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
收藏
页码：1187 / 1206
页数：20
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