Instability and non-existence in the nonlinear theory of thermoelasticity without energy dissipation

A new thermoelastic theory called the theory of thermoelasticity without energy dissipation has been proposed recently. In this paper we investigate, within the context of this theory, some qualitative aspects of solutions of the equations of materials which are nonlinear with respect to the gradients of displacements and temperature, but linear with respect to the thermal displacement. We obtain several results concerning instability and non-existence of solutions. The last section is devoted to the study of heat conduction tin the absence of mechanical effects) in the nonlinear theory. In this situation we also obtain instability and non-existence for some cases.