ON EXISTENCE, UNIFORM DECAY RATES AND BLOW UP FOR SOLUTIONS OF SYSTEMS OF NONLINEAR WAVE EQUATIONS WITH DAMPING AND SOURCE TERMS

被引：71

作者：

Alves, Claudianor O. ^{[1
]}

Cavalcanti, Marcelo M. ^{[2
]}

Domingos Cavalcanti, Valeria N. ^{[2
]}

Rammaha, Mohammad A. ^{[3
]}

Toundykov, Daniel ^{[3
]}

机构：

[1] Univ Fed Campina Grande, Dept Math & Stat, BR-58109970 Campina Grande, Paraiba, Brazil

[2] Univ Estadual Maringa, Dept Math, BR-87020900 Maringa, Parana, Brazil

[3] Univ Nebraska, Dept Math, Lincoln, NE 68588 USA

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S | 2009年 / 2卷 / 03期

基金：

巴西圣保罗研究基金会;

关键词：

wave equation; coupled system; source terms; blow-up; energy decay rates;

D O I：

10.3934/dcdss.2009.2.583

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is concerned with the study of the nonlinearly damped system of wave equations with Dirichlet boundary conditions: u(tt )- Delta u + vertical bar u(t)vertical bar(m-1)u(t) = F-u(u, v) in Omega x (0, infinity), v(tt )- Delta v + vertical bar v(t)vertical bar(r-1)v(t) = F-v(u, v) in Omega x (0, infinity), where Omega is a bounded domain in R-n, n = 1,2,3 with a smooth boundary partial derivative Omega = Gamma and F is a C-1 function given by F(u, v) = alpha vertical bar u + v vertical bar(p+1) + 2 beta vertical bar uv vertical bar(p+1/2). Under some conditions on the parameters in the system and with careful analysis involving the Nehari Manifold, we obtain several results on the global existence, uniform decay rates, and blow up of solutions in finite time when the initial energy is nonnegative.

引用

页码：583 / 608

页数：26

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