Uniform Decay Rates for Viscoelastic Dissipative Systems

被引：25

作者：

Mustafa, Muhammad I. ^{[1
]}

机构：

[1] King Fahd Univ Petr & Minerals, Dept Math & Stat, POB 860, Dhahran 31261, Saudi Arabia

来源：

JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS | 2016年 / 22卷 / 01期

关键词：

General decay; Stability; Weak frictional damping; Relaxation function; Viscoelasticity; Convexity; Wave equation; SEMILINEAR WAVE-EQUATION; GENERAL DECAY; ASYMPTOTIC-BEHAVIOR; ENERGY; STABILIZATION; STABILITY; CONVEXITY;

D O I：

10.1007/s10883-014-9256-1

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

In this paper, we consider the wave equation with both weak frictional damping and viscoelastic damping acting simultaneously and complementarily in the domain. We establish an explicit and general decay rate result, using some properties of the convex functions. Our result is obtained without imposing any restrictive growth assumption on the frictional damping term and strongly weakening the usual assumptions on the relaxation function.

引用

页码：101 / 116

页数：16

共 40 条

[1] Convexity and weighted integral inequalities for energy decay rates of nonlinear dissipative hyperbolic systems [J].

Alabau-Boussouira, F .

APPLIED MATHEMATICS AND OPTIMIZATION, 2005, 51 (01) :61-105

[2] Decay estimates for second order evolution equations with memory [J].

Alabau-Boussouira, Fatiha ;

Cannarsa, Piermarco ;

Sforza, Daniela .

JOURNAL OF FUNCTIONAL ANALYSIS, 2008, 254 (05) :1342-1372

[3]

[Anonymous], 2013, Mathematical methods of classical mechanics

[4]

[Anonymous], 1993, DIFFER INTEGR EQUATI

[5]

[Anonymous], 1999, Ricerche Mat

[6]

[Anonymous], 2002, J. Differ. Equ

[7]

Barreto R., 1996, Appl. Anal, V60, P263

[8]

Benaissa A., 2006, Journal of Inequalities in Pure and Applied Mathematics, V7, P1

[9] Existence and decay of solutions of a viscoelastic equation with a nonlinear source [J].

Berrimi, S ;

Messaoudi, SA .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2006, 64 (10) :2314-2331

[10]

Berrimi S., 2004, Electron. J. Differ. Equations, V2004, P1

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