On global solution of an initial boundary value problem for a class of damped nonlinear equations

被引：17

作者：

Lin, Qun ^{[1
]}

Wu, Yong Hong ^{[1
]}

Lai, Shaoyong ^{[2
]}

机构：

[1] Curtin Univ Technol, Dept Math & Stat, Perth, WA 6845, Australia

[2] S Western Univ Finance & Econ, Dept Econ Math, Chengdu 610074, Peoples R China

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2008年 / 69卷 / 12期

基金：

澳大利亚研究理事会;

关键词：

Initial boundary value problem; Potential wells; Global weak solution; Global strong solution;

D O I：

10.1016/j.na.2007.10.057

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider the following problem u(tt) - alpha Delta u(t) + Delta(2)u - Delta u = f(u), x is an element of Omega, t > 0, u(x, 0) = u(0)(x), u(t)(x, 0) = u(1)(x), x is an element of Omega, Delta u(x, t)vertical bar(partial derivative Omega) = u(x, t)vertical bar(partial derivative Omega) = 0, t >= 0, where Omega subset of R '' is a bounded domain with smooth boundary. Under some assumptions of the initial data u(0)(x), u(1)(x) and nonlinear function f(u), the existence of global weak solutions and global strong solutions are obtained by means of the potential well method. (C) 2007 Elsevier Ltd. All rights reserved.

引用

页码：4340 / 4351

页数：12

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