Asymptotics of Solutions in the Problem about Small Motions of a Compressible Maxwell Fluid

Abstract

A model of a viscoelastic compressible Maxwell fluid is studied. This model is described by a system of partial integro-differential equations with appropriate boundary and initial conditions. An abstract analog of the problem under study is also considered. It is proved that a uniformly exponentially stable C₀-semigroup emerges in this problem. Based on this fact, an estimate for the solution of the evolution problem is derived in the case where the external load is close to being almost periodic.