Asymptotic behaviour of the energy in partially viscoelastic materials

Abstract

In this paper we study models of materials consisting of an elastic part (without memory) and a viscoelastic part, where the dissipation given by the memory is effective. We show that the solutions of the corresponding partial viscoelastic model decay exponentially to zero, provided the relaxation function also decays exponentially, no matter how small is the viscoelastic part of the material