Renormalized and entropy solutions for nonlinear parabolic equations with variable exponents and L1 data

被引：87

作者：

Zhang, Chao ^{[1
]}

Zhou, Shulin ^{[1
]}

机构：

[1] Peking Univ, Sch Math Sci, LMAM, Beijing 100871, Peoples R China

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2010年 / 248卷 / 06期

关键词：

Variable exponents; Renormalized solutions; Entropy solutions; Existence; Uniqueness; ELLIPTIC-EQUATIONS; SOBOLEV SPACES; EXISTENCE; REGULARITY; UNIQUENESS; FUNCTIONALS;

D O I：

10.1016/j.jde.2009.11.024

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we prove the existence and uniqueness of both renormalized solutions and entropy solutions for nonlinear parabolic equations with variable exponents and L-1 data. And moreover, we obtain the equivalence of renormalized Solutions and entropy Solutions. (C) 2009 Elsevier Inc. All rights reserved.

引用

页码：1376 / 1400

页数：25

共 36 条

[1] Regularity results for parabolic systems related to a class of non-Newtonian fluids
Acerbi, E
Mingione, G
Seregin, GA
[J]. ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2004, 21 (01): : 25 - 60
[2] Regularity results for stationary electro-rheological fluids
Acerbi, E
Mingione, G
[J]. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2002, 164 (03) : 213 - 259
[3] Regularity results for a class of functionals with non-standard growth
Acerbi, E
Mingione, G
[J]. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2001, 156 (02) : 121 - 140
[4] [Anonymous], RIC MAT
[5] [Anonymous], 1983, Orlicz spaces and modular spaces, Lecture Note in Mahtematics
[6] Existence results for nonlinear elliptic equations with degenerate coercivity
Angelo Alvino
Lucio Boccardo
Vincenzo Ferone
Luigi Orsina
Guido Trombetti
[J]. Annali di Matematica Pura ed Applicata, 2003, 182 (1) : 53 - 79
[7] A model porous medium equation with variable exponent of nonlinearity: existence, uniqueness and localization properties of solutions
Antontsev, SN
Shmarev, SI
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2005, 60 (03) : 515 - 545
[8] B?nilan P., 1995, ANN SCUOLA NORM-SCI, V22, P241
[9] Renormalized solutions for nonlinear elliptic equations with variable exponents and L1 data
Bendahmane, Mostafa
Wittbold, Petra
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2009, 70 (02) : 567 - 583
[10] Renormalised solutions of nonlinear parabolic problems with L1 data:: existence and uniqueness
Blanchard, D
Murat, F
[J]. PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 1997, 127 : 1137 - 1152

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