Periodic solutions of the stefan problem with hysteresis-type boundary conditions |
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| Authors: | Ivan G. Götz Karl-Heinz Hoffmann Anvarbek M. Meirmanov |
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| Affiliation: | (1) Present address: Lavrent'ev Institute of Hydrodynamics, Siberian Division of the Russian Academy of Sciences, prospect Lavrent'eva 15, 630090 Novosibirsk 90, Russia;(2) Institute of Applied Mathematic and Statistic, Technical University of Munich, Dachauerstrasse 9a, 8000 Munich 2, Germany;(3) Universidade da Beira Interior, R. Marques d'Avila e Bolama, 6200 Covilha, Portugal |
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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. Dedicated to Professor Avner Friedman on occasion of his 60th birthday supported by Humboldt Foundation Scholarship |
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