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December  2002, 1(4): 495-511. doi: 10.3934/cpaa.2002.1.495

Phase-field systems with vectorial order parameters including diffusional hysteresis effects

Nobuyuki Kenmochi 1, and  Jürgen Sprekels 2,

1. 

Department of Mathematics, Faculty of Education, Chiba University, 1-33 Yayoi-chō, Inage-ku, Chiba, 263–8522, Japan
2. 

Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, D–10117 Berlin, Germany

Received  October 2001 Revised  June 2002 Published  September 2002

This paper is concerned with phase-field systems of Penrose-Fife type which model the dynamics of a phase transition with non-conserved vectorial order parameter. The main novelty of the model is that the evolution of the order parameter vector is governed by a system consisting of one partial differential equation and one partial differential inclusion, which in the simplest case may be viewed as a diffusive approximation of the so-called multi-dimensional stop operator, which is one of the fundamental hysteresis operators. Results concerning existence, uniqueness and continuous dependence on data are presented which can be viewed as generalizations of recent results by the authors to cases where a diffusive hysteresis occurs.
Keywords: Parabolic systems, phase transitions., hysteresis, phase-field models, a priori estimates, existence, uniqueness.
Mathematics Subject Classification: 35K45, 35K50, 47J40, 80A20, 80A22. .
Citation: Nobuyuki Kenmochi, Jürgen Sprekels. Phase-field systems with vectorial order parameters including diffusional hysteresis effects. Communications on Pure & Applied Analysis, 2002, 1 (4) : 495-511. doi: 10.3934/cpaa.2002.1.495
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