Energy decay for hyperbolic thermoelastic systems of memory type

Abstract

In this paper we study the hyperbolic thermoelastic system, which is obtained when, instead of Fourier’s law for the heat flux relation, we follow the linearized model proposed by Gurtin and Pipkin concerning the memory theory of heat conduction. In this case the thermoelastic model is fully hyperbolic. We show that the linear system is well posed and that the solution decays exponentially to zero as time goes to infinity.