Uniform boundedness and stability for a viscoelastic problem

In this paper we consider the following integro-differential problem which appears in viscoelasticityutρutt-Δu-Δutt+∫0tgt-τΔu(τ)dτ-γΔut=0on a bounded domain Ω with Dirichlet boundary condition and initial values. We prove an exponential decay result under different sufficient conditions on the relaxation function than the “standard” ones.