Communications on Pure and Applied Analysis (CPAA)

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

Pages: 495 - 511, Volume 1, Issue 4, December 2002      doi:10.3934/cpaa.2002.1.495

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Nobuyuki Kenmochi - Department of Mathematics, Faculty of Education, Chiba University, 1-33 Yayoi-chō, Inage-ku, Chiba, 263–8522, Japan (email)
Jürgen Sprekels - Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, D–10117 Berlin, Germany (email)

Abstract: 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-field models, hysteresis, a priori estimates, existence, uniqueness, phase transitions.
Mathematics Subject Classification:  35K45, 35K50, 47J40, 80A20, 80A22.

Received: October 2001;      Revised: June 2002;      Available Online: September 2002.