Phase-field systems for multi-dimensional Prandtl-Ishlinskii operators with non-polyhedral characteristics
- Sprekels, Jürgen
- Krejčí, Pavel
2010 Mathematics Subject Classification
- 34C55 35K60 47J40 74N30 80A22
- Phase-field systems, phase transitions, hysteresis operators, parabolic systems, Prandtl-Ishlinskii operators
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 nonlinearities 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 characteristic sets.
- Math. Methods Appl. Sci.,25 (2002), pp. 309--325