Uniqueness of the renormalized solution of an elliptic-parabolic problem in anisotropic Sobolev-Orlicz spaces

被引：19

作者：

Mukminov, F. Kh. ^{[1
]}

机构：

[1] Russian Acad Sci, Ufa Sci Ctr, Inst Math Comp Ctr, Ufa, Russia

来源：

SBORNIK MATHEMATICS | 2017年 / 208卷 / 08期

基金：

俄罗斯基础研究基金会;

关键词：

anisotropic parabolic equation; renormalized solution; variable nonlinearity; uniqueness of solution; N-function; ENTROPY SOLUTIONS; EXISTENCE; EQUATION; DECAY;

D O I：

10.1070/SM8691

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider the first mixed problem for a class of anisotropic elliptic-parabolic equations with double variable nonlinearities in a cylindrical domain (0, T) x Omega. The domain Omega subset of R-n can be unbounded. The uniqueness of the renormalized solution is proved using Kruzhkov's method of doubling the variable t. The same result is established for an equation with non-power law nonlinearities.

引用

页码：1187 / 1206

页数：20

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