Renormalized solutions for a nonlinear parabolic equation with variable exponents and L1-data

被引：108

作者：

Bendahmane, M. ^{[1
]}

Wittbold, P. ^{[2
]}

Zimmermann, A. ^{[2
]}

机构：

[1] Univ Victor Segalen Bordeaux 2, Inst Math Bordeaux, Bordeaux, France

[2] Tech Univ Berlin, Inst Math, D-10623 Berlin, Germany

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2010年 / 249卷 / 06期

关键词：

Parabolic equation; Variable exponents; Renormalized solution; Existence; Uniqueness; ENTROPY SOLUTIONS; SOBOLEV SPACES; EXISTENCE; UNIQUENESS;

D O I：

10.1016/j.jde.2010.05.011

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove the well-posedness (existence and uniqueness) of a re-normalized solution to nonlinear parabolic equations with variable exponents and L-1-data. The functional setting involves Lebesgue-Sobolev spaces with variable exponents. (C) 2010 Elsevier Inc. All rights reserved.

引用

页码：1483 / 1515

页数：33

共 34 条

[1]

ALT HW, 1983, MATH Z, V183, P311

[2] Existence and uniqueness for a degenerate parabolic equation with L1-data [J].

Andreu, F ;

Mazón, JM ;

De León, SS ;

Toledo, J .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1999, 351 (01) :285-306

[3]

[Anonymous], EVOLUTION E IN PRESS

[4] A model porous medium equation with variable exponent of nonlinearity: existence, uniqueness and localization properties of solutions [J].

Antontsev, SN ;

Shmarev, SI .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2005, 60 (03) :515-545

[5]

Antontsev S, 2005, ADV DIFFERENTIAL EQU, V10, P1053

[6]

B?nilan P., 1995, ANN SCUOLA NORM-SCI, V22, P241

[7]

Barbu V, 1976, Nonlinear Semigroups and Differential Equations in Banach Spaces, Editura Academiei Republicii Socialiste Romania

[8] Renormalized solutions of an anisotropic reaction-diffusion-advection system with L1 data [J].

Bendahmane, Mostafa ;

Karlsen, Kenneth H. .

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2006, 5 (04) :733-762

[9] Renormalized solutions for nonlinear elliptic equations with variable exponents and L1 data [J].

Bendahmane, Mostafa ;

Wittbold, Petra .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2009, 70 (02) :567-583

[10]

Benilan P., 2000, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), V29, P313

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