THIN-FILM LIMITS FOR LANDAU-LIFSHITZ-GILBERT EQUATIONS

We derive a damped wave-type limit for the Landau-Lifshitz-Gilbert equation in thin films starting from the full micromagnetic model. The result, previously encountered in [A. Capella, C. Melcher, and F. Otto, Nonlinearity, 20 (2007), pp. 2519 2537] in the context of reduced models for domain wall motion, applies in situations with topological singularities near the boundary. We also establish improved continuity properties for the limit equation and a relation between the kinetic energy in terms of the stray-field energy defect.