Long-time behavior for a nonlinear parabolic problem with variable exponents

被引：18

作者：

Niu, Weisheng ^{[1
]}

机构：

[1] Anhui Univ, Sch Math Sci, Hefei 230039, Peoples R China

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2012年 / 393卷 / 01期

关键词：

Global attractors; Variable exponents; Fractal dimension; INFINITE-DIMENSIONAL ATTRACTORS; GLOBAL ATTRACTORS; P-LAPLACIAN; EQUATIONS; REGULARITY; EMBEDDINGS; EXISTENCE;

D O I：

10.1016/j.jmaa.2012.03.039

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper addresses the question of the asymptotic behavior of solutions to the p(x)-Laplacian problem u(t) - div(vertical bar del u vertical bar(p(x)-2)del u) + f(x, u) = g. With general assumptions on f (x, u) and the exponent p(x), we prove the existence of global attractors in proper spaces. Then we consider the fractal dimension of global attractors for the problem. Under suitable conditions, we show that the problem admits an infinite-dimensional global attractor. (C) 2012 Elsevier Inc. All rights reserved.

引用

页码：56 / 65

页数：10

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