Phase-field models with hysteresis

Abstract

Phase-field systems as mathematical models for phase transitions have drawn increasing attention in recent years. However, while capable of capturing many of the experimentally observed phenomena, they are only of restricted value in modelling hysteresis effects occurring during phase transition processes. To overcome this shortcoming of existing phase-field theories, the authors have recently proposed a new approach to phase-field models which is based on the mathematical theory of hysteresis operators developed in the past 15 years. In particular, they have proved well-posedness and thermodynamic consistency for hysteretic phase field models which are related to the Caginalp and Penrose-Fife models. In this paper, these results are extended into different directions: we admit temperature-dependent relaxation coefficients and relax the growth conditions for the hysteresis operators considerably; also, a unified approach is used for a general class of systems that includes both the Caginalp and Penrose-Fife analogues. © 2000 Academic Press.