Optimal energy decay result for nonlinear abstract viscoelastic dissipative systems

被引：9

作者：

Mustafa, Muhammad, I ^{[1
]}

机构：

[1] Univ Sharjah, Dept Math, POB 27272, Sharjah, U Arab Emirates

来源：

ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK | 2021年 / 72卷 / 02期

关键词：

Energy decay rates; Viscoelastic damping; Frictional damping; Source term; 2ND-ORDER EVOLUTION-EQUATIONS; VON KARMAN SYSTEM; WAVE-EQUATION; GENERAL DECAY; ASYMPTOTIC STABILITY; RATES; MEMORY; EXISTENCE; BEHAVIOR;

D O I：

10.1007/s00033-021-01498-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider the nonlinear abstract equation u(tt) + Au - integral(t)(0) g(t - s)Au(s)ds + h(u(t)) = j(u) subject to a competing effect of viscoelastic and frictional dampings. With very general assumptions on the behavior of g at infinity and the behavior of h near 0, we establish explicit and optimal energy decay result. To the best of our knowledge, this is the first time we have such combination of generality and optimality in one explicit formula for the energy decay rates of this system.

引用

页数：15

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