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Asymptotic analysis of a diffusive model for shape memory alloys with Cattaneo-Maxwell heat flux law. (English) Zbl 1018.74031

Summary: This work is concerned with a diffusive model for some austenite-martensite phase transition processes ruled by 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.

MSC:

74N05 Crystals in solids
74F05 Thermal effects in solid mechanics
74H10 Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of dynamical problems in solid mechanics
35Q72 Other PDE from mechanics (MSC2000)
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