Polynomial stability and numerical simulation of porous-thermoelastic system with microtempratures effects

Abstract

In this article, we consider a one dimensional porous-thermoelastic system with dissipation only due to microtemperatures effect where the heat conduction is given by Cattaneo's law. First, By constructing a suitable Lyapunov functional using the multipliers method, we establish a polynomial decay result of the solution when ???0 which is the stability number obtained at the first in (<cite>Sac</cite>). Then, we give some numerical tests to illustrate the theoretical results by carrying out an Euler scheme for time discretization and the classical finite difference method for the spatial discretization.