Electronic Journal of Differential Equations,
Vol. 2004(2004), No. 88, pp. 1-10.

Title: Exponential decay of solutions to a viscoelastic equation
       with nonlinear localized damping

Authors: Said Berrimi (Univ. of Setif, Algeria)
         Salim A. Messaoudi (KFUPM, Dhahran, Saudi Arabia)
 
Abstract: 
 In this paper we consider the nonlinear viscoelastic equation
 $$
 u_{tt}-\Delta u+\int_{0}^{t}g(t-\tau)\Delta u(\tau)\,d\tau
 +a(x)|u_{t}|^{m}u_{t}+b|u|^{\gamma }u=0,
 $$
 in a bounded domain. Without imposing geometry restrictions
 on the boundary, we establish an exponential decay result,
 under weaker conditions than those in [3].
 
Submitted May 17, 2004. Published June 29, 2004.
Math Subject Classifications: 35B35, 35L20, 35L70.
Key Words: Exponential decay; global existence; nonlinear localized damping.