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Existence and Asymptotic Behaviour in Phase-Field Models with Hysteresis

In: Lectures on Applied Mathematics

Author

Listed:
  • P. Krejčí

    (Academy of Sciences, Mathematical Institute)

  • J. Sprekels

    (Weierstrass Institute for Applied Mathematics and Stochastics)

  • S. Zheng

    (Fudan University, Institute of Mathematics)

Abstract

Phase field systems as mathematical models for phase transitions have drawn increasing attention in recent years. However, while being capable of capturing many of the experimentally observed phenomena, they give only a simplified picture of intrinsic hysteresis effects occurring in phase transition processes. To overcome this shortcoming, the first two authors have recently proposed a new approach in a series of papers which is based on the mathematical theory of hysteresis operators developed in the past fifteen years, and obtained results on existence, uniqueness and regularity of solutions for a class of phase-field systems with hysteresis that includes among others the relaxed Stefan problem and hysteretic analogues of the models due to Caginalp and Penrose-Fife for nonconserved order parameters with zero interfacial energy. Here, we give a brief account of the method, with a special focus on new results obtained by the authors of the present paper and related to the asymptotic behaviour of the system as t → +∞.

Suggested Citation

  • P. Krejčí & J. Sprekels & S. Zheng, 2000. "Existence and Asymptotic Behaviour in Phase-Field Models with Hysteresis," Springer Books, in: Hans-Joachim Bungartz & Ronald H. W. Hoppe & Christoph Zenger (ed.), Lectures on Applied Mathematics, pages 77-88, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-59709-1_6
    DOI: 10.1007/978-3-642-59709-1_6
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