General and optimal decay rates for a system of wave equations with damping and a coupled source term

Abstract

In this article, we aim to investigate the decay characteristics of a system consisting of two viscoelastic wave equations with Dirichlet boundary conditions, where the dispersion term and nonlinear weak damping term are taken into account. Under appropriate conditions, we establish both general and optimal decay results. This work generalizes and improves earlier results in the literature.

Keywords

• general decay
• coupled equations
• lyapunov function
• relaxation function