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Asymptotic analysis, in a thin multidomain, of minimizing maps with values in S(2)

Abstract : We consider a thin multidomain of R(3) consisting of two vertical cylinders, one placed upon the other: the first one with given height and small cross section, the second one with small thickness and given cross section. The first part or this paper is devoted to analyze, in this thin multidomain, a "static Landau-Lifshitz equation", when the volumes of the two cylinders vanish. We derive the limit problem, which decomposes into two uncoupled problems, well posed oil the limit cylinders (with dimensions I and 2, respectively). We precise how the limit problem depends on limit of the ratio between the volumes of the two cylinders. In the second part of this paper, we study the asymptotic behavior of the two limit problems, when the exterior limit fields increase. We show that in some cases, contrary to the initial problem, the energies of the limit problems diverge and we find the order of these energies. (c) 2007 Elsevier Masson SAS. All rights reserved.
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Antonio Gaudiello, Rejeb Hadiji. Asymptotic analysis, in a thin multidomain, of minimizing maps with values in S(2). Annales de l'Institut Henri Poincaré (C) Non Linear Analysis, Elsevier, 2009, 26 (1), pp.59--80. ⟨10.1016/j.anihpc.2007.06.002⟩. ⟨hal-00693058⟩



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