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Periodic solutions of the stefan problem with hysteresis-type boundary conditions

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Abstract

We consider the Stefan problem with Dirichlet boundary conditions depending on a hysteresis functional where the free boundary is involved. We show existence of a positive valueT and existence of aT-periodic solution of the problem, provided the Stefan number is sufficiently small and the hysteresis functional is described by the elementary rectangular hysteresis loop. If in addition the Preisach hysteresis operator is Lipschitz-continuous we prove that every periodic solution must be stationary.

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Author notes

  1. Ivan G. Götz

    Present address: Lavrent'ev Institute of Hydrodynamics, Siberian Division of the Russian Academy of Sciences, prospect Lavrent'eva 15, 630090, Novosibirsk 90, Russia

Authors and Affiliations

  1. Institute of Applied Mathematic and Statistic, Technical University of Munich, Dachauerstrasse 9a, 8000, Munich 2, Germany

    Ivan G. Götz & Karl-Heinz Hoffmann

  2. Universidade da Beira Interior, R. Marques d'Avila e Bolama, 6200, Covilha, Portugal

    Anvarbek M. Meirmanov

Authors
  1. Ivan G. Götz
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  2. Karl-Heinz Hoffmann
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  3. Anvarbek M. Meirmanov
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Additional information

Dedicated to Professor Avner Friedman on occasion of his 60th birthday

supported by Humboldt Foundation Scholarship

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Götz, I.G., Hoffmann, KH. & Meirmanov, A.M. Periodic solutions of the stefan problem with hysteresis-type boundary conditions. Manuscripta Math 78, 179–199 (1993). https://doi.org/10.1007/BF02599308

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  • DOI: https://doi.org/10.1007/BF02599308

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