WIAS Preprint No. 497, (1999)

Hysteresis in phase-field models with thermal memory


  • Gilardi, Gianni
    ORCID: 0000-0002-0651-4307
  • Krejčí, Pavel
    ORCID: 0000-0002-7579-6002
  • Sprekels, Jürgen
    ORCID: 0009-0000-0618-8604

2010 Mathematics Subject Classification

  • 35K55 80A22 47H30


  • Phase transitions, hysteresis operators, phase-field models, heat conduction with memory, integrodifferential equations




Phase-field systems as mathematical models for phase transitions have drawn increasing attention in recent years. However, while capable of capturing many of the experimentally observed phenomena, they are only of restricted value in modelling hysteresis effects occurring during phase transition processes. To overcome this shortcoming, a new approach has recently been proposed by the last two authors which is based on the mathematical theory of hysteresis operators developed in the past fifteen years. In this paper this approach is extended to cases where the material exhibits an additional thermal memory, i.e., where the heat flux contains a time convolution of the spatial gradient of temperature. It is shown that the corresponding system of field equations admits a unique strong solution that depends continuously on the data of the system.

Appeared in

  • Math. Methods Appl. Sci., 23(2000), pp. 909-922

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