GENERAL DECAY RATE ESTIMATE FOR THE ENERGY OF A WEAK VISCOELASTIC EQUATION WITH AN INTERNAL TIME-VARYING DELAY TERM

被引：39

作者：

Liu, Wenjun ^{[1
]}

机构：

[1] Nanjing Univ Informat Sci & Technol, Coll Math & Stat, Nanjing 210044, Jiangsu, Peoples R China

来源：

TAIWANESE JOURNAL OF MATHEMATICS | 2013年 / 17卷 / 06期

基金：

中国国家自然科学基金;

关键词：

Weak viscoelastic equation; Time-varying delay; Internal feedback; General decay rate; FEEDBACK STABILIZATION; WAVE-EQUATIONS; HYPERBOLIC-EQUATIONS; EVOLUTION-EQUATIONS; BOUNDARY; STABILITY; SYSTEMS;

D O I：

10.11650/tjm.17.2013.2968

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we consider the weak viscoelastic equation with an internal time-varying delay term u(tt)(x, t)-Delta u(x, t)+alpha(t) integral(t)(0) g(t-s)Delta u(x, s) ds+a(0)u(t)(x, t)+a(1)u(t)(x, t-tau(t)) = 0 in a bounded domain. By introducing suitable energy and Lyapunov functionals, under suitable assumptions, we establish a general decay rate estimate for the energy, which depends on the behavior of both alpha and g.

引用

页码：2101 / 2115

页数：15

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