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Uniqueness and comparison theorems for solutions of doubly nonlinear parabolic equations with nonstandard growth conditions


Antontsev, Stansislav Nikolaevich; Chipot, Michel C (2013). Uniqueness and comparison theorems for solutions of doubly nonlinear parabolic equations with nonstandard growth conditions. Communications on Pure and Applied Analysis, 12(4):1527-1546.

Abstract

The paper addresses the Dirichlet problem for the doubly nonlinear parabolic equation with nonstandard growth conditions: ut = div (a(x, t, u)|u|α(x, t)|∇u|p(x, t)-2 with given variable exponents α(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.

Abstract

The paper addresses the Dirichlet problem for the doubly nonlinear parabolic equation with nonstandard growth conditions: ut = div (a(x, t, u)|u|α(x, t)|∇u|p(x, t)-2 with given variable exponents α(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.

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5 citations in Web of Science®
5 citations in Scopus®
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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:July 2013
Deposited On:06 Dec 2013 12:11
Last Modified:05 Apr 2016 17:13
Publisher:American Institute of Mathematical Sciences
ISSN:1534-0392
Publisher DOI:https://doi.org/10.3934/cpaa.2013.12.1527

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