theory	theory	PROPN
m-1057	342	17	.	.	PUNCT
m-1057	343	1	j	j	PROPN
m-1057	343	2	scicomput	scicomput	NOUN
m-1057	343	3	.	.	PUNCT
m-1057	344	1	102(62	102(62	NUM
m-1057	344	2	)	)	PUNCT
m-1057	344	3	(	(	PUNCT
m-1057	344	4	2025	2025	NUM
m-1057	344	5	)	)	PUNCT
m-1057	344	6	.	.	PUNCT
m-1057	345	1	[	[	X
m-1057	345	2	17	17	NUM
m-1057	345	3	]	]	X
m-1057	345	4	royden	royden	PROPN
m-1057	345	5	,	,	PUNCT
m-1057	345	6	h.	h.	PROPN
m-1057	345	7	l.	l.	PROPN
m-1057	345	8	,	,	PUNCT
m-1057	345	9	and	and	CCONJ
m-1057	345	10	fitzpatrick	fitzpatrick	PROPN
m-1057	345	11	,	,	PUNCT
m-1057	345	12	p.	p.	NOUN
m-1057	345	13	m.	m.	NOUN
m-1057	346	1	real	real	ADJ
m-1057	346	2	analysis	analysis	NOUN
m-1057	346	3	.	.	PUNCT
m-1057	347	1	4th	4th	ADJ
m-1057	347	2	ed	ed	NOUN
m-1057	347	3	.	.	PROPN
m-1057	347	4	,	,	PUNCT
m-1057	347	5	pearson	pearson	PROPN
m-1057	347	6	,	,	PUNCT
m-1057	347	7	2010	2010	NUM
m-1057	347	8	.	.	PUNCT
m-1057	348	1	[	[	X
m-1057	348	2	18	18	NUM
m-1057	348	3	]	]	X
m-1057	348	4	klaus	klaus	NOUN
m-1057	348	5	-	-	PUNCT
m-1057	348	6	jochenengel	jochenengel	PROPN
m-1057	348	7	and	and	CCONJ
m-1057	348	8	rainernagel	rainernagel	NOUN
m-1057	348	9	.	.	PUNCT
m-1057	349	1	one	one	NUM
m-1057	349	2	-	-	PUNCT
m-1057	349	3	parameter	parameter	NOUN
m-1057	349	4	semigroups	semigroup	NOUN
m-1057	349	5	for	for	ADP
m-1057	349	6	linear	linear	PROPN
m-1057	349	7	evolution	evolution	NOUN
m-1057	349	8	equations	equation	NOUN
m-1057	349	9	.	.	PUNCT
m-1057	350	1	springer(2000	springer(2000	NUM
m-1057	350	2	)	)	PUNCT
m-1057	350	3	.	.	PUNCT
m-1057	351	1	[	[	X
m-1057	351	2	19	19	NUM
m-1057	351	3	]	]	X
m-1057	351	4	lunardi	lunardi	NOUN
m-1057	351	5	a.	a.	NOUN
m-1057	351	6	analytic	analytic	ADJ
m-1057	351	7	semigroups	semigroup	NOUN
m-1057	351	8	and	and	CCONJ
m-1057	351	9	optimal	optimal	ADJ
m-1057	351	10	regurity	regurity	NOUN
m-1057	351	11	in	in	ADP
m-1057	351	12	parabolic	parabolic	ADJ
m-1057	351	13	problems	problem	NOUN
m-1057	351	14	.	.	PUNCT
m-1057	352	1	birkhauser	birkhaus	ADJ
m-1057	352	2	,	,	PUNCT
m-1057	352	3	(	(	PUNCT
m-1057	352	4	1995	1995	NUM
m-1057	352	5	)	)	PUNCT
m-1057	352	6	.	.	PUNCT
m-1057	353	1	[	[	X
m-1057	353	2	20	20	NUM
m-1057	353	3	]	]	SYM
m-1057	353	4	kato	kato	PROPN
m-1057	353	5	,	,	PUNCT
m-1057	353	6	t.	t.	NOUN
m-1057	353	7	perturbation	perturbation	NOUN
m-1057	353	8	theory	theory	NOUN
m-1057	353	9	for	for	ADP
m-1057	353	10	linear	linear	PROPN
m-1057	353	11	operators	operator	NOUN
m-1057	353	12	.	.	PUNCT
m-1057	354	1	springer	springer	NOUN
m-1057	354	2	-	-	PUNCT
m-1057	354	3	verlag	verlag	PROPN
m-1057	354	4	1980	1980	NUM
m-1057	354	5	.	.	PUNCT
m-1057	355	1	[	[	X
m-1057	355	2	21	21	NUM
m-1057	355	3	]	]	X
m-1057	355	4	de	de	X
m-1057	355	5	branges	brange	NOUN
m-1057	355	6	,	,	PUNCT
m-1057	355	7	l.	l.	PROPN
m-1057	355	8	hilbert	hilbert	PROPN
m-1057	355	9	spaces	space	NOUN
m-1057	355	10	of	of	ADP
m-1057	355	11	entire	entire	ADJ
m-1057	355	12	functions	function	NOUN
m-1057	355	13	and	and	CCONJ
m-1057	355	14	applications	application	NOUN
m-1057	355	15	in	in	ADP
m-1057	355	16	fluid	fluid	ADJ
m-1057	355	17	mechanics	mechanic	NOUN
m-1057	355	18	.	.	PUNCT
m-1057	356	1	cambridge	cambridge	PROPN
m-1057	356	2	university	university	PROPN
m-1057	356	3	press	press	NOUN
m-1057	356	4	,	,	PUNCT
m-1057	356	5	(	(	PUNCT
m-1057	356	6	2015	2015	NUM
m-1057	356	7	)	)	PUNCT
m-1057	356	8	.	.	PUNCT
m-1057	357	1	[	[	X
m-1057	357	2	22	22	NUM
m-1057	357	3	]	]	PUNCT
m-1057	357	4	triebel	triebel	NOUN
m-1057	357	5	,	,	PUNCT
m-1057	357	6	h.	h.	PROPN
m-1057	357	7	interpolation	interpolation	NOUN
m-1057	357	8	theory	theory	NOUN
m-1057	357	9	,	,	PUNCT
m-1057	357	10	function	function	NOUN
m-1057	357	11	spaces	space	NOUN
m-1057	357	12	,	,	PUNCT
m-1057	357	13	differential	differential	ADJ
m-1057	357	14	operators	operator	NOUN
m-1057	357	15	.	.	PUNCT
m-1057	358	1	north	north	NOUN
m-1057	358	2	-	-	PUNCT
m-1057	358	3	holland	holland	PROPN
m-1057	358	4	,	,	PUNCT
m-1057	358	5	(	(	PUNCT
m-1057	358	6	1978	1978	NUM
m-1057	358	7	)	)	PUNCT
m-1057	358	8	.	.	PUNCT
m-1057	359	1	[	[	X
m-1057	359	2	23	23	NUM
m-1057	359	3	]	]	X
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m-1057	359	5	,	,	PUNCT
m-1057	359	6	l.	l.	PROPN
m-1057	359	7	n.	n.	PROPN
m-1057	359	8	,	,	PUNCT
m-1057	359	9	and	and	CCONJ
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m-1057	359	11	,	,	PUNCT
m-1057	359	12	j.	j.	PROPN
m-1057	359	13	a.	a.	PROPN
m-1057	359	14	the	the	DET
m-1057	359	15	exponentially	exponentially	ADV
m-1057	359	16	convergent	convergent	ADJ
m-1057	359	17	sinc	sinc	PROPN
m-1057	359	18	method	method	NOUN
m-1057	359	19	for	for	ADP
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m-1057	359	21	equations	equation	NOUN
m-1057	359	22	.	.	PUNCT
m-1057	360	1	siam	siam	PROPN
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m-1057	360	3	,	,	PUNCT
m-1057	360	4	56(3	56(3	NUM
m-1057	360	5	)	)	PUNCT
m-1057	360	6	(	(	PUNCT
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m-1057	360	8	)	)	PUNCT
m-1057	360	9	,	,	PUNCT
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m-1057	360	11	-	-	SYM
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m-1057	361	3	]	]	PUNCT
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m-1057	361	5	,	,	PUNCT
m-1057	361	6	m	m	PRON
m-1057	361	7	and	and	CCONJ
m-1057	361	8	weiss	weiss	PROPN
m-1057	361	9	,	,	PUNCT
m-1057	361	10	g.	g.	PROPN
m-1057	361	11	observation	observation	NOUN
m-1057	361	12	and	and	CCONJ
m-1057	361	13	control	control	NOUN
m-1057	361	14	for	for	ADP
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m-1057	361	16	semigroups	semigroup	NOUN
m-1057	361	17	.	.	PUNCT
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m-1057	362	2	,	,	PUNCT
m-1057	362	3	(	(	PUNCT
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m-1057	362	5	)	)	PUNCT
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m-1057	363	2	25	25	NUM
m-1057	363	3	]	]	X
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m-1057	363	5	.	.	PUNCT
m-1057	364	1	a.	a.	PROPN
m-1057	364	2	,	,	PUNCT
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m-1057	364	4	md	md	PROPN
m-1057	364	5	.	.	PROPN
m-1057	364	6	r.	r.	PROPN
m-1057	364	7	,	,	PUNCT
m-1057	364	8	akter	akter	PROPN
m-1057	364	9	h.	h.	PROPN
m-1057	364	10	,	,	PUNCT
m-1057	364	11	nahar	nahar	PROPN
m-1057	364	12	n.	n.	PROPN
m-1057	364	13	,	,	PUNCT
m-1057	364	14	andmondal	andmondal	PROPN
m-1057	364	15	s.	s.	PROPN
m-1057	364	16	a	a	DET
m-1057	364	17	study	study	NOUN
m-1057	364	18	of	of	ADP
m-1057	364	19	banach	banach	ADV
m-1057	364	20	fixed	fix	VERB
m-1057	364	21	-	-	PUNCT
m-1057	364	22	point	point	NOUN
m-1057	364	23	theorem	theorem	NOUN
m-1057	364	24	and	and	CCONJ
m-1057	364	25	it	it	PRON
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m-1057	365	5	mathematics	mathematic	NOUN
m-1057	365	6	,	,	PUNCT
m-1057	365	7	11	11	NUM
m-1057	365	8	(	(	PUNCT
m-1057	365	9	2021	2021	NUM
m-1057	365	10	)	)	PUNCT
m-1057	365	11	,	,	PUNCT
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m-1057	365	13	-	-	SYM
m-1057	365	14	174	174	NUM
m-1057	365	15	.	.	PUNCT
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m-1057	367	1	|	|	ADV
m-1057	367	2	issue	issue	VERB
m-1057	367	3	04	04	NUM
m-1057	368	1	|	|	CCONJ
m-1057	368	2	april	april	PROPN
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m-1057	369	1	|	|	ADV
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m-1057	369	3	37	37	NUM
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