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Phase‐field systems for multi‐dimensional Prandtl–Ishlinskii operators with non‐polyhedral characteristics
Author(s) -
Sprekels Jürgen,
Krejčí Pavel
Publication year - 2002
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.288
Subject(s) - hysteresis , prandtl number , regular polygon , mathematics , field (mathematics) , phase (matter) , polyhedron , connection (principal bundle) , phase transition , class (philosophy) , series (stratigraphy) , pure mathematics , mathematical analysis , computer science , physics , combinatorics , geometry , artificial intelligence , condensed matter physics , mechanics , heat transfer , paleontology , quantum mechanics , biology
Hysteresis operators have recently proved to be a powerful tool in modelling phase transition phenomena which are accompanied by the occurrence of hysteresis effects. In a series of papers, the present authors have proposed phase‐field models in which hysteresis non‐linearities occur at several places. A very important class of hysteresis operators studied in this connection is formed by the so‐called Prandtl – Ishlinskii operators. For these operators, the corresponding phase‐field systems are in the multi‐dimensional case only known to admit unique solutions if the characteristic convex sets defining the operators are polyhedrons. In this paper, we use approximation techniques to extend the known results to multi‐dimensional Prandtl–Ishlinskii operators having non‐polyhedral convex characteristicsets. Copyright © 2002 John Wiley & Sons, Ltd.