General decay and blow-up of solution for a viscoelastic wave equation with nonlinear degenerate damping and source terms

Abstract

We are concerned with the initial-boundary value problem for a nonlinear viscoelastic problem with the degenerate damping and the nonlinear source term in this paper. Under appropriate assumptions on the initial data, memory kernel and parameters, we establish several results regarding the global solution, blow-up properties and general decay in the case of positive initial energy. We overcome the difficulties brought by positive initial energy by using the potential well theory.