A blow-up result for a system of coupled viscoelastic equations with arbitrary positive initial energy

Abstract

Abstract This article is devoted to a study of the blow-up result for a system of coupled viscoelastic wave equations. By establishing a new auxiliary function and using the reduction to absurdity method, we obtain some sufficient conditions on initial data such that the solution blows up in finite time at arbitrarily high initial energy. This work generalizes and improves earlier results in the literature.

Keywords

• Viscoelastic wave equation
• Relaxation function
• Blow up