Communications on Pure and Applied Analysis (CPAA)

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

Pages: 1345 - 1361, Volume 9, Issue 5, September 2010      doi:10.3934/cpaa.2010.9.1345

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Rejeb Hadiji - 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 (email)
Ken Shirakawa - Department of Applied Mathematics, Graduate School of System Informatics, Kobe University, 1-1 Rokkodai, Nada, Kobe, 657-8501, Japan (email)

Abstract: 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:  Micromagnetics of thin film, indefinite and degenerative material coefficient, 3D-2D asymptotic analysis.
Mathematics Subject Classification:  Primary: 74G65, 35J70; Secondary: 74K35, 82D40.

Received: August 2009;      Revised: November 2009;      Available Online: May 2010.