Local Existence and Blow Up of Solutions for a Coupled Viscoelastic Kirchhoff-Type Equations with Degenerate Damping

In this paper, we consider the initial boundary value problem of a coupled viscoelastic Kirchhofftype equations with degenerate damping. Firstly, we prove a local existence theorem by using the Faedo-Galerkin approximations. Then, we study blow up of solutions when initial energy is possitive.