WIAS Preprint No. 665, (2001)

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


  • Kenmochi, Nobuyuki
  • Sprekels, Jürgen
    ORCID: 0009-0000-0618-8604

2010 Mathematics Subject Classification

  • 35K45 35K50 47J40 80A20 80A22


  • Parabolic systems, phase-field models, hysteresis, a priori estimates, existence, uniqueness, phase transitions




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.

Appeared in

  • Comm. Pure Appl. Anal. 4 (2002), pp. 495-511

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