Loss of exponential stability for a thermoelastic system with memory

In this article we study a thermoelastic system considering the linearized model proposed by Gurtin and Pipkin [8] instead of the Fourier's law for the heat flux. We use theory of semigroups [9, 11] combining Pruss' Theorem [10] and the idea developed in [5] to show that the system is not exponentially stable.