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September  2010, 9(5): 1345-1361. doi: 10.3934/cpaa.2010.9.1345

Asymptotic analysis for micromagnetics of thin films governed by indefinite material coefficients

Rejeb Hadiji 1, and  Ken Shirakawa 2,

1. 

Université Paris-Est, Laboratoire d’Analyse et de Mathématiques Appliquées, CNRS UMR 8050, UFR des Sciences et Technologie, 61, Avenue du Général de Gaulle, P3, 4e étage, 94010 Créteil Cedex, France
2. 

Department of Applied Mathematics, Graduate School of System Informatics, Kobe University, 1-1 Rokkodai, Nada, Kobe, 657-8501, Japan

Received  August 2009 Revised  November 2009 Published  May 2010

In this paper, a class of minimization problems, associated with the micromagnetics of thin films, is dealt with. Each minimization problem is distinguished by the thickness of the thin film, denoted by $ 0 < h < 1 $, and it is considered under spatial indefinite and degenerative setting of the material coefficients. On the basis of the fundamental studies of the governing energy functionals, the existence of minimizers, for every $ 0 < h < 1 $, and the 3D-2D asymptotic analysis for the observing minimization problems, as $ h \to 0 $, will be demonstrated in the main theorem of this paper.
Keywords: 3D-2D asymptotic analysis., indefinite and degenerative material coefficient, Micromagnetics of thin film.
Mathematics Subject Classification: Primary: 74G65, 35J70; Secondary: 74K35, 82D4.
Citation: Rejeb Hadiji, Ken Shirakawa. Asymptotic analysis for micromagnetics of thin films governed by indefinite material coefficients. Communications on Pure &amp; Applied Analysis, 2010, 9 (5) : 1345-1361. doi: 10.3934/cpaa.2010.9.1345
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