Exponential stability of a type III thermo-porous-elastic system from a new approach in its coupling

In this article, we prove the well-posedness and stability of a one-dimensional thermo-porous-elastic system, considering a thermal coupling of the Green and Naghdi types III. In this scenario, we propose a new model where the temperature of the material directly affects the stress tensor of displacements and the equilibrated stress tensor on the volume fractions in the porous medium, thereby generalizing some existing results in the literature on the subject. Additionally, the exponential decay of energy is proven when the evolution equation corresponding to the dynamics of the elastic skeletal structure exhibits frictional-type damping.