High-order approximations of three-phase-lag heat conduction model: Some qualitative results

ABSTRACT

This article deals with some high-order approximations of the three-phase-lag heat transfer model aiming, at first, to identify the restrictions that make them well-posed consistence. Consequently, a first result about the uniqueness and continuous dependence of the solutions with respect to the given initial data and to the supply term is established for the related initial boundary value problems. Subsequently, to provide a more comprehensive analysis of the model, some further spatial decay results are established, this time conveniently relaxing the hypotheses about the delay times and the thermal conductivities. More precisely, a theorem of influence domain is proved for the wave propagating models and an exponential decaying estimate of Saint-Venant type is established for the diffusive models.

KEYWORDS:

• Continuous dependence
• delay times
• high-order approximations
• spatial behavior
• three-phase-lag heat conduction model
• uniqueness