Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

Martin Kruzik

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

kruzik@utia.cas.cz

Keywords

  • Ferromagnetism
  • fixed point theorem
  • hysteresis
  • periodic solution

Mathematics Subject Classification

35Q60, 49S05, 78A30, 78M30

Suggested citation

M. Kruzik. “Periodic Solutions to a Hysteresis Model in Micromagnetics.” Journal of Convex Analysis 13 (2006), No. 1, 81–99.

Copyright Heldermann Verlag 2006