Boundary vortices for thin ferromagnetic films
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Submission date: 19. Mar. 2003 (revised version: July 2003)
published in: Archive for rational mechanics and analysis, 174 (2004) 2, p. 267-300
DOI number (of the published article): 10.1007/s00205-004-0329-2
MSC-Numbers: 35J60, 35Q60, 58E20
Keywords and phrases: ginzburg-landau vortices, thin films, ferromagnetism
We consider a simplified version of the micromagnetic energy for ferromagnetic samples in the shape of thin films. We study (a) stationary, stable critical points, and (b) solutions of the corresponding Landau-Lifshitz equation under a stability condition. We determine the asymptotic behaviour of solutions of these variational problems in the thin film limit. A characteristic property of the limit is the development of Ginzburg-Landau-type vortices at the boundary.