In this paper we approach a generalized thermoelasticity theory based on a heat conduction equation in bodies with dipolar structure, the heat conduction depends on two distinct temperatures, the thermodynamic temperature and the conductive temperature. In our considerations the difference between two temperatures  is highlighted by the heat supply.  For the mixed initial boundary value problem defined in this context, we prove the uniqueness of a solution corresponding some specific initial and boundary conditions. Also, if the initial energy is negative or null, we prove that the solutions of the mixed problem are exponentially unstable.

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 Marin, M., Fudulu, I. M., Precup, G., Vlase, S.