Exponential and polynomial decay for a quasilinear viscoelastic equation

被引：116

作者：

Messaoudi, Salim A. ^{[1
]}

Tatar, Nasser-Eddine ^{[1
]}

机构：

[1] King Fahd Univ Petr & Minerals, Dept Math Sci, Dhahran 31261, Saudi Arabia

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2008年 / 68卷 / 04期

关键词：

exponential decay; memory term; modified energy functional; nonlinear viscoelastic equation; polynomial decay; relaxation function;

D O I：

10.1016/j.na.2006.11.036

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the following nonlinear viscoclastic equation: vertical bar u(1)vertical bar(rho) u(11) - Delta(u) - Delta u(11) + integral(t)(0) g(t - s)Delta u(s)ds = 0, in a bounded domain Omega for rho > 0. We show that the dissipation induced by the integral term is strong enough to stabilize the solution. This result improves an earlier one given by Cavalcanti et al. in [M.M. Cavalcaliti, V.N.D. Cavalcanti, J. Ferreira, Existence and uniform decay for nonlinear viscoelastic equation with strong damping, Math. Methods Appl. Sci. 24 (2001) 1043-1053]. (c) 2006 Elsevier Ltd. All rights reserved.

引用

页码：785 / 793

页数：9

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