Asymptotic Analysis for micromagnetics on thin films governed by indefinite material coefficient

• Published in: Communications on pure and applied mathematics Vol. 9; no. no 5
• Main Authors: Hadiji, Rejeb, Shirakawa, Ken
• Format: Journal Article
• Language: English
• Published: Wiley 2010
• Subjects: Analysis of PDEs; Mathematics; indefinite and degenerative material co-efficient; 3D-2D asymptotic analysis; Micromagnetics of thin film
• ISSN: 0010-3640; 1097-0312

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-2Dasymptotic analysis for the observing minimization problems, as h tends to 0, will be demonstrated in the main theorem of this paper