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

[31]

Ruzicka M, 2000, LECT NOTES MATH, V1748, P1

[32] ENTROPY SOLUTIONS FOR THE p(x)-LAPLACE EQUATION [J].

Sanchon, Manel ;

Urbano, Jose Miguel .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2009, 361 (12) :6387-6405

[33] Existence and uniqueness of renormalized solutions to nonlinear elliptic equations with variable exponents and L1-data [J].

Wittbold, P. ;

Zimmermann, A. .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2010, 72 (06) :2990-3008

[34]

Zhikov VV., 2004, ZAP NAUCHN SEM S PET, V310, P67

← 1 2 3 4 →