Global attractor for the generalized double dispersion equation

被引：19

作者：

Yang, Zhijian ^{[1
]}

Feng, Na ^{[1
]}

Ma, To Fu ^{[2
]}

机构：

[1] Zhengzhou Univ, Sch Math & Stat, Zhengzhou 450001, Peoples R China

[2] Univ Sao Paulo, Inst Math & Comp Sci, BR-13566590 Sao Carlos, SP, Brazil

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2015年 / 115卷

基金：

巴西圣保罗研究基金会;

关键词：

The generalized double dispersion equation; Elastic waveguide model; Global weak solutions; Non-uniqueness; Supercritical exponent; Global attractor; Exponential attractor; BOUNDARY-VALUE-PROBLEM; CAHN-HILLIARD EQUATION; DAMPED WAVE-EQUATIONS; POTENTIAL WELL METHOD; CAUCHY-PROBLEM; SPINODAL DECOMPOSITION; ASYMPTOTIC-BEHAVIOR; EXISTENCE;

D O I：

10.1016/j.na.2014.12.006

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The paper studies the existence of global attractor for the generalized double dispersion equation arising in elastic waveguide model u(tt) - Delta u - Delta u(tt) + Delta(2)u - Delta u(t) - Delta g(u) = f(x). The main result is concerned with nonlinearities g(u) with supercritical growth. In that case we construct a subclass G of the limit solutions and show that it has a weak global attractor. Especially, in non-supercritical case, the weak topology becomes strong, the further regularity of the global attractor is obtained and the exponential attractor is established in natural energy space. (C) 2014 Elsevier Ltd. All rights reserved.

引用

页码：103 / 116

页数：14

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