Well-posed dual-phase-lag model of a thermoelastic dipolar body

We consider a time differential model for dual-phase-lag thermoelastic dipolar material. For the heat flux with dual-phase-lag we introduce a time differential equation to describe the thermal effects, and this is coupled with elastic deformation. Some qualitative results on solutions of the mixed initial boundary value problem, associated with this model, are obtained under mild constitutive restrictions. We will deduce an identity of Lagrange type and will use a conservation law in order to prove the uniqueness of solution, whereas the result of continuous dependence of solution is established by using a Gronwall type inequality and a conservation law.