WIAS Preprint No. 520, (1999)

Asymptotic behaviour for a phase-field system with hysteresis


  • Krejčí, Pavel
    ORCID: 0000-0002-7579-6002
  • Sprekels, Jürgen
    ORCID: 0009-0000-0618-8604
  • Zheng, Songmu

2010 Mathematics Subject Classification

  • 35K55 80A22 47H30


  • Phase-field systems, phase transitions, hysteresis operators, asymptotic behaviour




The method of hysteresis operators in modelling phase transitions is applied here to the problem of asymptotic stabilization of solutions to a phase-field system with hysteresis. While it is known that a unique global strong solution exists for every initial data and that the evolution process described by this system is thermodynamically consistent in the sense that the absolute temperature remains positive for all times and the Clausius-Duhem inequality holds almost everywhere, we study here the asymptotic behaviour of the solution as t → ∞.

Appeared in

  • J. Differential Equations, 175 (2001), pp. 88--107

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