Existence and decay of solutions of a viscoelastic equation with a nonlinear source

In a bounded domain, we considerutt-Δu+∫0tg(t-τ)Δudτ=|u|γu,where γ>0γ>0, and gg is a nonnegative and decaying function. We prove a local existence theorem and show, for certain initial data and suitable conditions on gg and γγ, that this solution is global with energy which decays exponentially or polynomially depending on the rate of the decay of the relaxation function gg.