Blow-up of solutions to a semilinear heat equation with a viscoelastic term and a nonlinear boundary flux

Abstract

In this article, we study a semilinear heat equationut−Δu+∫0tg(t−s)Δu(x,s)ds=0 with a viscoelastic term and a nonlinear flux on the boundary. By defining a modified energy functional and using a concavity argument, a blow-up result for solutions with negative initial energy is proved.