One spatial variable thermoelastic transmission problem in viscoelasticity located in the second part

Abstract

We consider in this article a one spatial variable transmission problem in mixed type I and type II thermoelastic system with infinite memory acting in the second part. The main contributions are to show that the infinite memory lets our problem dissipative and that the t−1 is the sharp decay rate. That is to show that, for this types of materials, the dissipation produced by the viscoelastic part is not strong enough to produce an exponential decay of the solution even that the infinite memory satisfies assumptions (8) and (9).