Local existence and blow-up of solutions for coupled viscoelastic wave equations with degenerate damping terms

In this paper, we investigate a nonlinear system of viscoelastic equations with degenerate damping and source terms in a bounded domain. Under appropriate assumptions on the parameters, degenerate damping terms and the relaxation functions i, (= 1, 2), we prove local existence and uniqueness of the solution by using the Faedo-Galerkin method with a new scenario. Then, we prove the blow-up of weak solutions to problem (1.1). This improves earlier results in the literature