On the structural stability of thermoelastic model of porous media

Abstract In the present paper we study the structural stability of the mathematical model of the linear thermoelastic materials with voids. We prove that the solutions of problems depend continuously on the constitutive quantities, which may be subjected to error or perturbations in the mathematical modelling process. Thus, we assume to have changes in the various coupling coefficients of the model and then we establish estimates of continuous dependence of solutions. We have to outline that such estimates play a central role in obtaining approximations to these kinds of problems. To derive a priori estimates for a solution we first establish appropriate bounds for the solutions of certain auxiliary problems. These are achieved by means of so‐called Rellich‐like identities. We also investigate how the solution in the coupled model behaves as some coupling coefficients tend to zero. Copyright © 2007 John Wiley & Sons, Ltd.