Thermoelastic Systems with Fourier's law

These notes report on some achievements in thermoelasticity theory. In particular emphasis is placed on classical thermoelasticity for which the heat propagation is modeled by Fourier's law. Using decoupling technique, many results have been established. Taking into account the effect of heat on viscoelasticity of materials, some new theorems are presented. By introducing the concept of a continuum theory of granular materials with interstitial voids into the theory of elastic solids with voids an extension of the elastic theory arises, namely, porous elastic theory. To study the effect of the propagation of heat along a porous elastic material, porous thermoelasticity theory is the best suitable framework. Some compactness results for this type of systems have been given. These notes should appeal to applied mathematicians, physicians and theoretical engineers with an interest in thermoelasticity theory, as well as to graduate students in these areas.