Asymptotic Analysis for Micromagnetics of Thin Films Governed by Indefinite Material Coefficients

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 ↘ 0, will be demonstrated in the main theorem of this paper.