On the final boundary value problems in linear thermoelasticity

In the present study we derive some uniqueness criteria for solutions of the Cauchy problem for the standard equations of dynamical linear thermoelasticity backward in time. We use Lagrange-Brun identities combined with some differential inequalities in order to show that the final boundary value problem associated with the linear thermoelasticity backward in time has at most one solution in appropriate classes of displacement-temperature fields. The uniqueness results are obtained under the assumptions that the density mass and the specific heat are strictly positive and the conductivity tensor is positive definite.