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

共 50 条

[1] Long-time behavior for a nonlinear fourth-order parabolic equation
Cáceres, MJ
Carrillo, JA
Toscani, G
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2005, 357 (03) : 1161 - 1175
[2] Long-time behavior for a nonlinear Timoshenko system: Thermal damping versus weak damping of variable-exponents type
Al-Mahdi, Adel M.
AIMS MATHEMATICS, 2023, 8 (12): : 29577 - 29603
[3] LONG-TIME SMALL SOLUTIONS TO NONLINEAR PARABOLIC EQUATIONS
CHEN, ZM
ARKIV FOR MATEMATIK, 1990, 28 (02): : 371 - 381
[4] LONG-TIME BEHAVIOUR OF DOUBLY NONLINEAR PARABOLIC EQUATIONS
Khanmamedov, A. Kh.
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2009, 8 (04) : 1373 - 1400
[5] Nonlocal in time problem for anisotropic parabolic equations with variable exponents of nonlinearities
Buhrii, Oleh
Buhrii, Nataliya
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2019, 473 (02) : 695 - 711
[6] LONG-TIME BEHAVIOR FOR A CLASS OF DEGENERATE PARABOLIC EQUATIONS
Li, Hongtao
Ma, Shan
Zhong, Chengkui
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2014, 34 (07) : 2873 - 2892
[7] Long-time behaviour of solutions of a class of nonlinear parabolic equations
Liu, Xiaochuan
Qu, Changzheng
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2008, 69 (12) : 4470 - 4481
[8] Long-time asymptotics for fully nonlinear homogeneous parabolic equations
Scott N. Armstrong
Maxim Trokhimtchouk
Calculus of Variations and Partial Differential Equations, 2010, 38 : 521 - 540
[9] Long-time asymptotics for fully nonlinear homogeneous parabolic equations
Armstrong, Scott N.
Trokhimtchouk, Maxim
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2010, 38 (3-4) : 521 - 540
[10] Long-time behavior of nonlinear Landau damping
Dublin Inst for Advanced Studies, Dublin, Ireland
Phys Rev Lett, 15 (2815-2818):

← 1 2 3 4 5 →