On Global Solvability and Asymptotic Behavior of a Nonlinear Coupled System with Memory Condition at the Boundary

Abstract

We consider a nonlinear coupled system of two wave equations with memory condition at the boundary and we study the asymptotic behavior of the corresponding solutions. We proved that the energy decay with the same rate of decay of the relaxation functions, that is, the energy decays exponentially when the relaxation functions decay exponentially and decay polynomially when the relaxation functions decay polynomially.