Impossibility of localization in thermo-porous-elasticity with microtemperatures

Abstract

In this note, we prove the impossibility of the localization in-time for the solutions of the linear porous-thermo-elasticity with microtemperatures theory. This means that the only solution for this problem that vanishes after a finite time is the null solution. From a thermomechanical point of view, this result says that the combination of the porous dissipation, the temperature and the microtemperatures (in the linear theory) is not strong enough to guarantee that the thermomechanical deformations will vanish after a finite time. The main idea to prove this result is to show the uniqueness of solutions for the backward in-time problem.