Mathematical analysis of high-order three-phase-lagging models

The aim of this article is to provide an in-depth discussion about thermoelastic models able to take into account the effect of ultrafast strain of a deformable conductor coupled with a very refined behavior in terms of heat exchange, depicted through three distinct relaxation times and their related high-order effects. In particular, the well-posedness question is investigated dealing with a linear anisotropic and inhomogeneous medium, being able to prove the uniqueness as well as the continuous dependence of the solutions for suitable initial-boundary value problems. From a technical point of view, we underline that the main tools used are identifiable: i. in the introduction of an apposite integral operator that enters into the handling of the model, appropriately modifying the original initial-boundary value problem; ii. in the application of the Lagrange identity method in combination with the time-weighted function method and with an exponentially time-weighted Poincare inequality. It is worth emphasizing that the results achieved are valid under very weak assumptions made on the thermoelastic features of the model.