Blow-up of positive-initial-energy solutions of a nonlinear viscoelastic hyperbolic equation

In this paper, we consider the nonlinear viscoelastic equation utt − Δu+ t 0 g(t − τ)Δu(τ)dτ +ut |ut |m−2 = u|u|p−2 with initial conditions and Dirichlet boundary conditions. For nonincreasing positive functions g and for p >m, we prove that there are solutions with positive initial energy that blow up in finite time. © 2005 Elsevier Inc. All rights reserved