The main idea of this work is to develop a new model that combines the properties of porous-elastic materials and standard linear solids that depend in its model on Hooke’s law. In addition to the two previous mechanical systems, we have added a thermal effect of second sound which is modeled by a system that link the heat equation with the heat flow field equation. The model was introduced on the basis of evolution equations and basic equations for flexible-porous materials and a standard solids property whose model is based on Hooke’s law. It’s about a standard linear model of viscoelasticity for system of flexible structure materials with voids coupled to heat waves that propagate at a finite velocity according to Cattaneo’s law for thermal conduction. We show a global existence of the weak solutions and we then interest by the decay rate in time of solutions where the exponential stability has been proved. In this study, a systematization, important from a practical point of view, was carried out, devoted to completed studies for thermo-visco-elasticity on flexible structures.
Dridi et al. (Wed,) studied this question.