Exponential Decay of Swelling Porous Elastic Soils with Microtemperatures Effects

In this article, we considered the one-dimensional swelling problem in porous elastic soils with microtemperatures effects in the case of fluid saturation. First, we showed that the system is well-posed in the sens of semigroup. Then, we constructed a suitable Lyapunov functional based on the energy method and we proved that the dissipation given only by the microtemperatures is strong enough to provoke an exponential stability for the solution irrespective of the wave speeds of the system.