Spatial and continuous dependence estimates in linear viscoelasticity

Abstract

In this paper we consider the problem determined by the anti-plane shear dynamic deformations for the linear theory of viscoelasticity. First, we prove existence of solutions of the problem determined in a semi-infinite strip. Then, we show that the rate of decay of the end effects in this problem is faster than that known for the Laplace equation. In the last section, we study the influence of the mass density on the decay of end effects.