On Some Non-existence Results in a Semilinear Theory of the Dipolar Thermoelastic Bodies

We consider a thermoelastic theory in which the equations that govern the evolution are linear with respect to the thermal displacement and nonlinear with regards to gradients of displacements and temperature. Our results refer to the non-existence of solutions for some mixed problems, considered in this context. We also address the instability of solutions of the considered problems. We will treat separately the case where the mechanical effects are neglected, taking into account only the thermal effect. In this case our problem has a nonlinear structure.