General decay and blow-up of solutions for a nonlinear viscoelastic wave equation with strong damping

Abstract

This article is concerned with the decay and blow-up properties of a nonlinear viscoelastic wave equation with strong damping. We first show a local existence theorem. Then, we prove the global existence of solutions and establish a general decay rate estimate. Finally, we show the finite time blow-up result for some solutions with negative initial energy and positive initial energy.