Energy decay for a viscoelastic wave equation with space-time potential in [formula omitted

Abstract

In this paper, we consider the following viscoelastic wave equation{utt−(Δu−∫0tg(t−s)Δu(s)ds)+b(t,x)ut+|u|p−1u=0,t>0,x∈Rnu(0,x)=u0(x),ut(0,x)=u1(x),x∈Rn with space-time dependent potential and where the initial data u0(x), u1(x) have compact support. Under suitable assumptions on the relaxation function g and the potential b, we obtain a more general energy decay result using the perturbed energy method.