Global existence and uniform stability of solutions for a quasilinear viscoelastic problem期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Global existence and uniform stability of solutions for a quasilinear viscoelastic problem

Authors:	Salim A. Messaoudi Nasser‐eddine Tatar

Affiliation:	1. Department of Mathematical Sciences, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi ArabiaDepartment of Mathematical Sciences, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia===;2. Department of Mathematical Sciences, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia

Abstract:	In this paper the nonlinear viscoelastic wave equation in canonical form with Dirichlet boundary condition is considered. By introducing a new functional and using the potential well method, we show that the damping induced by the viscoelastic term is enough to ensure global existence and uniform decay of solutions provided that the initial data are in some stable set. Copyright © 2006 John Wiley & Sons, Ltd.

Keywords:	global existence exponential decay nonlinear source relaxation function polynomial decay viscoelasticity