In our study we approached the mixed problem in the context of linear theory of thermoelasticity for Cosserat bodies. After we define the finite energy solution for this mixed problem, some results with respect to the existence and uniqueness are proven of this kind of solution. To this aim, we generalized some analogous results established by Dafermos, for a mixed problem from linear theory of the classical elasticity.
In another important result of our study, we introduce some specific conditions  which give the possibility that the evolution of the finite energy solution to be controlled.



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Vlase, Sorin, Marin, Marin, Sangeorzan, Livia