Blow-up of solutions of a nonlinear viscoelastic wave equation

In this paper, we consider the nonlinear viscoelastic equation utt−Δu+∫0tg(t−τ)Δu(τ)dτ−△ut=∣u∣p−2u,in Ω×[0,T], with initial conditions and Dirichlet boundary conditions. For nonincreasing positive functions gg, we prove that there are solutions with positive initial energy that blow up in finite time.