id	sid	eid	entity	type
ma-257	1	1	2025	CARDINAL
ma-257	2	1	j. math	PERSON
ma-257	4	1	5 (	CARDINAL
ma-257	5	1	1doi	CARDINAL
ma-257	5	2	10.28924	CARDINAL
ma-257	5	3	salah a. khafagy1	PERSON
ma-257	5	4	a. ezzat mohamed2∗	PERSON
ma-257	5	5	1department	CARDINAL
ma-257	5	6	al-azhar university	ORG
ma-257	5	7	11884	DATE
ma-257	5	8	cairo	GPE
ma-257	5	9	egypt	GPE
ma-257	5	10	2department	TIME
ma-257	5	11	fayoum university	ORG
ma-257	5	12	63514	DATE
ma-257	5	13	fayoum	GPE
ma-257	5	14	egypt	GPE
ma-257	8	1	∈ ω	ORG
ma-257	8	2	∈ ω	ORG
ma-257	8	3	∈	ORG
ma-257	8	4	∆rw = div(|∇w	PERSON
ma-257	8	5	1	CARDINAL
ma-257	8	6	∈	ORG
ma-257	8	7	0	CARDINAL
ma-257	8	8	1	CARDINAL
ma-257	8	9	ω	ORG
ma-257	8	10	1	CARDINAL
ma-257	9	1	0	CARDINAL
ma-257	9	2	g(υ1	GPE
ma-257	9	3	0.with	CARDINAL
ma-257	10	1	1	CARDINAL
ma-257	13	1	∈ ω	ORG
ma-257	13	2	∈ ω	ORG
ma-257	13	3	∈	ORG
ma-257	13	4	1	CARDINAL
ma-257	13	5	1	CARDINAL
ma-257	13	6	∈	ORG
ma-257	13	7	0	CARDINAL
ma-257	13	8	1	CARDINAL
ma-257	13	9	ω	ORG
ma-257	13	10	1	CARDINAL
ma-257	14	1	0	CARDINAL
ma-257	14	2	g(υ1	GPE
ma-257	14	3	0.with	CARDINAL
ma-257	15	1	17	CARDINAL
ma-257	18	1	j. math	PERSON
ma-257	20	1	10.28924	CARDINAL
ma-257	21	1	∈ ω	ORG
ma-257	21	2	vt =	GPE
ma-257	21	3	∈ ω	ORG
ma-257	21	4	∈	ORG
ma-257	21	5	2	CARDINAL
ma-257	21	6	1	CARDINAL
ma-257	21	7	η	ORG
ma-257	22	1	2	CARDINAL
ma-257	23	1	η	PRODUCT
ma-257	23	2	1	CARDINAL
ma-257	24	1	1	CARDINAL
ma-257	24	2	two	CARDINAL
ma-257	24	3	two	CARDINAL
ma-257	25	1	6	CARDINAL
ma-257	25	2	λ[f	DATE
ma-257	25	3	∈ ω	ORG
ma-257	25	4	∈	ORG
ma-257	25	5	3	CARDINAL
ma-257	26	1	0	CARDINAL
ma-257	26	2	0	CARDINAL
ma-257	26	3	lim ε→∞	PERSON
ma-257	26	4	ω ⊂	GPE
ma-257	26	5	1	CARDINAL
ma-257	27	1	1they	CARDINAL
ma-257	29	1		CARDINAL
ma-257	31	1	∈ ω	ORG
ma-257	32	1	1	CARDINAL
ma-257	32	2	∈ ω	ORG
ma-257	32	3	∈	ORG
ma-257	32	4	4	CARDINAL
ma-257	32	5	1	CARDINAL
ma-257	33	1	0	CARDINAL
ma-257	33	2	g(ω	ORG
ma-257	34	1	0	CARDINAL
ma-257	35	1	lim	PERSON
ma-257	35	2	mg(ω	ORG
ma-257	35	3	1 q−1	CARDINAL
ma-257	35	4	ωp−1	EVENT
ma-257	35	5	0	CARDINAL
ma-257	37	1	8	CARDINAL
ma-257	37	2	4	CARDINAL
ma-257	37	3	2.also	CARDINAL
ma-257	37	4	9	CARDINAL
ma-257	37	5	1	CARDINAL
ma-257	37	6	2	CARDINAL
ma-257	37	7	lim	PERSON
ma-257	37	8	ω	ORDINAL
ma-257	37	9	mg(ω	GPE
ma-257	37	10	ω	GPE
ma-257	39	1	lim ω→∞	PERSON
ma-257	39	2	g(ω	GPE
ma-257	39	3	ω	GPE
ma-257	39	4	0	CARDINAL
ma-257	42	1	j. math	PERSON
ma-257	44	1	10.28924	CARDINAL
ma-257	44	2	first	ORDINAL
ma-257	44	3	1	CARDINAL
ma-257	44	4	4	CARDINAL
ma-257	44	5	ξ→∞	CARDINAL
ma-257	44	6	1 q−1	CARDINAL
ma-257	44	7	0	CARDINAL
ma-257	44	8	0	CARDINAL
ma-257	44	9	lim ξ→∞ g(ξ	PERSON
ma-257	44	10	0	CARDINAL
ma-257	45	1	10–12	CARDINAL
ma-257	46	1	13	CARDINAL
ma-257	47	1	14–17	CARDINAL
ma-257	47	2	20–22	CARDINAL
ma-257	48	1	shivaji	PERSON
ma-257	48	2	11	CARDINAL
ma-257	48	3	∈ ω	ORG
ma-257	48	4	∈	ORG
ma-257	48	5	5	CARDINAL
ma-257	48	6	5	CARDINAL
ma-257	49	1	0	CARDINAL
ma-257	49	2	12	CARDINAL
ma-257	50	1	maya	PERSON
ma-257	50	2	shivaji	PERSON
ma-257	50	3	16	CARDINAL
ma-257	51	1	simon	PERSON
ma-257	51	2	14	CARDINAL
ma-257	52	1	0	CARDINAL
ma-257	52	2	′′	ORG
ma-257	53	1	0	CARDINAL
ma-257	53	2	5	CARDINAL
ma-257	54	1	9	CARDINAL
ma-257	54	2	1	CARDINAL
ma-257	54	3	2	CARDINAL
ma-257	55	1	23	CARDINAL
ma-257	56	1	∈ ω	ORG
ma-257	56	2	∈	ORG
ma-257	56	3	6	CARDINAL
ma-257	56	4	ω×	ORG
ma-257	57	1	0,∞)→	CARDINAL
ma-257	58	1	6	CARDINAL
ma-257	61	1	up−1	ORG
ma-257	62	1	second	ORDINAL
ma-257	62	2	1	CARDINAL
ma-257	62	3	10,17,18,24–26]).let	CARDINAL
ma-257	62	4	0	CARDINAL
ma-257	62	5	∈ ω	ORG
ma-257	62	6	∈	ORG
ma-257	62	7	7	CARDINAL
ma-257	63	1	j. math	PERSON
ma-257	65	1	10.28924	CARDINAL
ma-257	65	2	ϕ1,r	PERSON
ma-257	65	3	0	CARDINAL
ma-257	66	1	1.suppose	CARDINAL
ma-257	66	2	1− r s s + 1	TIME
ma-257	66	3	8) µ ≤ ϕ1,r ≤ 1	MONEY
ma-257	66	4	ω̄δ	ORG
ma-257	66	5	9)for	ORG
ma-257	66	6	sr	ORG
ma-257	66	7	+ 1)r−1	DATE
ma-257	66	8	∈ ω	ORG
ma-257	66	9	d(x	ORG
ma-257	67	1	0	CARDINAL
ma-257	68	1	6=	DATE
ma-257	70	1	∈	ORG
ma-257	70	2	1	CARDINAL
ma-257	70	3	∈ ω	ORG
ma-257	70	4	∈	ORG
ma-257	70	5	10	CARDINAL
ma-257	70	6	0	CARDINAL
ma-257	70	7	ω	GPE
ma-257	70	8	27	CARDINAL
ma-257	71	1	two	CARDINAL
ma-257	71	2	•	CARDINAL
ma-257	71	3	a(x	PERSON
ma-257	71	4	a0	ORG
ma-257	75	1	case(ii	PERSON
ma-257	75	2	a(x	PERSON
ma-257	76	1	2	CARDINAL
ma-257	77	1	2.1	CARDINAL
ma-257	78	1	1	CARDINAL
ma-257	78	2	∈	ORG
ma-257	78	3	0	CARDINAL
ma-257	78	4	ω	CARDINAL
ma-257	79	1	λ ∫ ω a(x)[f	ORG
ma-257	79	2	dx,∫ ω |∇v	GPE
ma-257	80	1	λ ∫ ω b(x)[g(u	ORG
ma-257	80	2	∀	ORG
ma-257	80	3	∈	ORG
ma-257	80	4	∈	ORG
ma-257	82	1	2.2	CARDINAL
ma-257	83	1	1	CARDINAL
ma-257	83	2	0	CARDINAL
ma-257	85	1	λ ∫ ω a(x)[f	ORG
ma-257	85	2	1	CARDINAL
ma-257	85	3	dx,∫ ω |∇ψ2|q−2∇ψ2	PERSON
ma-257	87	1	1	CARDINAL
ma-257	88	1	j. math	PERSON
ma-257	90	1	10.28924	CARDINAL
ma-257	91	1	∇ζ	DATE
ma-257	91	2	λ ∫ ω a(x)[f	ORG
ma-257	91	3	dx,∫ ω |∇z2|q−2∇z2	ORG
ma-257	92	1	∇ζ	DATE
ma-257	92	2	λ ∫ ω b(x)[g(z1	ORG
ma-257	92	3	∀	ORG
ma-257	92	4	∈	ORG
ma-257	92	5	∈	ORG
ma-257	93	1	2.1	CARDINAL
ma-257	94	1	2	CARDINAL
ma-257	94	2	1	CARDINAL
ma-257	95	1	1	CARDINAL
ma-257	96	1	0	CARDINAL
ma-257	96	2	g(υ1	GPE
ma-257	96	3	0	CARDINAL
ma-257	97	1	lim ξ→∞	PERSON
ma-257	97	2	1 q−1	CARDINAL
ma-257	98	1	lim ξ→∞ g(ξ	PERSON
ma-257	98	2	0	CARDINAL
ma-257	98	3	0	CARDINAL
ma-257	99	1	1	CARDINAL
ma-257	99	2	0	CARDINAL
ma-257	99	3	1	CARDINAL
ma-257	101	1	0	CARDINAL
ma-257	102	1	o	DATE
ma-257	108	1	1	CARDINAL
ma-257	110	1	λ1,q	LOC
ma-257	112	1	αpa0 λ1,p ε α p−1	ORG
ma-257	115	1	q−1	PRODUCT
ma-257	115	2	1)p−1	DATE
ma-257	116	1	g0	ORG
ma-257	116	2	0	CARDINAL
ma-257	117	1	2	CARDINAL
ma-257	117	2	g(υ1	GPE
ma-257	117	3	1	CARDINAL
ma-257	117	4	2	CARDINAL
ma-257	117	5	∈	ORG
ma-257	117	6	0	CARDINAL
ma-257	117	7	1	CARDINAL
ma-257	117	8	1	CARDINAL
ma-257	118	1	λo(εo	GPE
ma-257	118	2	λo(εo	GPE
ma-257	118	3	mεo pa0f	ORG
ma-257	118	4	1	CARDINAL
ma-257	118	5	o	DATE
ma-257	118	6	mεo qb0g(ε 1 p−1	ORG
ma-257	120	1	ε α+p−1 p−1	ORG
ma-257	120	2	ε β+q−1	PERSON
ma-257	122	1	λ1,q mβqb1	ORG
ma-257	124	1	j. math	PERSON
ma-257	126	1	10.28924	CARDINAL
ma-257	126	2	6	CARDINAL
ma-257	126	3	2.1	CARDINAL
ma-257	128	1	2 +	DATE
ma-257	128	2	g(υ1	GPE
ma-257	129	1	1 +	DATE
ma-257	129	2	2	CARDINAL
ma-257	131	1	q−1	PRODUCT
ma-257	131	2	1	CARDINAL
ma-257	131	3	1	CARDINAL
ma-257	131	4	1	CARDINAL
ma-257	131	5	1	CARDINAL
ma-257	131	6	lim ξ→∞	ORG
ma-257	131	7	1 q−1	CARDINAL
ma-257	131	8	0	CARDINAL
ma-257	131	9	0	CARDINAL
ma-257	131	10	lim ξ→∞ g(ξ	PERSON
ma-257	131	11	0	CARDINAL
ma-257	131	12	lim ξ→∞ g(ξ	PERSON
ma-257	131	13	0	CARDINAL
ma-257	133	1	2.1	CARDINAL
ma-257	136	1	2.1	CARDINAL
ma-257	137	1	1	CARDINAL
ma-257	137	2	λo(εo	GPE
ma-257	137	3	λo(εo	GPE
ma-257	139	1	ε 1 p−1	ORG
ma-257	140	1	1	CARDINAL
ma-257	141	1	1	CARDINAL
ma-257	141	2	o ∇ϕ po α+1	DATE
ma-257	141	3	1	CARDINAL
ma-257	141	4	∫ ω |∇ψ1|p−2∇ψ1	ORG
ma-257	141	5	∫ ω ϕ	ORG
ma-257	143	1	∫ ω |∇ϕ1,p|p−2∇ϕ1,p	ORG
ma-257	143	2	∇	ORG
ma-257	143	3	1,p	ORDINAL
ma-257	146	1	∫ ω	ORG
ma-257	147	1	1,p	ORDINAL
ma-257	147	2	1,p	CARDINAL
ma-257	147	3	∫ ω	ORG
ma-257	147	4	1,p	CARDINAL
ma-257	147	5	∫ ω |∇ψ1|p−2∇ψ1	ORG
ma-257	148	1	∫ ω	ORG
ma-257	148	2	1,p	CARDINAL
ma-257	149	1	11	CARDINAL
ma-257	149	2	|∇ψ2|q−2∇ψ2	ORG
ma-257	150	1	∫ ω	ORG
ma-257	150	2	1−	LANGUAGE
ma-257	150	3	−βq	PRODUCT
ma-257	150	4	β+1 1,q |∇ϕ1,q|q	DATE
ma-257	152	1	j. math	PERSON
ma-257	154	1	10.28924	CARDINAL
ma-257	156	1	1	CARDINAL
ma-257	156	2	o	DATE
ma-257	158	1	ε 1 p−1	ORG
ma-257	158	2	o	DATE
ma-257	158	3	ε 1 p−1	ORG
ma-257	159	1	ε 1 p−1	ORG
ma-257	160	1	12	CARDINAL
ma-257	160	2	ε α+p−1 p−1	ORG
ma-257	161	1	λ1,p ϕ p	GPE
ma-257	161	2	1,p αp ≤ εo λ1,p αp ≤	MONEY
ma-257	163	1	13	CARDINAL
ma-257	163	2	12	CARDINAL
ma-257	163	3	13	CARDINAL
ma-257	163	4	11	CARDINAL
ma-257	164	1	∇ζ dx ≤ ∫ ω λa0 ζ( ε 1 p−1	ORG
ma-257	165	1	1	CARDINAL
ma-257	166	1	ζdx	ORG
ma-257	168	1	∫ ω a0[f	ORG
ma-257	168	2	1	CARDINAL
ma-257	169	1	λ ∫ ω a(x)[f	ORG
ma-257	169	2	1	CARDINAL
ma-257	170	1	case(ii	PERSON
ma-257	173	1	j. math	PERSON
ma-257	175	1	10.28924	CARDINAL
ma-257	176	1	∫ ω	ORG
ma-257	176	2	1,p	CARDINAL
ma-257	176	3	1,p |∇φ1,p|p	MONEY
ma-257	177	1	∫ ω	ORG
ma-257	178	1	1,p	CARDINAL
ma-257	179	1	∫ ω a1nζ dx	ORG
ma-257	179	2	λ ∫ ω	ORG
ma-257	179	3	1	CARDINAL
ma-257	181	1	1	CARDINAL
ma-257	181	2	o φ po α+1	PERSON
ma-257	182	1	φ qo	PERSON
ma-257	182	2	β+1 1,q qo	DATE
ma-257	183	1	1	CARDINAL
ma-257	183	2	1	CARDINAL
ma-257	184	1	o φ po α+1	PERSON
ma-257	185	1	λ ∫ ω	ORG
ma-257	185	2	1	CARDINAL
ma-257	186	1	λ ∫ ω a(x)[f	ORG
ma-257	186	2	1	CARDINAL
ma-257	187	1	also∫	CARDINAL
ma-257	188	1	ω |∇ψ2|q−2∇ψ2	PERSON
ma-257	190	1	1	CARDINAL
ma-257	191	1	1	CARDINAL
ma-257	192	1	1	CARDINAL
ma-257	195	1	λµbg(cµp	GPE
ma-257	195	2	cµp	GPE
ma-257	195	3	q.	PERSON
ma-257	195	4	cµp	ORG
ma-257	195	5	λµbg(cµp	GPE
ma-257	195	6	cµp	GPE
ma-257	195	7	1	CARDINAL
ma-257	195	8	∫ ω |∇z1|p−2∇z1	ORG
ma-257	195	9	cp−1 ∫ ω |∇ep|p−2∇ep	ORG
ma-257	195	10	cp−1 ∫ ω ζ dx ≥	ORG
ma-257	196	1	∫ ω	ORG
ma-257	196	2	cµp	ORG
ma-257	196	3	λµbg(cµp	GPE
ma-257	196	4	cµp	GPE
ma-257	196	5	1	CARDINAL
ma-257	197	1	ζ dx	PERSON
ma-257	197	2	λ ∫ ω a(x)f	ORG
ma-257	197	3	λµbg(cµp	GPE
ma-257	197	4	cµp	GPE
ma-257	198	1	ζ dx	PERSON
ma-257	199	1	ζ dx	PERSON
ma-257	200	1	j. math	PERSON
ma-257	202	1	10.28924	CARDINAL
ma-257	202	2	9	CARDINAL
ma-257	202	3	λ ∫ ω a(x)[f	ORG
ma-257	203	1	cµp ≥ µq[λµbg(cµp	GPE
ma-257	203	2	cµp	GPE
ma-257	204	1	1 q−1	CARDINAL
ma-257	206	1	λ ∫ ω	ORG
ma-257	206	2	g(cµp	GPE
ma-257	206	3	λ ∫ ω	ORG
ma-257	206	4	g(cµp	GPE
ma-257	206	5	cµp	GPE
ma-257	207	1	ζ dx	PERSON
ma-257	207	2	λ ∫ ω b(x)g	ORG
ma-257	208	1	λµbg(cµp	GPE
ma-257	208	2	cµp	GPE
ma-257	209	1	ζ dx	PERSON
ma-257	209	2	λ ∫ ω	ORG
ma-257	210	1	ζ dx	PERSON
ma-257	210	2	λ ∫ ω b(x)[g(z1	ORG
ma-257	211	1	1	CARDINAL
ma-257	212	1	1	CARDINAL
ma-257	213	1	2.2	CARDINAL
ma-257	216	1	1	CARDINAL
ma-257	217	1	1	CARDINAL
ma-257	217	2	λmax	ORDINAL
ma-257	217	3	λmin	GPE
ma-257	217	4	max	PERSON
ma-257	217	5	λ1,p −2	GPE
ma-257	218	1	λ1,q	ORG
ma-257	218	2	λmin = min	PERSON
ma-257	218	3	{λ1,p 2s	PERSON
ma-257	219	1	2s	CARDINAL
ma-257	221	1	1	CARDINAL
ma-257	223	1	the 1st and 2nd	DATE
ma-257	223	2	1	CARDINAL
ma-257	224	1	applyingyoung	PERSON
ma-257	224	2	∫ ω |∇u|pdx ≤ λ ∫ ω f0a(x	ORG
ma-257	224	3	14	CARDINAL
ma-257	225	1	1+γ1	CARDINAL
ma-257	225	2	1	CARDINAL
ma-257	226	1	1	CARDINAL
ma-257	226	2	|qdx ≤	DATE
ma-257	226	3	λ ∫ ω g0b(x	ORG
ma-257	226	4	15	CARDINAL
ma-257	226	5	1	CARDINAL
ma-257	227	1	1+γ2	CARDINAL
ma-257	227	2	1	CARDINAL
ma-257	227	3	λ1,p ∫ ω updx ≤ ∫ ω |∇u|pdx	ORG
ma-257	227	4	λ1,q ∫ ω vqdx ≤ ∫	ORG
ma-257	228	1	|qdx	DATE
ma-257	229	1	16	CARDINAL
ma-257	229	2	14)-(16	CARDINAL
ma-257	229	3	λ1,p ∫ ω	ORG
ma-257	229	4	λ1,q ∫ ω vqdx ≤	ORG
ma-257	229	5	∫ ω	ORG
ma-257	231	1	17	CARDINAL
ma-257	232	1	j. math	PERSON
ma-257	234	1	10.28924	CARDINAL
ma-257	237	1	18	CARDINAL
ma-257	237	2	2λs	ORDINAL
ma-257	238	1	2λs	ORDINAL
ma-257	239	1	19	CARDINAL
ma-257	240	1	3	CARDINAL
ma-257	240	2	1	CARDINAL
ma-257	241	1	1	CARDINAL
ma-257	241	2	1)div(|∇u|p−2∇ϕ)−	CARDINAL
ma-257	243	1	∈ ω	ORG
ma-257	243	2	−(q − 1)div(|∇v |q−2∇ψ)− λb(x	ORG
ma-257	243	3	∈ ω	ORG
ma-257	243	4	∈	ORG
ma-257	243	5	20	CARDINAL
ma-257	243	6	30	CARDINAL
ma-257	244	1	first	ORDINAL
ma-257	244	2	20	CARDINAL
ma-257	244	3	0	CARDINAL
ma-257	244	4	ω	GPE
ma-257	245	1	3.1	CARDINAL
ma-257	246	1	1	CARDINAL
ma-257	246	2	20	CARDINAL
ma-257	246	3	first	ORDINAL
ma-257	246	4	0	CARDINAL
ma-257	248	1	0	CARDINAL
ma-257	248	2	gu	PERSON
ma-257	249	1	0	CARDINAL
ma-257	250	1	/up−1	ORG
ma-257	250	2	t3	ORG
ma-257	250	3	0	CARDINAL
ma-257	250	4	g(u	PRODUCT
ma-257	252	1	3.1	CARDINAL
ma-257	253	1	1	CARDINAL
ma-257	253	2	ω̄δ	ORG
ma-257	255	1	1	CARDINAL
ma-257	256	1	the 1st and 2nd	DATE
ma-257	256	2	1)ϕ1	ORDINAL
ma-257	256	3	1)ψ1	CARDINAL
ma-257	256	4	ω	DATE
ma-257	257	1	1	CARDINAL
ma-257	259	1	1)λ	CARDINAL
ma-257	259	2	∫ ω ϕ1(x)a(x	ORG
ma-257	260	1	1	CARDINAL
ma-257	260	2	uoα	ORG
ma-257	260	3	dx	ORG
ma-257	260	4	21	CARDINAL
ma-257	261	1	j. math	PERSON
ma-257	263	1	10.28924	CARDINAL
ma-257	264	1	1	CARDINAL
ma-257	266	1	1)λ	ORDINAL
ma-257	266	2	∫ ω ψ1(x)b(x	ORG
ma-257	267	1	1	CARDINAL
ma-257	268	1	22	CARDINAL
ma-257	268	2	1st	ORDINAL
ma-257	268	3	20	CARDINAL
ma-257	268	4	−vo	PRODUCT
ma-257	268	5	−µ1 ∫ ω	ORG
ma-257	269	1	1	CARDINAL
ma-257	272	1	∫ ω ϕ1(x)a(x	ORG
ma-257	273	1	uoα	ORG
ma-257	274	1	λ ∫ ω ψ1(x)a(x)fvuo dx	ORG
ma-257	274	2	23	CARDINAL
ma-257	274	3	−µ1 ∫ ω voψ1(x)dx	ORG
ma-257	274	4	1	CARDINAL
ma-257	279	1	24	CARDINAL
ma-257	279	2	21	CARDINAL
ma-257	279	3	24	CARDINAL
ma-257	280	1	1	CARDINAL
ma-257	283	1	1	CARDINAL
ma-257	283	2	div(|∇vo	NORP
ma-257	285	1	λ ∫ ω ϕ1(x)a(x	ORG
ma-257	286	1	uoα	ORG
ma-257	287	1	λ ∫ ω ψ1(x)b(x	ORG
ma-257	289	1	1)λ	CARDINAL
ma-257	289	2	∫ ω ϕ1(x)a(x	ORG
ma-257	290	1	1	CARDINAL
ma-257	290	2	uoα	ORG
ma-257	290	3	1)λ	CARDINAL
ma-257	290	4	∫ ω ψ1(x)b(x)[g(uo	ORG
ma-257	290	5	1	CARDINAL
ma-257	291	1	λ ∫ ω a(x)ψ1(x)fvuo dx	ORG
ma-257	292	1	∫ ω b(x)ϕ1(x)guvo	ORG
ma-257	293	1	−µ1 ∫ ω	ORG
ma-257	294	1	25	CARDINAL
ma-257	294	2	first	ORDINAL
ma-257	294	3	then∫ ω	ORG
ma-257	295	1	26	CARDINAL
ma-257	295	2	∫ ω vo	ORG
ma-257	295	3	div(|∇vo	NORP
ma-257	297	1	27	CARDINAL
ma-257	298	1	j. math	PERSON
ma-257	300	1	10.28924	CARDINAL
ma-257	300	2	26	CARDINAL
ma-257	300	3	27	CARDINAL
ma-257	300	4	25	CARDINAL
ma-257	302	1	1)f	CARDINAL
ma-257	303	1	1	CARDINAL
ma-257	303	2	uoα	ORG
ma-257	304	1	λ ∫ ω ψ1(x)b(x	ORG
ma-257	305	1	1)g(uo	CARDINAL
ma-257	306	1	1	CARDINAL
ma-257	308	1	λ ∫ ω ψ1(x)a(x)fvuodx +	ORG
ma-257	308	2	λ ∫ ω ϕ1(x)b(x)guvodx	ORG
ma-257	310	1	28	CARDINAL
ma-257	311	1	0	CARDINAL
ma-257	311	2	0	CARDINAL
ma-257	312	1	1)f	CARDINAL
ma-257	313	1	1)uo	CARDINAL
ma-257	313	2	0	CARDINAL
ma-257	313	3	29	CARDINAL
ma-257	314	1	q−1	PRODUCT
ma-257	314	2	0	CARDINAL
ma-257	314	3	0	CARDINAL
ma-257	315	1	1)g(uo	CARDINAL
ma-257	316	1	0	CARDINAL
ma-257	317	1	30	CARDINAL
ma-257	318	1	28	CARDINAL
ma-257	318	2	− µ1 ∫ ω	ORG
ma-257	319	1	0	CARDINAL
ma-257	319	2	31	CARDINAL
ma-257	319	3	0	CARDINAL
ma-257	320	1	0	CARDINAL
ma-257	321	1	28	CARDINAL
ma-257	321	2	− µ1 ∫ ω	ORG
ma-257	322	1	0	CARDINAL
ma-257	322	2	32	CARDINAL
ma-257	323	1	3.1	CARDINAL
ma-257	324	1	0	CARDINAL
ma-257	324	2	gu	PERSON
ma-257	325	1	0	CARDINAL
ma-257	325	2	/up−1	ORG
ma-257	325	3	0	CARDINAL
ma-257	325	4	g(u	PRODUCT
ma-257	327	1	3.1	CARDINAL
ma-257	327	2	1	CARDINAL
ma-257	327	3	ω̄δ	ORG
ma-257	329	1	3.1	CARDINAL
ma-257	330	1	3.2	CARDINAL
ma-257	332	1	3.3	CARDINAL
ma-257	333	1	2	CARDINAL
ma-257	333	2	1	CARDINAL
ma-257	333	3	9	CARDINAL
ma-257	335	1	j. math	PERSON
ma-257	337	1	10.28924	CARDINAL
ma-257	338	1	1	CARDINAL
ma-257	338	2	prentice-hall	ORG
ma-257	338	3	s. cui	PERSON
ma-257	339	1	41	CARDINAL
ma-257	339	2	1-2	CARDINAL
ma-257	339	3	2000	CARDINAL
ma-257	339	4	149–176	CARDINAL
ma-257	340	1	s. khafagy	PERSON
ma-257	340	2	e. a. el-zahrani	PERSON
ma-257	340	3	h. m. serag	PERSON
ma-257	340	4	q)-laplacian	NORP
ma-257	340	5	jordan j.	PERSON
ma-257	342	1	15	CARDINAL
ma-257	342	2	4a	CARDINAL
ma-257	342	3	2022	CARDINAL
ma-257	342	4	983–998.[4	CARDINAL
ma-257	342	5	e. k. lee	PERSON
ma-257	342	6	r. shivaji	PERSON
ma-257	342	7	j. ye	PERSON
ma-257	342	8	r. soc	PERSON
ma-257	343	1	edinburgh	GPE
ma-257	345	1	139	CARDINAL
ma-257	345	2	4)(2009	CARDINAL
ma-257	345	3	853–865	CARDINAL
ma-257	346	1	s. khafagy	PERSON
ma-257	346	2	z. sadeghi	PERSON
ma-257	347	1	j. math	PERSON
ma-257	349	1	4	CARDINAL
ma-257	349	2	2024	CARDINAL
ma-257	349	3	1	CARDINAL
ma-257	350	1	m. ramaswamy	PERSON
ma-257	350	2	r. shivaji	PERSON
ma-257	350	3	j. ye	PERSON
ma-257	350	4	2007	DATE
ma-257	350	5	1423–1433	DATE
ma-257	351	1	s. rasouli	PERSON
ma-257	353	1	univ	GPE
ma-257	353	2	brasov	ORG
ma-257	357	1	sci	ORG
ma-257	358	1	9	CARDINAL
ma-257	359	1	2	CARDINAL
ma-257	360	1	2016	CARDINAL
ma-257	360	2	71–78.[8	CARDINAL
ma-257	361	1	s. rasouli	PERSON
ma-257	361	2	j. model	PERSON
ma-257	363	1	11	CARDINAL
ma-257	363	2	1	CARDINAL
ma-257	363	3	2015	CARDINAL
ma-257	363	4	15–19.[9	CARDINAL
ma-257	363	5	s. khafagy	PERSON
ma-257	363	6	a. ezzat mohamed	PERSON
ma-257	364	1	j. math	PERSON
ma-257	365	1	4	CARDINAL
ma-257	365	2	2	CARDINAL
ma-257	365	3	2024	CARDINAL
ma-257	365	4	1–12	DATE
ma-257	366	1	i. ali	PERSON
ma-257	366	2	a. castro	PERSON
ma-257	366	3	r. shivaji	PERSON
ma-257	367	1	amer	PERSON
ma-257	369	1	117	CARDINAL
ma-257	369	2	3	CARDINAL
ma-257	369	3	1993	DATE
ma-257	371	1	k. brown	PERSON
ma-257	371	2	r. shivaji	PERSON
ma-257	372	1	amer	PERSON
ma-257	373	1	112	CARDINAL
ma-257	373	2	1	CARDINAL
ma-257	373	3	1991	DATE
ma-257	374	1	121–124	DATE
ma-257	375	1	a. tertikas	PERSON
ma-257	376	1	amer	PERSON
ma-257	378	1	114	CARDINAL
ma-257	378	2	4)(1992	CARDINAL
ma-257	378	3	1035–1040	DATE
ma-257	379	1	g. afrouzi	PERSON
ma-257	379	2	z. sadeeghi	PERSON
ma-257	380	1	j. nonlinear sci	PERSON
ma-257	380	2	6	CARDINAL
ma-257	380	3	2	CARDINAL
ma-257	380	4	2008	DATE
ma-257	380	5	j. karátson	PERSON
ma-257	380	6	p. simon	PERSON
ma-257	380	7	j. comput	PERSON
ma-257	382	1	131	CARDINAL
ma-257	382	2	2001	DATE
ma-257	383	1	497–501	CARDINAL
ma-257	384	1	00714-7.[15	CARDINAL
ma-257	385	1	j. shi	PERSON
ma-257	386	1	j.	PERSON
ma-257	388	1	2000	DATE
ma-257	388	2	311–322.[16	CARDINAL
ma-257	388	3	r. shivaji	PERSON
ma-257	388	4	j. comput	PERSON
ma-257	390	1	88	CARDINAL
ma-257	390	2	1	CARDINAL
ma-257	390	3	1998	DATE
ma-257	390	4	125–128	DATE
ma-257	391	1	https://doi.org/10.1016/s0377-0427(97)00209-4.[17] i. voros	PERSON
ma-257	392	1	2004	DATE
ma-257	392	2	2004	DATE
ma-257	392	3	1–6.[18	CARDINAL
ma-257	392	4	s. khafagy	PERSON
ma-257	392	5	a. ezzat mohamed	PERSON
ma-257	392	6	j. math.anal.	GPE
ma-257	392	7	8	CARDINAL
ma-257	392	8	2	CARDINAL
ma-257	392	9	2024	CARDINAL
ma-257	392	10	1	CARDINAL
ma-257	392	11	s. khafagy	PERSON
ma-257	394	1	8	CARDINAL
ma-257	394	2	2024	CARDINAL
ma-257	394	3	76-79.[20	DATE
ma-257	394	4	s. khafagy	PERSON
ma-257	394	5	s. rasouli	PERSON
ma-257	394	6	h. serag	PERSON
ma-257	394	7	fisher	PERSON
ma-257	396	1	3 (	CARDINAL
ma-257	396	2	2023	CARDINAL
ma-257	397	1	c. atkinson	PERSON
ma-257	397	2	k. el-ali	PERSON
ma-257	397	3	j. non-newtonian	PERSON
ma-257	398	1	41	CARDINAL
ma-257	398	2	339–363	DATE
ma-257	400	1	https://doi.org/10.1017/s0308210508000255	ORG
ma-257	402	1	j. math	PERSON
ma-257	404	1	10.28924	CARDINAL
ma-257	405	1	22	CARDINAL
ma-257	405	2	s. khafagy	PERSON
ma-257	405	3	h. serag	PERSON
ma-257	405	4	kolmogoroff steady statetype	ORG
ma-257	405	5	j. math	PERSON
ma-257	406	1	sci	ORG
ma-257	407	1	optim	PERSON
ma-257	408	1	2	CARDINAL
ma-257	408	2	1	CARDINAL
ma-257	408	3	2024	CARDINAL
ma-257	408	4	97	CARDINAL
ma-257	409	1	g. afrouzi	PERSON
ma-257	409	2	s. rasouli	PERSON
ma-257	409	3	29	CARDINAL
ma-257	409	4	5	CARDINAL
ma-257	409	5	2006	DATE
ma-257	410	1	j. karátson	PERSON
ma-257	410	2	p. simon	PERSON
ma-257	412	1	47	CARDINAL
ma-257	412	2	7	CARDINAL
ma-257	412	3	2001	DATE
ma-257	412	4	4513–4520	CARDINAL
ma-257	414	1	1016	CARDINAL
ma-257	414	2	546x(01)00564-8.[25	CARDINAL
ma-257	414	3	s. khafagy	PERSON
ma-257	414	4	h. serag	PERSON
ma-257	415	1	j. appl.math	PERSON
ma-257	416	1	36	CARDINAL
ma-257	416	2	3	CARDINAL
ma-257	416	3	2018	DATE
ma-257	417	1	173–179	CARDINAL
ma-257	418	1	https://doi.org/10.14317/jami.2018.173.[26	PERSON
ma-257	418	2	s. khafagy	PERSON
ma-257	418	3	h. serag	PERSON
ma-257	418	4	q)-laplacian	NORP
ma-257	419	1	20	CARDINAL
ma-257	419	2	2020	DATE
ma-257	419	3	l. c. evans	PERSON
ma-257	419	4	19	CARDINAL
ma-257	419	5	american mathematical society	ORG
ma-257	419	6	2022	CARDINAL
ma-257	421	1	1090	CARDINAL
ma-257	425	1	57	CARDINAL
ma-257	425	2	2	CARDINAL
ma-257	425	3	1974)150–165	CARDINAL
ma-257	425	4	https://doi.org/10.1007/bf00248417.[29	ORG
ma-257	425	5	d. h. sattinger	PERSON
ma-257	425	6	indiana	GPE
ma-257	425	7	univ	NORP
ma-257	426	1	math.j. 21	DATE
ma-257	426	2	11	CARDINAL
ma-257	426	3	1972	DATE
ma-257	426	4	979–1000	CARDINAL
ma-257	427	1	p. krejcí	PERSON
ma-257	427	2	p. takác	PERSON
ma-257	428	1	404	CARDINAL
ma-257	428	2	crc press	ORG
ma-257	428	3	1999	DATE
ma-257	430	1	1201/9780429332555	DATE
ma-257	431	1	https://doi.org/10.1016/j.chaos.2005.08.165	ORG
ma-257	431	2	https://doi.org/10.1016/s0362-546x(01)00564-8 https://doi.org/10.1016/s0362-546x(01)00564-8 https://doi.org/10.14317/jami.2018.173 https://doi.org/10.1090/gsm/019 https://doi.org/10.1090/gsm/019	PRODUCT
ma-257	431	3	1	CARDINAL
ma-257	432	1	2	CARDINAL
ma-257	432	2	3	CARDINAL