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

Rejeb Hadiji; Ken Shirakawa

doi:10.3934/cpaa.2010.9.1345

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2010, Volume 9, Issue 5: 1345-1361. Doi: 10.3934/cpaa.2010.9.1345

This issue Previous Article On positive solution to a second order elliptic equation with a singular nonlinearity Next Article On the convergence of singular perturbations of Hamilton-Jacobi equations

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
2.
Department of Applied Mathematics, Graduate School of System Informatics, Kobe University, 1-1 Rokkodai, Nada, Kobe, 657-8501

Received: July 31, 2009

Revised: October 31, 2009

Published: August 2010

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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.

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