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.
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References
A. Aharoni: Introduction to the Theory of Ferromagnetism. Oxford University Press, London, 1996.
W.F. Brown: Magnetoelastic Interactions. Springer Tracts in Natural Philosophy, Vol. 9. Springer, New York-Heidelberg-Berlin, 1966.
P.G. Ciarlet: Introduction to Linear Shell Theory. Gauthier-Villars, Paris, 1998.
P.G. Ciarlet, Ph. Destuynder: A justification of the two-dimensional linear plate model. J. Mécanique 18 (1979), 315–344.
A. Hubert, R. Schäfer: Magnetic Domains: The Analysis of Magnetic Microstructures. Springer, New York-Berlin, 1998.
L.D. Landau, E.M. Lifshitz: Electrodynamics of Continuous Media. Pergamon Press, Oxford, 1986.
J.-L. Lions: Quelques Méthodes de Résolution des Probl`emes aux Limites Non Linéaires. Dunod & Gauthier-Villars, Paris, 1969. (In French.)
J. Simon: Compact sets in the space L p(0, T; B). Ann. Mat. Pura Appl. 146 (1987), 65–96.
V. Valente: 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.
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Tilioua, M. 2D-1D Dimensional reduction in a toy model for magnetoelastic interactions. Appl Math 56, 287–295 (2011). https://doi.org/10.1007/s10492-011-0017-0
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DOI: https://doi.org/10.1007/s10492-011-0017-0