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Journal of Convex Analysis 13 (2006), No. 1, 081--099
Copyright Heldermann Verlag 2006

Periodic Solutions to a Hysteresis Model in Micromagnetics

Martin Kruzik
Inst. of Information Theory and Automation, Academy of Sciences, Pod vodarenskou vezi 4, 182 08 Praha 8, Czech Republic

We show the existence of periodic solutions to a model describing a rate-independent hysteresis response in bulk ferromagnets. The magnetic microstructure is treated in terms of Young measures and the whole formulation is based on energy functionals for the Gibbs and dissipative energies. Our proof of the periodicity of solutions is mainly based on uniqueness of a solution to time incremental problems and on the Tychonoff fixed point theorem.

Keywords: Ferromagnetism, fixed point theorem, hysteresis, periodic solution.

MSC: 35Q60, 49S05, 78A30, 78M30

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