Energy decay for a viscoelastic wave equation with space-time potential in Rn

Abstract

Abstract In this paper, we consider the following viscoelastic wave equation { u t t − ( Δ u − ∫ 0 t g ( t − s ) Δ u ( s ) d s ) + b ( t , x ) u t + | u | p − 1 u = 0 , t > 0 , x ∈ R n u ( 0 , x ) = u 0 ( x ) , u t ( 0 , x ) = u 1 ( x ) , x ∈ R n with space-time dependent potential and where the initial data u 0 ( x ) , u 1 ( 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.