# Hysteresis operators in phase-field models of Penrose-fife type

Applications of Mathematics (1998)

- Volume: 43, Issue: 3, page 207-222
- ISSN: 0862-7940

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topKrejčí, Pavel, and Sprekels, Jürgen. "Hysteresis operators in phase-field models of Penrose-fife type." Applications of Mathematics 43.3 (1998): 207-222. <http://eudml.org/doc/33007>.

@article{Krejčí1998,

abstract = {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.},

author = {Krejčí, Pavel, Sprekels, Jürgen},

journal = {Applications of Mathematics},

keywords = {phase-field systems; phase transitions; hysteresis operators; well-posedness of parabolic systems; thermodynamic consistency; Penrose-Fife model; phase-field systems; phase transitions; hysteresis operators; well-posedness of parabolic systems; thermodynamic consistency; Penrose-Fife model},

language = {eng},

number = {3},

pages = {207-222},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {Hysteresis operators in phase-field models of Penrose-fife type},

url = {http://eudml.org/doc/33007},

volume = {43},

year = {1998},

}

TY - JOUR

AU - Krejčí, Pavel

AU - Sprekels, Jürgen

TI - Hysteresis operators in phase-field models of Penrose-fife type

JO - Applications of Mathematics

PY - 1998

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 43

IS - 3

SP - 207

EP - 222

AB - 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.

LA - eng

KW - phase-field systems; phase transitions; hysteresis operators; well-posedness of parabolic systems; thermodynamic consistency; Penrose-Fife model; phase-field systems; phase transitions; hysteresis operators; well-posedness of parabolic systems; thermodynamic consistency; Penrose-Fife model

UR - http://eudml.org/doc/33007

ER -

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