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3D-2D Asymptotic Analysis for Micromagnetic Thin Films

Published online by Cambridge University Press:  15 August 2002

Roberto Alicandro
Affiliation:
SISSA, Via Beirut 4, 34013 Trieste, Italy; alicandr@sissa.it.
Chiara Leone
Affiliation:
Dipartimento di Matematica, Università di Roma I, P.le A. Moro 2, 00185 Roma, Italy; leone@mat.uniroma1.it.
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Abstract

Γ-convergence techniques and relaxation results of constrained energy functionals are used to identify the limiting energy as the thickness ε approaches zero of a ferromagnetic thin structure $\Omega_\varepsilon=\omega\times(-\varepsilon,\varepsilon)$ , $\omega\subset\mathbb R^2$ , whose energy is given by $$ {\cal E}_{\varepsilon}({\overline{m}})=\frac{1}{\varepsilon} \int_{\Omega_{\varepsilon}}\left(W({\overline{m}},\nabla{\overline{m}}) +{\frac{1}{2}}\nabla {\overline{u}}\cdot {\overline{m}}\right)\,{\rm d}x $$ subject to $$ \hbox{div}(-\nabla {\overline{u}}+{\overline{m}}\chi_{\Omega_\varepsilon})=0 \quad\hbox{ on }\mathbb R^3, $$ and to the constraint $$ |\overline{m}|=1 \hbox{ on }\Omega_\varepsilon, $$ where W is any continuous function satisfying p-growth assumptions with p> 1. Partial results are also obtained in the case p=1, under an additional assumption on W.

Type
Research Article
Copyright
© EDP Sciences, SMAI, 2001

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