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Asymptotic behaviour of thin ferromagnetic films. (English) Zbl 1108.82339

Summary: The effect of thin ferromagnetic films is studied in this paper. We shall adopt the Landau-Lifschitz-Gilbert equation as a phenomenological model for the ferromagnetic materials. Asymptotic analysis of the fields and the magnetization vector inside thin ferromagnetic films are performed and their convergences are established. Our results reveal the physical nature of this nonlinear model. They also provide an effective method for overcoming the computational difficulties that arise in thin ferromagnetic coatings.

MSC:

82D40 Statistical mechanics of magnetic materials
35B40 Asymptotic behavior of solutions to PDEs
35Q60 PDEs in connection with optics and electromagnetic theory
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