Blow-up of solutions of a semilinear heat equation with a memory term

Abstract

We consider an initial boundary value problem related to the equation $u_t-\Delta u+{\int }_0^{t}g\left(t-s\right)\Delta u\left(x,s\right)ds={\left|u\right|}^{p-2}u$ and prove, under suitable conditions on $g$ and $p$, a blow-up result for certain solutions with positive initial energy.