Global existence and decay estimates for a coupled system of wave equations with nonlinear dampings

Cheheb Farida; Bahlil Mounir; Miloudi Mustafa

Cheheb Farida Laboratory of Analysis and Control of PDEs, \\ Djillali Liabes University,\\ P. O. Box 89, Sidi Bel Abbes 22000, ALGERIA. \\
Bahlil Mounir Department of Mathematics, Faculty of Exact Sciences of Mascara Mustapha Stambouli University, P.O. Box 305, Mascara 29000, Algeria.
Miloudi Mustafa Laboratory of Analysis and Control of PDEs, \\ Djillali Liabes University,\\ P. O. Box 89, Sidi Bel Abbes 22000, ALGERIA. \\

Abstract

Our interest in this paper is to analyse the asymptotic behaviour of a coupled system of wave equations
with non-linear dampings. We show that the system is well-posed using the semigroup theory. Furthermore,
under suitable conditions on functions g(.), we estimate the energy decay rate by using the multiplier method.