Geodesic
Hysteresis operators in phase-field models of Penrose-fife type
Applications of Mathematics, Tome 43 (1998) no. 3, pp. 207-222 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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Phase-field systems as mathematical models for phase transitions have drawn a considerable attention in recent years. However, while they are suitable for 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 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.
Phase-field systems as mathematical models for phase transitions have drawn a considerable attention in recent years. However, while they are suitable for 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 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.
DOI : 10.1023/A:1023276524286
Classification : 35K55, 47H30, 80A22
Keywords: phase-field systems; phase transitions; hysteresis operators; well-posedness of parabolic systems; thermodynamic consistency; Penrose-Fife model 
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     title = {Hysteresis operators in phase-field models of {Penrose-fife} type},
     journal = {Applications of Mathematics},
     pages = {207--222},
     year = {1998},
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Krejčí, Pavel; Sprekels, Jürgen. Hysteresis operators in phase-field models of Penrose-fife type. Applications of Mathematics, Tome 43 (1998) no. 3, pp. 207-222. doi: 10.1023/A:1023276524286

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