On the well-posedness of the time-differential three-phase-lag thermoelasticity model

This paper analyzes the time differential three-phase-lag model of coupled thermoelasticity. The uniqueness and continuous dependence results are established for the solutions of the corresponding initial boundary value problems associated with the model in concern. The key tool of the method is to associate with the basic initial boundary value problem of the model an appropriate auxiliary initial boundary value problem and then to establish an identity of Lagrange type. This last identity is used to analyze the uniqueness of solutions under appropriate mild restrictions assumed upon the constitutive coefficients and upon the delay times. Uniqueness question is also discussed for a set of models of thermoelasticity developed in literature. Further, for the continuous dependence problem an appropriate estimate of the solution is obtained in terms of the given data. This expresses the continuous dependence of solution with respect to the initial data and with respect to the given supply loads, provided some appropriate constitutive assumptions are considered. These results give information upon the well-posedness of the time differential three-phase-lag model of coupled thermoelasticity.