# 2D-1D dimensional reduction in a toy model for magnetoelastic interactions

Applications of Mathematics (2011)

- Volume: 56, Issue: 3, page 287-295
- ISSN: 0862-7940

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topTilioua, Mouhcine. "2D-1D dimensional reduction in a toy model for magnetoelastic interactions." Applications of Mathematics 56.3 (2011): 287-295. <http://eudml.org/doc/116527>.

@article{Tilioua2011,

abstract = {The paper deals with the dimensional reduction from 2D to 1D in magnetoelastic interactions. We adopt a simplified, but nontrivial model described by the Landau-Lifshitz-Gilbert equation for the magnetization field coupled to an evolution equation for the displacement. We identify the limit problem by using the so-called energy method.},

author = {Tilioua, Mouhcine},

journal = {Applications of Mathematics},

keywords = {magnetoelastic materials; Landau-Lifshitz-Gilbert equation; dimensional reduction; magnetoelastic materials; Landau-Lifshitz-Gilbert equation; dimensional reduction},

language = {eng},

number = {3},

pages = {287-295},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {2D-1D dimensional reduction in a toy model for magnetoelastic interactions},

url = {http://eudml.org/doc/116527},

volume = {56},

year = {2011},

}

TY - JOUR

AU - Tilioua, Mouhcine

TI - 2D-1D dimensional reduction in a toy model for magnetoelastic interactions

JO - Applications of Mathematics

PY - 2011

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 56

IS - 3

SP - 287

EP - 295

AB - The paper deals with the dimensional reduction from 2D to 1D in magnetoelastic interactions. We adopt a simplified, but nontrivial model described by the Landau-Lifshitz-Gilbert equation for the magnetization field coupled to an evolution equation for the displacement. We identify the limit problem by using the so-called energy method.

LA - eng

KW - magnetoelastic materials; Landau-Lifshitz-Gilbert equation; dimensional reduction; magnetoelastic materials; Landau-Lifshitz-Gilbert equation; dimensional reduction

UR - http://eudml.org/doc/116527

ER -

## References

top- Aharoni, A., Introduction to the Theory of Ferromagnetism, Oxford University Press London (1996). (1996)
- Brown, W. F., 10.1007/978-3-642-87396-6, Springer New York-Heidelberg-Berlin (1966). (1966) DOI10.1007/978-3-642-87396-6
- Ciarlet, P. G., Introduction to Linear Shell Theory, Gauthier-Villars Paris (1998). (1998) Zbl0912.73001MR1648549
- Ciarlet, P. G., Destuynder, Ph., A justification of the two-dimensional linear plate model, J. Mécanique 18 (1979), 315-344. (1979) Zbl0415.73072MR0533827
- Hubert, A., Schäfer, R., Magnetic Domains: The Analysis of Magnetic Microstructures, Springer New York-Berlin (1998). (1998)
- Landau, L. D., Lifshitz, E. M., Electrodynamics of Continuous Media, Pergamon Press Oxford (1986). (1986) MR0766230
- Lions, J.-L., Quelques Méthodes de Résolution des Problèmes aux Limites Non Linéaires, Dunod & Gauthier-Villars Paris (1969), French. (1969) Zbl0189.40603MR0259693
- Simon, J., Compact sets in the space ${L}^{p}(0,T;B)$, Ann. Mat. Pura Appl. 146 (1987), 65-96. (1987) MR0916688
- Valente, V., An evolutive model for magnetorestrictive interactions: existence of weak solutions, SPIE-Proceeding on Smart Structures and Materials, Modeling, Signal Processing and Control Elsevier Amsterdam (2006). (2006)

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