Homogenization of micromagnetics large bodies

Giovanni Pisante

ESAIM: Control, Optimisation and Calculus of Variations (2010)

  • Volume: 10, Issue: 2, page 295-314
  • ISSN: 1292-8119

Abstract

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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 ε ( m ) = ∫ Ω φ x , x ε , m ( x ) d x - ∫ Ω h e ( x ) · m ( x ) d x + 1 2 ∫ ℝ 3 | ∇ u ( x ) | 2 d x of a large ferromagnetic body is obtained.

How to cite

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Pisante, Giovanni. "Homogenization of micromagnetics large bodies." ESAIM: Control, Optimisation and Calculus of Variations 10.2 (2010): 295-314. <http://eudml.org/doc/90731>.

@article{Pisante2010,
abstract = { 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 $$ \mathcal\{E\}\_\{\varepsilon\}(m)=\int\_\{\Omega\} \phi\left(x,\frac\{x\}\{\varepsilon\},m(x)\right)\,\{\rm d\}x -\int\_\{\Omega\}h\_e(x)\cdot m(x)\,\{\rm d\}x+\frac\{1\}\{2\}\int\_\{\mathbb R^3\}|\nabla u(x)|^2\,\{\rm d\}x $$ of a large ferromagnetic body is obtained. },
author = {Pisante, Giovanni},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Micromagnetics; homogenization; Γ-convergence.; micromagnetics; integral representation; homgenized limit},
language = {eng},
month = {3},
number = {2},
pages = {295-314},
publisher = {EDP Sciences},
title = {Homogenization of micromagnetics large bodies},
url = {http://eudml.org/doc/90731},
volume = {10},
year = {2010},
}

TY - JOUR
AU - Pisante, Giovanni
TI - Homogenization of micromagnetics large bodies
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/3//
PB - EDP Sciences
VL - 10
IS - 2
SP - 295
EP - 314
AB - 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 $$ \mathcal{E}_{\varepsilon}(m)=\int_{\Omega} \phi\left(x,\frac{x}{\varepsilon},m(x)\right)\,{\rm d}x -\int_{\Omega}h_e(x)\cdot m(x)\,{\rm d}x+\frac{1}{2}\int_{\mathbb R^3}|\nabla u(x)|^2\,{\rm d}x $$ of a large ferromagnetic body is obtained.
LA - eng
KW - Micromagnetics; homogenization; Γ-convergence.; micromagnetics; integral representation; homgenized limit
UR - http://eudml.org/doc/90731
ER -

References

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  16. L. Tartar, On mathematical tools for studying partial differential equations of continuum physics: H-measures and Young measures. Plenum, New York, in Developments in partial differential equations and applications to mathematical physics (Ferrara, 1991), (1992) 201-217.  
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