Structural and Microthermal Effects on the Exponential Stabilization of Poroelastic Systems

ABSTRACT In this work, we study the well‐posedness and the asymptotic behavior of the solutions of a poroelastic system under the effects of viscoporosity, viscoelasticity, and microtemperature. We present the surprising fact of the exponential stabilization of the system, even under the condition , which reduces the internal energy dissipation of the system. This finding contrasts with recent results in the literature, where it is shown that destroys the exponential stability of the thermal system. Furthermore, we prove that the microthermal effect is not sufficient to guarantee the analyticity of the solutions.