Existence And Exponential Decay For The Solution Of Viscoelastic Wave Equations With Boundary Damping

LetΩbe a bounded star-shaped domain of R",n≥1, with a smooth boundary F=Γ0 UΓ1. Here,Γ0 andΓ1 are closed and disjoint, v represents the unit vector outward normal toΓ. In this article, we study the nonlinear viscoelastic equationWhere b>0. The existence of global solutions is povered by means of Faedo-Galerkin method, and make use of the perturbed energy method to prove the exponential decay for the strong and weak solutions when the kernel h in the memory term decays exponentially, and the nonlinear term F satisfies suitable conditions.