Asymptotic analysis for micromagnetics of thin films governed by indefinite material coefficients
Rejeb Hadiji, Ken Shirakawa · Communications on Pure & Applied Analysis · 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 degenerativesetting 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 analysisfor the observing minimization problems, as $ h \to 0 $, will be demonstrated inthe main theorem of this paper.