Blow-Up of Solutions for a System Viscoelastic Equation with Balakrishnan–Taylor Damping and Nonlinear Source of Polynomial Type

Abstract

In this paper, we study the initial-boundary value problem for a system of nonlinear viscoelastic equations with Balakrishnan–Taylor damping terms and nonlinear source of polynomial type. We demonstrate that the nonlinear source of polynomial type is able to force solutions to blow up infinite time even in presence of stronger damping with non positive initial energy combined with a positive initial energy.