ON THE UNIQUENESS AND CONTINUOUS DEPENDENCE OF SOLUTIONS IN DYNAMICAL THERMOELASTICITY BACKWARD IN TIME

This article studies the uniqueness and continuous dependence problems for the thermoelastic processes backward in time. Using some Lagrange-Brun identities combined with Gronwall's lemma, it is shown that the boundary final value problem associated with the linear thermoelasticity has at most one solution provided that some mild requirements are assumed concerning the thermoelastic coefficients. Some estimates are outlined that exhibit continuous dependence with respect to the final data, on the whole time interval without any kind of constraint on the solutions.