A study of a thermoelastic body possessing microtemperatures

Abstract In our study we approach a Cosserat thermoelastic body in which we take into account both the usual temperature and the microtemperature, that is, the temperature of the microparticles of the body. After constructing the mixed problem with initial and boundary values, in this context, we define an appropriate Hilbert space in which we obtain a temporal evolutionary equation which is equivalent to the already constructed mixed problem. With the help of some known results from the theory of contraction semigroups we prove both the existence and the uniqueness of the solution of the evolution equation, therefore of the considered mixed problem. Furthermore, the same semigroup theory allows us to obtain the continuous dependence of the solution of the mixed problem, both with respect to the initial data and with respect to the loading.