Blow-up of arbitrarily positive initial energy solutions for a viscoelastic wave system with nonlinear damping and source terms

Abstract

Abstract This work is concerned with the Dirichlet initial boundary problem for a semilinear viscoelastic wave system with nonlinear weak damping and source terms. For nonincreasing positive functions g and h, we show the finite time blow-up of some solutions whose initial data have arbitrarily high initial energy.

Keywords

• Viscoelastic wave system
• Nonlinear damping
• Blow-up
• Arbitrarily positive initial energy