A model of dual-phase-lag thermoelasticity for a Cosserat body

We consider a thermoelastic Cosserat body with dual-phase lag. In order to formulate a dual-phase-lag model, an equation is introduced, of the time differential type, to characterize the thermal effects and the coupling with the deformation from an elastic point of view. We associate with this model a mixed problem with initial data and conditions to the limit. We then obtain some qualitative estimates on the solutions of this mixed problem, without resorting to restrictive conditions on the thermoelastic coefficients. In order to obtain the uniqueness of the solution, we appeal to a Lagrange-type identity, easily obtained in the given context, and to a law of conservation, previously demonstrated. Then, we establish an inequality which is of the Gronwall’s type, that is useful for proving the continuous dependence of the solutions in relation to initial values and loads, which is another important result of our study.