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 𝜛 𝑖 , ( 𝑖 = 1 , 2), we prove local existence and unique- ness 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 [ 6 , 23 , 25 ].