WIAS Preprint No. 698, (2001)

Global existence and asymptotic behaviour for a nonlocal phase-field model for non-isothermal phase transitions


  • Sprekels, Jürgen
    ORCID: 0009-0000-0618-8604
  • Zheng, Songmu

2010 Mathematics Subject Classification

  • 35B40 35K50 45J05 45K05


  • Phase transitions, nonlocal models, initial-boundary value problems, a priori estimates, asymptotic behaviour, well-posedness, integrodifferential equations




In this paper a nonlocal phase-field model for non-isothermal phase transitions with a non-conserved order parameter is studied. The paper extends recent investigations to the non-isothermal situation, complementing results obtained by H. Gajewski for the non-isothermal case for conserved order parameters in phase separation phenomena. The resulting field equations studied in this paper form a system of integro-partial differential equations which are highly nonlinearly coupled. For this system, results concerning global existence, uniqueness and large-time asymptotic behaviour are derived. The main results are proved using techniques that have been recently developed by P. Krejčí and the authors for phase-field systems involving hysteresis operators.

Appeared in

  • J. Math. Anal. Appl., 279 (2003), pp. 97-110

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