Asymptotic analysis of a diffusive model for shape memory alloys with Cattaneo-Maxwell heat flux law

Abstract

This work is concerned with a diffusive model for some austenite-martensite phase transition processes ruled by the Cattaneo-Maxwell heat flux law, namely assuming for the heat flux a relaxed version of the classical Fourier law. A rigorous asymptotic analysis of the macroscopic model is performed and it is shown that such model is nothing but a singular perturbation of the standard Frémond model for shape memory alloys. Convergence results are proved along with error estimates.