id	sid	eid	entity	type
ma-55	1	1	2022	CARDINAL
ma-55	2	1	j. math	PERSON
ma-55	3	1	2 (	CARDINAL
ma-55	3	2	2022	CARDINAL
ma-55	3	3	10.28924	CARDINAL
ma-55	3	4	c. pereira1	PERSON
ma-55	3	5	geraldo m. de araújo2	PERSON
ma-55	3	6	carlos a. raposo3,∗ 1department	PERSON
ma-55	3	7	university of pará	ORG
ma-55	3	8	66113-200	DATE
ma-55	3	9	brazil	GPE
ma-55	4	1	2department	CARDINAL
ma-55	4	2	university of pará	ORG
ma-55	4	3	66075	CARDINAL
ma-55	4	4	brazil	GPE
ma-55	5	1	3department	CARDINAL
ma-55	5	2	university of são joão del-rei	ORG
ma-55	5	3	são joão del-rei	PERSON
ma-55	5	4	36307-352	DATE
ma-55	5	5	brazil	GPE
ma-55	5	6	raposo@ufsj.edu.br	PERSON
ma-55	9	1	nehari	GPE
ma-55	10	1	1	CARDINAL
ma-55	10	2	0	CARDINAL
ma-55	10	3	1,p	ORDINAL
ma-55	10	4	∇v dx	GPE
ma-55	11	1	3	CARDINAL
ma-55	12	1	0	CARDINAL
ma-55	12	2	ω×	ORG
ma-55	12	3	1.1	CARDINAL
ma-55	12	4	0	CARDINAL
ma-55	12	5	γ×	ORG
ma-55	12	6	1.2	CARDINAL
ma-55	12	7	ω	GPE
ma-55	12	8	1.3	CARDINAL
ma-55	12	9	ω	ORG
ma-55	12	10	1.1	CARDINAL
ma-55	14	1	1	CARDINAL
ma-55	14	2	2	CARDINAL
ma-55	15	1	− a(u2 x	PERSON
ma-55	15	2	0	CARDINAL
ma-55	15	3	13 nov 2021	CARDINAL
ma-55	17	1	source.1 https://adac.ee	PERSON
ma-55	18	1	j. math	PERSON
ma-55	20	1	10.28924	CARDINAL
ma-55	20	2	2a	CARDINAL
ma-55	21	1	+ h2(u	DATE
ma-55	21	2	yang et al	PERSON
ma-55	22	1	22–24	CARDINAL
ma-55	24	1	− div(f0(∇u	PERSON
ma-55	26	1	12]the	CARDINAL
ma-55	26	2	1.1	CARDINAL
ma-55	26	3	fourth	ORDINAL
ma-55	27	1	g(t	NORP
ma-55	27	2	10	CARDINAL
ma-55	28	1	1.1	CARDINAL
ma-55	30	1	11,13].a	CARDINAL
ma-55	30	2	1.1	CARDINAL
ma-55	31	1	0	CARDINAL
ma-55	32	1	1.4	CARDINAL
ma-55	32	2	hartman	PERSON
ma-55	32	3	stampacchia	GPE
ma-55	32	4	1966	DATE
ma-55	33	1	14	CARDINAL
ma-55	33	2	1.4	CARDINAL
ma-55	33	3	16	CARDINAL
ma-55	34	1	nonlinear hyperbolic variational inequalities	ORG
ma-55	35	1	hartman	PERSON
ma-55	35	2	stampacchia	GPE
ma-55	35	3	1966	DATE
ma-55	36	1	14	CARDINAL
ma-55	37	1	1982	DATE
ma-55	38	1	9	CARDINAL
ma-55	39	1	5	CARDINAL
ma-55	40	1	6	CARDINAL
ma-55	42	1	8	CARDINAL
ma-55	44	1	kikuchi-oden	PERSON
ma-55	45	1	15	CARDINAL
ma-55	46	1	18	CARDINAL
ma-55	47	1	j. math	PERSON
ma-55	49	1	10.28924	CARDINAL
ma-55	51	1	19]was	CARDINAL
ma-55	52	1	proved.in	GPE
ma-55	52	2	1.4	CARDINAL
ma-55	52	3	−|u|r−2u	DATE
ma-55	54	1	1.5	CARDINAL
ma-55	54	2	0	CARDINAL
ma-55	55	1	ω	GPE
ma-55	55	2	1.6	CARDINAL
ma-55	56	1	0	CARDINAL
ma-55	56	2	γ×	ORG
ma-55	57	1	1.7	CARDINAL
ma-55	57	2	section 2	LAW
ma-55	58	1	section 3	LAW
ma-55	59	1	1.5)-(1.7	CARDINAL
ma-55	60	1	section 5	LAW
ma-55	62	1	section 6	LAW
ma-55	63	1	2	CARDINAL
ma-55	63	2	ω	ORG
ma-55	64	1	0	CARDINAL
ma-55	64	2	qthe cylinder ω×(0	ORG
ma-55	64	3	σ	CARDINAL
ma-55	65	1	〉	CARDINAL
ma-55	67	1	1.5	CARDINAL
ma-55	68	1	∈	ORG
ma-55	68	2	0	CARDINAL
ma-55	70	1	ω	CARDINAL
ma-55	70	2	u(x	ORG
ma-55	70	3	− |u|r−2u	PERSON
ma-55	70	4	− ut	PERSON
ma-55	70	5	0	CARDINAL
ma-55	70	6	2.1	CARDINAL
ma-55	71	1	k a.e.	PERSON
ma-55	72	1	0	CARDINAL
ma-55	72	2	0	CARDINAL
ma-55	72	3	γ×	ORG
ma-55	72	4	0	CARDINAL
ma-55	72	5	2.2	CARDINAL
ma-55	72	6	ω	CARDINAL
ma-55	73	1	2.3) https://doi.org/10.28924/ada/ma.2.5 eur	MONEY
ma-55	74	1	j. math	PERSON
ma-55	76	1	10.28924	CARDINAL
ma-55	76	2	4to	ORDINAL
ma-55	76	3	1.5)-(1.7	CARDINAL
ma-55	76	4	 2 ≤	MONEY
ma-55	76	5	1	CARDINAL
ma-55	76	6	2 2 ≤	MONEY
ma-55	76	7	2n	CARDINAL
ma-55	76	8	2	CARDINAL
ma-55	76	9	2	CARDINAL
ma-55	76	10	n ≥ 3.h2	DATE
ma-55	77	1	2	CARDINAL
ma-55	77	2	1	CARDINAL
ma-55	77	3	2 2	CARDINAL
ma-55	77	4	2n	CARDINAL
ma-55	77	5	2	CARDINAL
ma-55	77	6	n ≥ 3	DATE
ma-55	78	1	0,+∞)→	DATE
ma-55	78	2	1−	CARDINAL
ma-55	78	3	0	CARDINAL
ma-55	78	4	|∇u|	GPE
ma-55	79	1	∈	PRODUCT
ma-55	81	1	0	CARDINAL
ma-55	82	1	0	CARDINAL
ma-55	84	1	0	CARDINAL
ma-55	85	1	0(ω	DATE
ma-55	88	1	2.1	CARDINAL
ma-55	89	1	sobolev poincaré	ORG
ma-55	89	2	2	CARDINAL
ma-55	89	3	1	CARDINAL
ma-55	89	4	2	CARDINAL
ma-55	89	5	2 ≤	MONEY
ma-55	89	6	2	CARDINAL
ma-55	89	7	n ≥ 3	DATE
ma-55	89	8	0	CARDINAL
ma-55	89	9	|u|p	ORG
ma-55	89	10	∈	ORG
ma-55	89	11	2.2	CARDINAL
ma-55	90	1	0(ω	DATE
ma-55	90	2	g(t	NORP
ma-55	91	1	1 2	CARDINAL
ma-55	91	2	1 2	CARDINAL
ma-55	91	3	g(t)|∇v(t)|2	ORG
ma-55	92	1	− s)|∇u(s)−∇u(t)|2ds	PERSON
ma-55	96	1	j. math	PERSON
ma-55	98	1	10.28924	CARDINAL
ma-55	100	1	payne-sattinger	PERSON
ma-55	100	2	17	CARDINAL
ma-55	104	1	20	CARDINAL
ma-55	108	1	0	CARDINAL
ma-55	109	1	1 2	CARDINAL
ma-55	109	2	|ut(t)|2 + |∆u(t)|2 + 2	PRODUCT
ma-55	111	1	+ 2	DATE
ma-55	111	2	2	CARDINAL
ma-55	111	3	∫ ω |u(t)|r	ORG
ma-55	111	4	3.1	CARDINAL
ma-55	113	1	3.2	CARDINAL
ma-55	114	1	1 2	CARDINAL
ma-55	114	2	1−	CARDINAL
ma-55	114	3	+ 2	DATE
ma-55	114	4	2	CARDINAL
ma-55	115	1	∫ ω |u(t)|r	ORG
ma-55	116	1	3.3	CARDINAL
ma-55	117	1	1 2	CARDINAL
ma-55	117	2	1−	CARDINAL
ma-55	119	1	+ 2	DATE
ma-55	119	2	2	CARDINAL
ma-55	119	3	∫ ω |u(t)|r	ORG
ma-55	120	1	3.4	CARDINAL
ma-55	121	1	j. math	PERSON
ma-55	123	1	10.28924	CARDINAL
ma-55	123	2	∈	PRODUCT
ma-55	124	1	2	CARDINAL
ma-55	124	2	1−	CARDINAL
ma-55	125	1	2	CARDINAL
ma-55	125	2	r2 |u(t)|rr	FAC
ma-55	125	3	∫ ω |u(t)|r	ORG
ma-55	126	1	3.5	CARDINAL
ma-55	126	2	nehari manifold	ORG
ma-55	126	3	∈	PRODUCT
ma-55	126	4	0	CARDINAL
ma-55	127	1	0	CARDINAL
ma-55	127	2	3.6	CARDINAL
ma-55	127	3	∈	PRODUCT
ma-55	128	1	0	CARDINAL
ma-55	128	2	1−	CARDINAL
ma-55	129	1	+ 1 2	MONEY
ma-55	130	1	3.7	CARDINAL
ma-55	131	1	21	CARDINAL
ma-55	131	2	∈	PRODUCT
ma-55	132	1	0	CARDINAL
ma-55	132	2	two	CARDINAL
ma-55	132	3	1−	CARDINAL
ma-55	134	1	+ 2	DATE
ma-55	134	2	2	CARDINAL
ma-55	134	3	∫ ω |u(t)|r	ORG
ma-55	134	4	0	CARDINAL
ma-55	134	5	3.8	CARDINAL
ma-55	134	6	1−	CARDINAL
ma-55	136	1	+ 2	DATE
ma-55	136	2	2	CARDINAL
ma-55	136	3	∫ ω |u(t)|r	ORG
ma-55	137	1	3.9	CARDINAL
ma-55	137	2	1.5)-(1.7	CARDINAL
ma-55	137	3	thatw1	PERSON
ma-55	138	1	1	CARDINAL
ma-55	139	1	∈	ORG
ma-55	143	1	j. math	PERSON
ma-55	145	1	10.28924	CARDINAL
ma-55	146	1	0	CARDINAL
ma-55	147	1	3.2	CARDINAL
ma-55	150	1	0	CARDINAL
ma-55	151	1	1 2	CARDINAL
ma-55	151	2	∫ ω |ut(t)|2 dx	ORG
ma-55	154	1	0	CARDINAL
ma-55	155	1	3.10	CARDINAL
ma-55	155	2	0	CARDINAL
ma-55	156	1	0	CARDINAL
ma-55	157	1	1−	CARDINAL
ma-55	157	2	+ 2	PERCENT
ma-55	157	3	2	CARDINAL
ma-55	157	4	∫ ω |u(t0)|r	ORG
ma-55	157	5	j(u(t0	GPE
ma-55	158	1	1 2	CARDINAL
ma-55	158	2	∫ ω |ut(t0)|2 dx	ORG
ma-55	161	1	3.10	CARDINAL
ma-55	162	1	u(t	ORG
ma-55	163	1	0	CARDINAL
ma-55	164	1	4	CARDINAL
ma-55	165	1	4.1	CARDINAL
ma-55	168	1	0	CARDINAL
ma-55	169	1	∩h3 γ(ω	GPE
ma-55	170	1	∈	ORG
ma-55	170	2	h1)-(h4	ORG
ma-55	170	3	ω×	ORG
ma-55	170	4	0	CARDINAL
ma-55	170	5	∩ l∞(0	PERSON
ma-55	170	6	4.1	CARDINAL
ma-55	170	7	4.2	CARDINAL
ma-55	170	8	4.3	CARDINAL
ma-55	171	1	k a.e.	PERSON
ma-55	172	1	0	CARDINAL
ma-55	172	2	4.4	CARDINAL
ma-55	172	3	s)∆u(s)ds	ORDINAL
ma-55	172	4	∆ut	ORG
ma-55	172	5	0	CARDINAL
ma-55	173	1	j. math	PERSON
ma-55	175	1	10.28924	CARDINAL
ma-55	175	2	0(ω	DATE
ma-55	176	1	k a.e.	PERSON
ma-55	178	1	4.1	CARDINAL
ma-55	178	2	section 5	LAW
ma-55	179	1	1.5	CARDINAL
ma-55	179	2	dependingon	ORG
ma-55	179	3	0	CARDINAL
ma-55	180	1	zero	CARDINAL
ma-55	181	1	first	ORDINAL
ma-55	183	1	16	CARDINAL
ma-55	183	2	370	CARDINAL
ma-55	184	1	0(ω	DATE
ma-55	186	1	0	CARDINAL
ma-55	188	1	g(t	NORP
ma-55	190	1	+ 1	DATE
ma-55	191	1	0	CARDINAL
ma-55	191	2	4.6	CARDINAL
ma-55	191	3	ω	DATE
ma-55	193	1	0	CARDINAL
ma-55	194	1	4.7	CARDINAL
ma-55	194	2	4.2	CARDINAL
ma-55	194	3	∈	ORG
ma-55	196	1	∈	ORG
ma-55	196	2	∈	ORG
ma-55	196	3	0(ω	DATE
ma-55	196	4	∈	ORG
ma-55	196	5	ε(t	NORP
ma-55	198	1	w)−(|uε(t)|r−2uε(t	ORG
ma-55	198	2	0 https://doi.org/10.28924/ada/ma.2.5	MONEY
ma-55	199	1	j. math	PERSON
ma-55	201	1	10.28924	CARDINAL
ma-55	202	1	4.3	CARDINAL
ma-55	203	1	uε0 ∈ w1	PERSON
ma-55	204	1	∈	ORG
ma-55	204	2	4.8	CARDINAL
ma-55	205	1	5	CARDINAL
ma-55	205	2	4.1	CARDINAL
ma-55	205	3	first	ORDINAL
ma-55	205	4	4.3	CARDINAL
ma-55	207	1	first	ORDINAL
ma-55	209	1	5.1	CARDINAL
ma-55	210	1	{wj	PERSON
ma-55	210	2	eigenfunctions	CARDINAL
ma-55	211	1	0	CARDINAL
ma-55	211	2	γ ×	ORG
ma-55	212	1	⊂	GPE
ma-55	212	2	wm	PERSON
ma-55	213	1	gεjm(t)wj	PERSON
ma-55	213	2	w)+ ∫	ORG
ma-55	213	3	− s)(∆uεm(t	PERSON
ma-55	213	4	w)ds −(|uεm(t)|r−2uεm(t	PERSON
ma-55	213	5	w	GPE
ma-55	213	6	+ 1	CARDINAL
ma-55	213	7	5.1	CARDINAL
ma-55	213	8	5.2	CARDINAL
ma-55	215	1	5.3	CARDINAL
ma-55	215	2	5.1	CARDINAL
ma-55	215	3	0	CARDINAL
ma-55	215	4	0	CARDINAL
ma-55	217	1	0	CARDINAL
ma-55	219	1	j. math	PERSON
ma-55	221	1	10.28924	CARDINAL
ma-55	221	2	105.2	CARDINAL
ma-55	222	1	first	ORDINAL
ma-55	223	1	w	ORG
ma-55	223	2	5.1	CARDINAL
ma-55	223	3	1 2 |uεmt	QUANTITY
ma-55	224	1	1	CARDINAL
ma-55	224	2	∫ ω |uεm(t)|r ln |uεm(t)|dx ]	ORG
ma-55	226	1	s)(∇uεm(s),∇uεmt	TIME
ma-55	226	2	t))ds	NORP
ma-55	227	1	5.4	CARDINAL
ma-55	227	2	0	CARDINAL
ma-55	228	1	2.2	CARDINAL
ma-55	228	2	1 2	QUANTITY
ma-55	228	3	|uεmt	GPE
ma-55	229	1	2	CARDINAL
ma-55	229	2	∫ ω |uεm(t)|r ln |uεm(t)|dx ]	ORG
ma-55	231	1	5.5	CARDINAL
ma-55	231	2	1 2	CARDINAL
ma-55	233	1	2	CARDINAL
ma-55	233	2	∫ ω |uεm(t)|r ln |uεm(t)|dx ]	ORG
ma-55	234	1	5.6	CARDINAL
ma-55	234	2	5.5	CARDINAL
ma-55	234	3	5.8	CARDINAL
ma-55	235	1	0	CARDINAL
ma-55	235	2	eεm(t	PERSON
ma-55	236	1	0 |∇uεmt	QUANTITY
ma-55	237	1	5.7	CARDINAL
ma-55	237	2	1 2	CARDINAL
ma-55	237	3	1−	CARDINAL
ma-55	238	1	2	CARDINAL
ma-55	238	2	∫ ω |uεm(t)|r ln |uεm(t)|dx ]	ORG
ma-55	239	1	0 |∇uεmt |2ds ≤ eεm(t	QUANTITY
ma-55	240	1	1 2	CARDINAL
ma-55	240	2	5.8	CARDINAL
ma-55	240	3	0	CARDINAL
ma-55	242	1	j. math	PERSON
ma-55	244	1	10.28924	CARDINAL
ma-55	245	1	5.3	CARDINAL
ma-55	245	2	0	CARDINAL
ma-55	246	1	|uεmt	GPE
ma-55	246	2	1−	CARDINAL
ma-55	247	1	2	CARDINAL
ma-55	247	2	∫ ω |uεm(t)|r ln |uεm(t)|dx	ORG
ma-55	248	1	0 |∇uεmt |2ds ≤	QUANTITY
ma-55	249	1	5.9	CARDINAL
ma-55	249	2	3.7	CARDINAL
ma-55	249	3	5.9	CARDINAL
ma-55	249	4	∆uεm	ORG
ma-55	249	5	l∞(0	GPE
ma-55	249	6	5.10	CARDINAL
ma-55	250	1	5.11	CARDINAL
ma-55	252	1	5.12	CARDINAL
ma-55	252	2	l∞(0	NORP
ma-55	252	3	0(ω	DATE
ma-55	252	4	5.13	CARDINAL
ma-55	255	1	5.14	CARDINAL
ma-55	255	2	5.13	CARDINAL
ma-55	256	1	aubin-lions	PERSON
ma-55	256	2	0	CARDINAL
ma-55	256	3	0(ω	DATE
ma-55	256	4	a.e.	GPE
ma-55	257	1	q.	GPE
ma-55	257	2	5.15	CARDINAL
ma-55	258	1	ε(t	NORP
ma-55	259	1	∈	ORG
ma-55	259	2	2	CARDINAL
ma-55	263	1	5.16)is	CARDINAL
ma-55	264	1	5.16	CARDINAL
ma-55	264	2	2 2(p	CARDINAL
ma-55	264	3	1	CARDINAL
ma-55	264	4	1	CARDINAL
ma-55	264	5	1	CARDINAL
ma-55	268	1	|∇uεm(t)|p−2∇uεm(t)−	LAW
ma-55	269	1	∇v	DATE
ma-55	270	1	∣∣∣∣ ≤	ORG
ma-55	275	1	c2 ∫	ORG
ma-55	275	2	5.17	CARDINAL
ma-55	277	1	j. math	PERSON
ma-55	279	1	10.28924	CARDINAL
ma-55	279	2	5.10	CARDINAL
ma-55	279	3	5.11	CARDINAL
ma-55	279	4	|∇uεm(t)−∇uε(t)|2 ≤ 2|∆(uεm(t)−	FAC
ma-55	279	5	t)− uεt	ORG
ma-55	279	6	t))| ≤ c3	ORG
ma-55	279	7	c3	PERSON
ma-55	280	1	∈ h1[0	GPE
ma-55	281	1	a. e.	PERSON
ma-55	281	2	0	CARDINAL
ma-55	286	1	5.18	CARDINAL
ma-55	286	2	function s → |s|r−2s ln |s| and	ORG
ma-55	286	3	5.15	CARDINAL
ma-55	289	1	q.	GPE
ma-55	289	2	5.19	CARDINAL
ma-55	289	3	5.18	CARDINAL
ma-55	289	4	5.19	CARDINAL
ma-55	289	5	1.3	CARDINAL
ma-55	289	6	12	CARDINAL
ma-55	289	7	16	CARDINAL
ma-55	290	1	5.20	CARDINAL
ma-55	290	2	5.3	CARDINAL
ma-55	290	3	second	ORDINAL
ma-55	291	1	∈	ORG
ma-55	291	2	∈	ORG
ma-55	291	3	0	CARDINAL
ma-55	291	4	γ	GPE
ma-55	292	1	5.21	CARDINAL
ma-55	292	2	1 2 |∇uεmt	QUANTITY
ma-55	293	1	∆puεmt (t),∆uεmt	GPE
ma-55	295	1	|uεm(t)|r−2uεm	ORG
ma-55	298	1	s)(∆uεm(s),∆uεmt	GPE
ma-55	298	2	t))ds	NORP
ma-55	299	1	∆puεm(t),∆uεmt	PERSON
ma-55	299	2	〉	CARDINAL
ma-55	300	1	〉	CARDINAL
ma-55	301	1	j. math	PERSON
ma-55	303	1	10.28924	CARDINAL
ma-55	303	2	j1 = ∫ ω	ORG
ma-55	303	3	2)|∇uεm(t)|p−4(∇uεm(t	CARDINAL
ma-55	303	4	∇uεmt	DATE
ma-55	304	1	∇∆uεm(t)dx.	PERSON
ma-55	305	1	1 2 |∇uεmt	QUANTITY
ma-55	305	2	〉	CARDINAL
ma-55	306	1	t)),−∆uεmt	PRODUCT
ma-55	308	1	5.22	CARDINAL
ma-55	308	2	j2 = ∫	ORG
ma-55	309	1	j3 = ∫	ORG
ma-55	311	1	s)(∆uεm(s),∆uεmt	GPE
ma-55	311	2	t))ds	NORP
ma-55	311	3	5.22	CARDINAL
ma-55	312	1	dependingon m	PERSON
ma-55	313	1	5.9	CARDINAL
ma-55	313	2	2 2(p	CARDINAL
ma-55	313	3	1	CARDINAL
ma-55	314	1	1	CARDINAL
ma-55	314	2	1	CARDINAL
ma-55	314	3	1	CARDINAL
ma-55	315	1	1)|∇uεm(t)|p−2 2(p−1	DATE
ma-55	320	1	5.23) https://doi.org/10.28924/ada/ma.2.5 eur	MONEY
ma-55	321	1	j. math	PERSON
ma-55	323	1	10.28924	CARDINAL
ma-55	323	2	∈ ω :	ORG
ma-55	323	3	∈ ω :	ORG
ma-55	324	1	5.9	CARDINAL
ma-55	324	2	|j2| ≤	MONEY
ma-55	324	3	||uεm(t)|r−2uεm	ORG
ma-55	324	4	t)|dx +	DATE
ma-55	324	5	||uεm(t)|r−2uεm	ORG
ma-55	324	6	1))−1	CARDINAL
ma-55	324	7	∫ ω	ORG
ma-55	324	8	t)|dx +	DATE
ma-55	324	9	1))−1	CARDINAL
ma-55	324	10	∫ ω	ORG
ma-55	324	11	t)|dx	DATE
ma-55	325	1	1))−2|uεm(t)|2(r−1	CARDINAL
ma-55	326	1	+ 1 8	DATE
ma-55	329	1	+ 1 4	DATE
ma-55	329	2	5.24	CARDINAL
ma-55	331	1	1))−1	CARDINAL
ma-55	331	2	1))−1x	CARDINAL
ma-55	331	3	r−1	GPE
ma-55	331	4	1	CARDINAL
ma-55	331	5	5.1	CARDINAL
ma-55	332	1	‖g	GPE
ma-55	333	1	5.9	CARDINAL
ma-55	333	2	5.1 |j3| ≤	MONEY
ma-55	333	3	g(t	NORP
ma-55	334	1	+ 1 4	DATE
ma-55	334	2	5.22)-(5.25	CARDINAL
ma-55	336	1	1 2 |∇uεmt	QUANTITY
ma-55	337	1	t)),−∆uεmt	PRODUCT
ma-55	339	1	5.26	CARDINAL
ma-55	339	2	|〈∆puεm(t),∆uεm(t)〉| ≤ ∫ ω |∇uεm(t)|p−1|∇∆uεm(t)|dx ≤ |∆uεm(t)|p−1 2(p−1	ORG
ma-55	339	3	5.27	CARDINAL
ma-55	341	1	j. math	PERSON
ma-55	343	1	10.28924	CARDINAL
ma-55	345	1	〉	CARDINAL
ma-55	345	2	0	CARDINAL
ma-55	346	1	0	CARDINAL
ma-55	347	1	1 2 |∇uεmt	QUANTITY
ma-55	348	1	t)),−∆uεmt	PRODUCT
ma-55	348	2	〉	CARDINAL
ma-55	349	1	5.28	CARDINAL
ma-55	349	2	0	CARDINAL
ma-55	349	3	5.21	CARDINAL
ma-55	349	4	0	CARDINAL
ma-55	349	5	5.29	CARDINAL
ma-55	351	1	5.30	CARDINAL
ma-55	352	1	5.31	CARDINAL
ma-55	352	2	l∞(0	GPE
ma-55	352	3	0(ω	DATE
ma-55	353	1	5.32	CARDINAL
ma-55	353	2	5.4	CARDINAL
ma-55	353	3	third	ORDINAL
ma-55	356	1	5.2	CARDINAL
ma-55	357	1	5.1	CARDINAL
ma-55	357	2	0(ω	DATE
ma-55	359	1	5.12	CARDINAL
ma-55	360	1	16	CARDINAL
ma-55	360	2	75-76	DATE
ma-55	360	3	5.2	CARDINAL
ma-55	362	1	5.33	CARDINAL
ma-55	362	2	5.31	CARDINAL
ma-55	362	3	5.33	CARDINAL
ma-55	362	4	aubin-lions	ORG
ma-55	362	5	0(ω	DATE
ma-55	362	6	a.e.	GPE
ma-55	362	7	q.	GPE
ma-55	362	8	5.34	CARDINAL
ma-55	362	9	4.1	CARDINAL
ma-55	364	1	j. math	PERSON
ma-55	366	1	10.28924	CARDINAL
ma-55	366	2	165.5	CARDINAL
ma-55	367	1	0(ω	DATE
ma-55	367	2	k a. e.	PERSON
ma-55	367	3	t ∈	ORG
ma-55	367	4	0	CARDINAL
ma-55	368	1	4.6)1follows	DATE
ma-55	368	2	∫ t 0	ORG
ma-55	368	3	uεtt	NORP
ma-55	372	1	g(t	NORP
ma-55	372	2	− s)∆uε(s)ds	PERSON
ma-55	373	1	−∆uεt	ORG
ma-55	375	1	1	CARDINAL
ma-55	375	2	ε ∫	ORG
ma-55	376	1	1	CARDINAL
ma-55	376	2	ε ∫	ORG
ma-55	376	3	0	CARDINAL
ma-55	376	4	5.35	CARDINAL
ma-55	376	5	∈	ORG
ma-55	376	6	5.11	CARDINAL
ma-55	376	7	5.12	CARDINAL
ma-55	376	8	5.15	CARDINAL
ma-55	376	9	5.20	CARDINAL
ma-55	376	10	5.30	CARDINAL
ma-55	376	11	5.31	CARDINAL
ma-55	376	12	5.33	CARDINAL
ma-55	376	13	5.34	CARDINAL
ma-55	376	14	l∞(r+;h1	ORG
ma-55	376	15	5.36	CARDINAL
ma-55	378	1	5.37	CARDINAL
ma-55	378	2	0(ω))and	DATE
ma-55	378	3	a.e.	GPE
ma-55	379	1	5.38	CARDINAL
ma-55	379	2	5.39	CARDINAL
ma-55	379	3	5.40	CARDINAL
ma-55	379	4	5.41	CARDINAL
ma-55	379	5	5.42	CARDINAL
ma-55	379	6	0(ω	DATE
ma-55	379	7	a.e.	GPE
ma-55	380	1	q.	GPE
ma-55	380	2	5.43	CARDINAL
ma-55	380	3	5.35	CARDINAL
ma-55	382	1	4.1	CARDINAL
ma-55	383	1	5.10)-(5.16	DATE
ma-55	383	2	5.30)-(5.32	CARDINAL
ma-55	383	3	5.1	CARDINAL
ma-55	383	4	g(t	NORP
ma-55	383	5	− |uε|r−2uε	PERSON
ma-55	384	1	0	CARDINAL
ma-55	385	1	5.44	CARDINAL
ma-55	387	1	g(t	NORP
ma-55	388	1	5.45	CARDINAL
ma-55	388	2	0	CARDINAL
ma-55	390	1	j. math	PERSON
ma-55	392	1	10.28924	CARDINAL
ma-55	392	2	5.45	CARDINAL
ma-55	394	1	5.46	CARDINAL
ma-55	394	2	5.45	CARDINAL
ma-55	395	1	0 ≤	MONEY
ma-55	395	2	5.47	CARDINAL
ma-55	397	1	5.48	CARDINAL
ma-55	397	2	− β(ϕ	PERSON
ma-55	397	3	0(ω	DATE
ma-55	400	1	β(ϕ	GPE
ma-55	400	2	0	CARDINAL
ma-55	400	3	5.49	CARDINAL
ma-55	400	4	5.40	CARDINAL
ma-55	400	5	5.46	CARDINAL
ma-55	400	6	5.48	CARDINAL
ma-55	400	7	β(ϕ	GPE
ma-55	402	1	5.50	CARDINAL
ma-55	402	2	0(ω	DATE
ma-55	403	1	0	CARDINAL
ma-55	404	1	0	CARDINAL
ma-55	404	2	5.51	CARDINAL
ma-55	404	3	k a. e. 6	PERSON
ma-55	405	1	u2 two	CARDINAL
ma-55	405	2	4.5	CARDINAL
ma-55	405	3	0	CARDINAL
ma-55	406	1	0(ω	DATE
ma-55	407	1	u2 t	PERSON
ma-55	407	2	4.5	CARDINAL
ma-55	408	1	− ∫	ORG
ma-55	409	1	wtt	ORG
ma-55	410	1	1	CARDINAL
ma-55	411	1	2	CARDINAL
ma-55	413	1	∆wt	ORG
ma-55	414	1	wt)ds	PERSON
ma-55	414	2	wt)ds	PERSON
ma-55	415	1	j. math	PERSON
ma-55	417	1	10.28924	CARDINAL
ma-55	417	2	1 2	CARDINAL
ma-55	420	1	wt(t)〉ds + ∫	ORG
ma-55	420	2	∫	ORG
ma-55	420	3	t 0	DATE
ma-55	421	1	2.2	CARDINAL
ma-55	421	2	1 2	CARDINAL
ma-55	424	1	|〈∆pu1(t)−	NORP
ma-55	427	1	6.1	CARDINAL
ma-55	427	2	|〈∆pu1(t)−	NORP
ma-55	429	1	6.2	CARDINAL
ma-55	429	2	0	CARDINAL
ma-55	433	1	1− θ)u2(t))|r−2|w(t)||wt(t)|dxds	WORK_OF_ART
ma-55	433	2	1	CARDINAL
ma-55	434	1	1− θ)u2|r−2	TIME
ma-55	435	1	1− θ)u2(t)||w(t)|wt(t)|dxds	DATE
ma-55	435	2	1	CARDINAL
ma-55	435	3	6.3	CARDINAL
ma-55	437	1	1− θ)u2(t)|r−2	DATE
ma-55	437	2	2n	CARDINAL
ma-55	438	1	6.4	CARDINAL
ma-55	438	2	c3	PERSON
ma-55	439	1	1− θ)u2(t)|r−2	DATE
ma-55	440	1	2n	CARDINAL
ma-55	442	1	j. math	PERSON
ma-55	444	1	10.28924	CARDINAL
ma-55	444	2	2	CARDINAL
ma-55	444	3	2n	CARDINAL
ma-55	444	4	2	CARDINAL
ma-55	445	1	5.24	CARDINAL
ma-55	446	1	1− θ)u2|r−2	TIME
ma-55	448	1	− 2))−n|θu1(t	PERSON
ma-55	449	1	1− θ)u2(t)|n(r−2	DATE
ma-55	450	1	1− θ)u2(t)|n(r−2	EVENT
ma-55	450	2	6.5	CARDINAL
ma-55	450	3	6.5	CARDINAL
ma-55	450	4	1	CARDINAL
ma-55	452	1	1− θ)u2|r−2	TIME
ma-55	453	1	1	CARDINAL
ma-55	455	1	∫ ω	ORG
ma-55	456	1	1− θ)u2|r−2	TIME
ma-55	457	1	1	CARDINAL
ma-55	458	1	2n	CARDINAL
ma-55	460	1	6.6	CARDINAL
ma-55	460	2	6.1	CARDINAL
ma-55	460	3	6.2	CARDINAL
ma-55	460	4	6.4	CARDINAL
ma-55	460	5	6.6	CARDINAL
ma-55	463	1	6.7	CARDINAL
ma-55	465	1	0	CARDINAL
ma-55	466	1	∇w)(t	GPE
ma-55	466	2	6.7	CARDINAL
ma-55	468	1	0	CARDINAL
ma-55	469	1	1	CARDINAL
ma-55	469	2	a. pierce	PERSON
ma-55	469	3	j. appl	PERSON
ma-55	470	1	54(3	CARDINAL
ma-55	470	2	1994	DATE
ma-55	470	3	708	CARDINAL
ma-55	472	1	a. pierce	PERSON
ma-55	472	2	j. appl	PERSON
ma-55	473	1	55(1)(1995	CARDINAL
ma-55	473	2	136	CARDINAL
ma-55	474	1	a. andrade	PERSON
ma-55	474	2	m. a. jorge silva	PERSON
ma-55	474	3	t. f. ma	PERSON
ma-55	477	1	sci. 35(4	ORG
ma-55	477	2	2012	DATE
ma-55	477	3	417	CARDINAL
ma-55	477	4	https://doi.org/10.1137/s0036139992238498 https://doi.org/10.1137/s0036139993255327 https://doi.org/10.1002/mma.1552 eur	PERSON
ma-55	478	1	j. math	PERSON
ma-55	480	1	10.28924	CARDINAL
ma-55	480	2	20	CARDINAL
ma-55	481	1	4	CARDINAL
ma-55	482	1	p. h. rabinowitz	ORG
ma-55	482	2	j. functionalanalysis 14(4	PERSON
ma-55	482	3	1973	DATE
ma-55	482	4	349	CARDINAL
ma-55	483	1	g. m. araújo	PERSON
ma-55	483	2	s. b. menezes	PERSON
ma-55	487	1	1(3	CARDINAL
ma-55	487	2	2006	DATE
ma-55	487	3	583	CARDINAL
ma-55	488	1	https://doi.org/10.3934/cpaa.2006.5.583[6] g. m. araújo	PERSON
ma-55	488	2	s. b. menezes	PERSON
ma-55	488	3	a. o. marinho	PERSON
ma-55	488	4	69	CARDINAL
ma-55	488	5	2009	DATE
ma-55	488	6	1	CARDINAL
ma-55	489	1	g. m. araújo	PERSON
ma-55	489	2	m. a. f. araújo	PERSON
ma-55	489	3	d. c. pereira	PERSON
ma-55	491	1	1 (	CARDINAL
ma-55	491	2	2020	DATE
ma-55	491	3	1	CARDINAL
ma-55	492	1	m. bokalo	PERSON
ma-55	492	2	o. sus	PERSON
ma-55	492	3	2019	CARDINAL
ma-55	492	4	182	CARDINAL
ma-55	493	1	j. l. lions	PERSON
ma-55	493	2	contrôle impulsionnel	ORG
ma-55	495	1	sci	ORG
ma-55	495	2	11	CARDINAL
ma-55	495	3	paris	GPE
ma-55	495	4	m. m. cavalcanti	PERSON
ma-55	495	5	v. n. domigos cavalcanti	PERSON
ma-55	495	6	t. f. ma	PERSON
ma-55	497	1	17(5-6	CARDINAL
ma-55	497	2	2004	DATE
ma-55	497	3	495	CARDINAL
ma-55	497	4	m. m. cavalcanti	PERSON
ma-55	497	5	h. p. oquendo	PERSON
ma-55	497	6	siam j.control	GPE
ma-55	498	1	optim	PERSON
ma-55	499	1	14(4	CARDINAL
ma-55	499	2	2003	DATE
ma-55	499	3	1324	CARDINAL
ma-55	500	1	i. chueshov	PERSON
ma-55	500	2	i. lasiecka	PERSON
ma-55	500	3	2dkirchhoff	ORG
ma-55	501	1	contin	PERSON
ma-55	502	1	dyn.	PERSON
ma-55	503	1	s. 15(3	PERSON
ma-55	503	2	2006	DATE
ma-55	503	3	777	CARDINAL
ma-55	505	1	2006.15.777[13	CARDINAL
ma-55	505	2	c. m. dafermos	PERSON
ma-55	509	1	37	CARDINAL
ma-55	509	2	1970	DATE
ma-55	509	3	297	CARDINAL
ma-55	510	1	p. hartman	PERSON
ma-55	510	2	g. stampacchia	PERSON
ma-55	511	1	115	CARDINAL
ma-55	511	2	1966)271-310	DATE
ma-55	512	1	n. kikuchi	PERSON
ma-55	512	2	j. t. oden	PERSON
ma-55	512	3	siam	GPE
ma-55	512	4	philadelphia	GPE
ma-55	512	5	1988.[16	ORG
ma-55	512	6	j. l. lions	PERSON
ma-55	512	7	quelques méthodes de resolution des problémes aux limites non	ORG
ma-55	512	8	dunod	PERSON
ma-55	512	9	paris	GPE
ma-55	512	10	1969.[17	CARDINAL
ma-55	512	11	l. e. payne	PERSON
ma-55	512	12	d. h. sattinger	PERSON
ma-55	512	13	israel	GPE
ma-55	513	1	22(1975	CARDINAL
ma-55	513	2	273	CARDINAL
ma-55	514	1	c. a. raposo	PERSON
ma-55	514	2	d. c. pereira	PERSON
ma-55	514	3	g. araújo	PERSON
ma-55	514	4	a. baena	PERSON
ma-55	514	5	klein	PERSON
ma-55	514	6	nonlinearityof kirchhoff-carrier	ORG
ma-55	514	7	137	CARDINAL
ma-55	514	8	2015	CARDINAL
ma-55	514	9	1	CARDINAL
ma-55	515	1	d. c. pereira	PERSON
ma-55	515	2	c. h. maranhão	PERSON
ma-55	515	3	j. appl	ORG
ma-55	517	1	comput	PERSON
ma-55	518	1	2021	CARDINAL
ma-55	518	2	546	CARDINAL
ma-55	521	1	2007	DATE
ma-55	521	2	2007	DATE
ma-55	521	3	1-9	CARDINAL
ma-55	522	1	m. willem	PERSON
ma-55	523	1	24	CARDINAL
ma-55	523	2	boston	GPE
ma-55	523	3	ma	ORG
ma-55	523	4	1996.[22	CARDINAL
ma-55	526	1	2009	DATE
ma-55	526	2	1082-1104	DATE
ma-55	527	1	kirchhoff models	ORG
ma-55	527	2	j. math	ORG
ma-55	529	1	032701	DATE
ma-55	530	1	j. baoxia	PERSON
ma-55	530	2	kirchhoff models	ORG
ma-55	530	3	j. math	ORG
ma-55	532	1	50(3	CARDINAL
ma-55	532	2	2009) 032701	DATE
ma-55	533	1	https	PERSON
ma-55	537	1	2	CARDINAL
ma-55	537	2	3	CARDINAL
ma-55	537	3	4	CARDINAL
ma-55	537	4	5	CARDINAL
ma-55	537	5	5.1	CARDINAL
ma-55	537	6	5.2	CARDINAL
ma-55	538	1	first	ORDINAL
ma-55	538	2	5.3	CARDINAL
ma-55	538	3	second	ORDINAL
ma-55	538	4	5.4	CARDINAL
ma-55	538	5	third	ORDINAL
ma-55	538	6	5.5	CARDINAL
ma-55	539	1	6	CARDINAL