| Title:
|
2D-1D dimensional reduction in a toy model for magnetoelastic interactions (English) |
| Author:
|
Tilioua, Mouhcine |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
56 |
| Issue:
|
3 |
| Year:
|
2011 |
| Pages:
|
287-295 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
magnetoelastic materials |
| Keyword:
|
Landau-Lifshitz-Gilbert equation |
| Keyword:
|
dimensional reduction |
| MSC:
|
35B40 |
| MSC:
|
35D30 |
| MSC:
|
35M33 |
| MSC:
|
35Q60 |
| MSC:
|
35Q74 |
| MSC:
|
74B05 |
| MSC:
|
78A25 |
| MSC:
|
82D40 |
| idZBL:
|
Zbl 1224.35058 |
| idMR:
|
MR2800579 |
| DOI:
|
10.1007/s10492-011-0017-0 |
| . |
| Date available:
|
2011-05-17T08:27:22Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141489 |
| . |
| Reference:
|
[1] Aharoni, A.: Introduction to the Theory of Ferromagnetism.Oxford University Press London (1996). |
| Reference:
|
[2] Brown, W. F.: Magnetoelastic Interactions. Springer Tracts in Natural Philosophy, Vol. 9.Springer New York-Heidelberg-Berlin (1966). 10.1007/978-3-642-87396-6 |
| Reference:
|
[3] Ciarlet, P. G.: Introduction to Linear Shell Theory.Gauthier-Villars Paris (1998). Zbl 0912.73001, MR 1648549 |
| Reference:
|
[4] Ciarlet, P. G., Destuynder, Ph.: A justification of the two-dimensional linear plate model.J. Mécanique 18 (1979), 315-344. Zbl 0415.73072, MR 0533827 |
| Reference:
|
[5] Hubert, A., Schäfer, R.: Magnetic Domains: The Analysis of Magnetic Microstructures.Springer New York-Berlin (1998). |
| Reference:
|
[6] Landau, L. D., Lifshitz, E. M.: Electrodynamics of Continuous Media.Pergamon Press Oxford (1986). MR 0766230 |
| Reference:
|
[7] Lions, J.-L.: Quelques Méthodes de Résolution des Problèmes aux Limites Non Linéaires.Dunod & Gauthier-Villars Paris (1969), French. Zbl 0189.40603, MR 0259693 |
| Reference:
|
[8] Simon, J.: Compact sets in the space $L^p(0,T;B)$.Ann. Mat. Pura Appl. 146 (1987), 65-96. MR 0916688 |
| Reference:
|
[9] 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). |
| . |
