UNIQUENESS AND COMPARISON THEOREMS FOR SOLUTIONS OF DOUBLY NONLINEAR PARABOLIC EQUATIONS WITH NONSTANDARD GROWTH CONDITIONS

被引：24

作者：

Antontsev, Stanislav ^{[1
]}

Chipot, Michel ^{[2
]}

Shmarev, Sergey ^{[3
]}

机构：

[1] Univ Lisbon, CMAF, P-1699 Lisbon, Portugal

[2] Univ Zurich, CH-8006 Zurich, Switzerland

[3] Univ Oviedo, Oviedo, Spain

来源：

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2013年 / 12卷 / 04期

基金：

瑞士国家科学基金会;

关键词：

Nonlinear parabolic equations; double nonlinearity; nonstandard growth conditions; BLOW-UP PHENOMENON; LEBESGUE SPACES; EXISTENCE;

D O I：

10.3934/cpaa.2013.12.1527

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The paper addresses the Dirichlet problem for the doubly nonlinear parabolic equation with nonstandard growth conditions: u(t) = div (a(x, t, u) vertical bar u vertical bar (alpha(x,t)) vertical bar del u vertical bar(p(x,t)-2)del u) + f(x, t) with given variable exponents alpha(x, t) and p(x, t). We establish conditions on the data which guarantee the comparison principle and uniqueness of bounded weak solutions in suitable function spaces of Orlicz-Sobolev type.

引用

页码：1527 / 1546

页数：20

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