The Landau-Lifshitz equations and the damping parameter

K. Hamdache; M. Tilioua

Bollettino dell'Unione Matematica Italiana (2006)

  • Volume: 9-B, Issue: 2, page 283-297
  • ISSN: 0392-4041

Abstract

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The present paper is particularly devoted to the damping effect in ferromagnetic materials. We are interested in determining the sensitivity of the LLG method solution to the phenomenological damping parameter a. We discuss the behaviour of the global weak solutions with finite energy of the Landau-Lifshitz equations when the damping parameter a tends either to 0 (underdamped case) or + ∞ (overdamped case).

How to cite

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Hamdache, K., and Tilioua, M.. "The Landau-Lifshitz equations and the damping parameter." Bollettino dell'Unione Matematica Italiana 9-B.2 (2006): 283-297. <http://eudml.org/doc/289629>.

@article{Hamdache2006,
abstract = {The present paper is particularly devoted to the damping effect in ferromagnetic materials. We are interested in determining the sensitivity of the LLG method solution to the phenomenological damping parameter a. We discuss the behaviour of the global weak solutions with finite energy of the Landau-Lifshitz equations when the damping parameter a tends either to 0 (underdamped case) or $+\infty$ (overdamped case).},
author = {Hamdache, K., Tilioua, M.},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {6},
number = {2},
pages = {283-297},
publisher = {Unione Matematica Italiana},
title = {The Landau-Lifshitz equations and the damping parameter},
url = {http://eudml.org/doc/289629},
volume = {9-B},
year = {2006},
}

TY - JOUR
AU - Hamdache, K.
AU - Tilioua, M.
TI - The Landau-Lifshitz equations and the damping parameter
JO - Bollettino dell'Unione Matematica Italiana
DA - 2006/6//
PB - Unione Matematica Italiana
VL - 9-B
IS - 2
SP - 283
EP - 297
AB - The present paper is particularly devoted to the damping effect in ferromagnetic materials. We are interested in determining the sensitivity of the LLG method solution to the phenomenological damping parameter a. We discuss the behaviour of the global weak solutions with finite energy of the Landau-Lifshitz equations when the damping parameter a tends either to 0 (underdamped case) or $+\infty$ (overdamped case).
LA - eng
UR - http://eudml.org/doc/289629
ER -

References

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  2. BERTSCH, M. - DAL PASSO, R. - VAN DER HOUT, R., Nonuniqueness for the heat flow of harmonic maps on the disk, Arch. Ration. Mech. Anal., 161 (2) (2002, 93-112. È Zbl1006.35050
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  6. GUSTAFSON, S. - SHATAH, J., The stability of localized solutions of Landau-Lifshitz equations, Comm. Pure Appl. Math., 55 (9) (2002), 1136-1159. Zbl1028.35059
  7. HAMDACHE, K., Homogenization of layered ferromagnetic media, Preprint CMAP495, 2002. http://www.cmap.polytechnique.fr/preprint/ 
  8. HAMDACHE, K. - TILIOUA, M., Interlayer exchange coupling for ferromagnets through spacers, SIAM J. Appl. Math., 64 (3) (2004), 1077-1097. Zbl1058.35060
  9. INGVARSSON, S. P., Magnetization dynamics in transition metal ferromagnets studied by magneto-tunneling and ferromagnetic resonance, PhD thesis, Brown University, 2001. 
  10. MIZOHATA, S., The theory of partial differential equations, Cambridge University Press, New York, 1973. Zbl0263.35001
  11. MOSER, R., Partial regularity for the Landau-Lifshitz equation in small dimensions, Preprint no. 26, 2002, 12 pages, Max Planck Institute for Mathematics in the Sciences, Leipzig. 
  12. PAZY, A., Semigroups of linear operators and applications to partial differential equations, volume 44 of Applied Mathematical Sciences, Springer-Verlag, New York, 1983. Zbl0516.47023
  13. SHATAH, J. - STRUWE, M., The Cauchy problem for wave maps, Int. Math. Res. Not., 11 ( 2002), 555-571. Zbl1024.58014
  14. STRUWE, M., On the evolution of harmonic mappings of Riemannian surfaces, Comment. Math. Helv., 60 (4) (1985), 558-581. Zbl0595.58013
  15. SULEM, P.-L. - SULEM, C. - BARDOS, C., On the continuous limit for a system of classical spins, Comm. Math. Phys., 107 (3) (1986), 431-454. Zbl0614.35087
  16. VISINTIN, A., On Landau-Lifshitz equations for ferromagnetism, Japan J. Appl. Math., 2 (1) (1985) 69-84. Zbl0613.35018

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