Hysteresis operators in phase-field models of Penrose-Fife type
- Krejčí, Pavel
- Sprekels, Jürgen
2010 Mathematics Subject Classification
- 35K55 80A22 47H30
- Phase-field systems, phase transitions, hysteresis operators, well-posedness of parabolic systems, thermodynamic consistency, Penrose-Fife model
Phase-field systems as mathematical models for phase transitions have drawn a considerable interest in recent years. However, while they are capable of capturing many of the experimentally observed phenomena, they are only of restricted value in modelling hysteresis effects occuring during phase transition processes. To overcome this shortcoming of existing phase-field theories, the authors recently proposed a new approach to phase-field models which is based on the mathematical theory of hysteresis operators developed in the past fifteen years. Well-posedness and thermodynamic consistency were proved for a phase-field system with hysteresis which is closely related to the model advanced by Caginalp in a series of papers. In this note the more difficult case of a phase-field system of Penrose-Fife type with hysteresis is investigated. Under slightly more restrictive assumptions than in the Caginalp case it is shown that the system is well-posed and thermodynamically consistent.
- Appl. Math. 43 (1998), pp.207-222