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Summary: ASYMPTOTIC BEHAVIOUR OF THIN FERROMAGNETIC FILMS
Habib Ammari
Centre de Mathematiques Appliquees, CNRS UMR 7641, Ecole Polytechnique
F-91128 Palaiseau Cedex, France
e-mail address: ammari@cmapx.polytechnique.fr
Laurence Halpern
Institut Galilee, CNRS UMR 7539, Universite Paris XIII
F-93430 Villetaneuse, France
e-mail address: halpern@math.univ-paris13.fr
Kamel Hamdache
Centre de Mathematiques Appliquees, CNRS UMR 7641, Ecole Polytechnique
F-91128 Palaiseau cedex, France
e-mail address: hamdache@cmapx.polytechnique.fr
Abstract. The e ect of thin ferromagnetic lms 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 elds
and the magnetization vector inside thin ferromagnetic lms are performed and their convergences are established.
Our results reveal the physical nature of this nonlinear model. They also provide an e ective method for overcoming
the computational diÆculties that arise in thin ferromagnetic coatings.
1 Introduction
The development of techniques for the vacuum deposition of thin solid layers has resulted
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