Electron. J. Diff. Eqns., Vol. 2004(2004), No. 88, pp. 1-10.

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

Said Berrimi, Salim A. Messaoudi

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.

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Said Berrimi
Math Department
University of Setif
Setif, Algeria
email: berrimi@yahoo.fr
Salim A. Messaoudi
Mathematical Sciences Department
KFUPM, Dhahran 31261, Saudi Arabia
email: messaoud@kfupm.edu.sa

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