Homogenization of micromagnetics large bodies

Pisante, Giovanni

ESAIM: Control, Optimisation and Calculus of Variations, Tome 10 (2004) no. 2, pp. 295-314.

A homogenization problem related to the micromagnetic energy functional is studied. In particular, the existence of the integral representation for the homogenized limit of a family of energies

$${ℰ}_{\epsilon }\left(m\right)={\int }_{\Omega }\phi \left(x,\frac{x}{\epsilon },m\left(x\right)\right)\mathrm{d}x-{\int }_{\Omega }{h}_e\left(x\right)·m\left(x\right)\mathrm{d}x+\frac{1}{2}{\int }_{{ℝ}^3}{\left|\nabla u\left(x\right)\right|}^2\mathrm{d}x$$

of a large ferromagnetic body is obtained.

Classification : 35B27, 74Q99, 82D40
Mots clés : micromagnetics, homogenization, $\Gamma $-convergence

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