General decay rate estimates for viscoelastic dissipative systems

被引：176

作者：

Cavalcanti, M. M.

Cavalcanti, V. N. Domingos

Martinez, P.

机构：

[1] Univ Estadual Maringa, BR-87020900 Maringa, Parana, Brazil

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

[3] Univ Toulouse 3, F-31062 Toulouse, France

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2008年 / 68卷 / 01期

关键词：

nonlinear stabilization; asymptotic behavior at zero and infinity;

D O I：

10.1016/j.na.2006.10.040

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The linear viscoelastic equation is considered. We prove uniform decay rates of the energy by assuming a nonlinear feedback acting on the boundary, without imposing any restrictive growth assumption on the damping term and strongly weakening the usual assumptions on the relaxation function. Our estimate depends both on the behavior of the damping term near zero and on the behavior of the relaxation function at infinity. The proofs are based on the multiplier method and on a general lemma about convergent and divergent series for obtaining the uniform decay rates. (C) 2006 Elsevier Ltd. All rights reserved.

引用

页码：177 / 193

页数：17

共 25 条

[1] Asymptotic stability and energy decay rates for solutions of the wave equation with memory in a star-shaped domain [J].