GENERAL DECAY OF SOLUTIONS FOR A VISCOELASTIC EQUATION WITH NONLINEAR DAMPING AND SOURCE TERMS

被引：0

作者：

吴舜堂

机构：

[1] GeneralEducationCenter,NationalTaipeiUniversityofTechnology

来源：

Acta Mathematica Scientia | 2011年 / 31卷 / 04期

关键词：

global existence; asymptotic behavior; general decay;

D O I：

暂无

中图分类号：

O241 [数值分析];

学科分类号：

070102 ;

摘要：

The initial boundary value problem for a viscoelastic equation | u t | ρ u tt △u-△u tt + t 0 g(ts)△u(s)ds + | u t | m u t = | u | p u in a bounded domain is considered, where ρ, m, p > 0 and g is a nonnegative and decaying function. The general uniform decay of solution energy is discussed under some conditions on the relaxation function g and the initial data by adopting the method of [14, 15, 19]. This work generalizes and improves earlier results in the literature.

引用

页码：1436 / 1448

页数：13

共 19 条

[1]

Global existence and blow-up for a nonlinear porous medium equation. Li F C,Xie C H. Applied Mathematics Letters . 2003

[2]

Global existence and uniform stability of solutions for a quasilinear viscoelastic problem. S. A. Messaoudi,N. -E. Tatar. Mathematical Methods in the Applied Sciences . 2007

[3]

Global solutions for a nonlinear wave equation with the p-Laplacian operator. Gao,H.,Ma,T. F. Electron. J. Qual. Theory Differ. Equations . 1999

[4]

Exponential decay for the solution of semilinear viscoelastic wave equation with localized damping. Cavalcanti M M,Domingos Cavalcanti V N,Soriano J A. Elect J Diff Eqns . 2002

[5]

Exponential decay of solutions to a viscoelastic equation with nonlinear localized damping. Berrimi S,Messaoudi S A. Elect J Diff Eqns . 2004

[6]

Existence and decay of solutions of a viscoelastic equation with a nonlinear source. Berrimi S,Messaoudi S A. Nonlinear Analysis Theory Methods Applications . 2006

[7]

Asymptotic stability and energy decay rates of solutions of the wave equation with memory in a star-shaped domain. Aassila M,Cavalcanti M M,Soriano J A. The SIAM Journal on Control and Optimization . 2000

[8] GLOBAL EXISTENCE AND EXPONENTIAL STABILITY OF SMALL SOLUTIONS TO NONLINEAR VISCOELASTICITY [J].

KAWASHIMA, S ;

SHIBATA, Y .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1992, 148 (01) :189-208

[9]

Blow-up of positive-initial-energy solutions of a nonlinear viscoelastic hyperbolic equation. Messaoudi S.A. Journal of Mathematical Analysis and Applications . 2006

[10]

Global existence and uniform decay rates for the Kirchhoff-Carrier equation with nonlinear dissipation, Adv. M.M. Cavalcanti,V.N. Domingos Cavalcanti,J.A. Soriano. Differ. Equ . 2001

← 1 2 →