Thermoelastic theory with microtemperatures and dissipative thermodynamics

In this article we derive a nonlinear theory of thermoelastic materials with microtemperatures based on the entropy balance of type III postulated by Green and Naghdi. The work is motivated by an increasing use of materials which possess thermal variation at a microstructure level such that both thermal and microtemperatures waves can propagate with finite speeds and energy dissipation. The equations of the linear theory are also obtained. Then, we use a semigroup approach to derive an existence and uniqueness result for the solutions to the anisotropic problem and to study the asymptotic behavior. Finally, we investigate the impossibility of the localization in time of solutions.