On thermoelastic bodies with inner structure and microtemperatures

In the first part of this paper we present a linear theory of thermoelastic bodies with microstructure and microtemperatures which permits the transmission of heat as thermal waves at finite speed. The theory is based on the entropy balance postulated by Green and Naghdi [A.E. Green, P.M. Naghdi, A re-examination of the basic postulates of thermomechanics, Proc. R. Soc. London A 432 (1991) 171–194]. We consider bodies with microstructure whose microelements can stretch and contract independently of their translations. Then we establish existence and uniqueness results in the context of the dynamic theory.