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

D'Apice C., Chirita S., Zampoli V.

Archives of Mechanics

2016

Vol. 68, nr 5

371--393

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.

On the exponential decay for viscoelastic mixtures

Passarella F., Zampoli V.

Archives of Mechanics

2007

Vol. 59, nr 2

97-117

This paper concerns the study of mixtures composed of a thermoelastic solid and a viscous fluid. For these mixtures, the dissipation effects are connected with the viscosity rate of one constituent and with the relative velocity vector. Using the time-weighted surface power method, associated with the linear process, we obtain some spatial decay estimates, characterized by time-independent and time-dependent decay rates, respectively. The first type of estimate is appropriate for large values of time, while the other is useful for short values of the same variable.