Existence, uniqueness and asymptotic behaviour of solutions to the equations of viscoelasticity with voids

Abstract

This paper is concerned with the linear theroy of viscoelastic materials with voids. We study uniqueness, existence and asymptotic behaviour for the solutions of the dynamical problem. The uniqueness theorem is obtained by means of the power type function method. We use the semigroup theory of linear operators to obtain existence and continuous dependence of solutions. In the last section, we study the asymptotic behaviour of solutions.