Uniform Decay of Solutions for a Nonlinear Viscoelastic Wave Equation with Boundary Dissipation

被引：7

作者：

Wu, Shun-Tang ^{[1
]}

Chen, Hsueh-Fang ^{[2
]}

机构：

[1] Natl Taipei Univ Technol, Gen Educ Ctr, Taipei 106, Taiwan

[2] Yu Da Univ, Dept Business Adm, Miaoli 366, Taiwan

来源：

JOURNAL OF FUNCTION SPACES AND APPLICATIONS | 2012年

关键词：

GENERAL DECAY; GLOBAL EXISTENCE; SOURCE TERMS; ENERGY; RATES; CONVEXITY; SYSTEMS;

D O I：

10.1155/2012/421847

中图分类号：

学科分类号：

摘要：

We consider a nonlinear viscoelastic wave equation u(tt)(t) - k(0)Delta u(t) + integral(t)(0)g(t - s)div(a(x)del u(s))ds + b(x)u(t) = f(u), with nonlinear boundary damping in a bounded domain Omega. Under appropriate assumptions imposed on g and with certain initial data, we establish the general decay rate of the solution energy which is not necessarily of exponential or polynomial type. This work generalizes and improves earlier results in the literature.

引用

页数：17

共 18 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]

[Anonymous], 2002, J. Differ. Equ

[3] 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

[4]

BERRIMI S, 2004, ELECT J DIFFERENTIAL, P1

[5] General decay rate estimates for viscoelastic dissipative systems [J].

Cavalcanti, M. M. ;

Cavalcanti, V. N. Domingos ;

Martinez, P. .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2008, 68 (01) :177-193

[6]

Cavalcanti M.M., 2001, Diff. Integ. Eqs, V14, P85

[7] Frictional versus viscoelastic damping in a semilinear wave equation [J].

Cavalcanti, MM ;

Oquendo, HP .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2003, 42 (04) :1310-1324

[8] Uniform energy decay rates for nonlinear viscoelastic wave equation with nonlocal boundary damping [J].

Li, Fushan ;

Zhao, Cuiling .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2011, 74 (11) :3468-3477

[9] Global existence uniqueness and decay estimates for nonlinear viscoelastic wave equation with boundary dissipation [J].

Li, Fushan ;

Zhao, Zengqin ;

Chen, Yanfu .

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2011, 12 (03) :1759-1773

[10] On decay and blow-up of the solution for a viscoelastic wave equation with boundary damping and source terms [J].

Liu, Wenjun ;

Yu, Jun .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2011, 74 (06) :2175-2190

← 1 2 →