On the stability of porous-elastic system with microtemparatures

In this article, we investigate a porous-elastic system with dissipation due to only microtemperatures. It is well-known that such a system with a single damping term lacks exponential stability unless another damping mechanism is added. In this article, however, we prove that the unique dissipation due to the microtemperatures is strong enough to exponentially stabilize the system if and only if the wave speeds of the system are equal. In the case of lack of exponential stability, we show that the solution decays polynomially. Moreover, we show that this rate of decay is optimal. Our result is new and improves previous results in the literature.