The Landau-Lifshitz equations and the damping parameter
Bollettino della Unione matematica italiana, Série 8, 9B (2006) no. 2, pp. 283-297.

Voir la notice de l'article dans Biblioteca Digitale Italiana di Matematica

In questo articolo si tratta l'effetto damping nei materiali ferromagnetici. In particolare, ci si occupa di determinare la sensibilità della soluzione ottenuta con il metodo LLG rispetto al parametro di damping a. Si analizza qui il comportamento della soluzione debole globale ad energia finita delle equazioni di Landau-Lifshitz quando il parametro di damping a tende verso 0 (underdamping) o verso $+\infty$ (overdamping).
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Hamdache, K.; Tilioua, M. The Landau-Lifshitz equations and the damping parameter. Bollettino della Unione matematica italiana, Série 8, 9B (2006) no. 2, pp. 283-297. https://geodesic-test.mathdoc.fr/item/BUMI_2006_8_9B_2_a2/

[1] F. Alouges - A. Soyeur, On global weak solutions for Landau-Lifshitz equations: existence and nonuniqueness, Nonlinear Anal., 18 (11) (1992), 1071-1084. | Zbl

[2] M. Bertsch - R. Dal Passo - R. Van Der Hout, Nonuniqueness for the heat flow of harmonic maps on the disk, Arch. Ration. Mech. Anal., 161 (2) (2002, 93-112. È | Zbl

[3] N.-H. Chang - J. Shatah - K. Uhlenbeck, Schrodinger maps, Comm. Pure Appl. Math., 53 (5) (2000), 590-602.

[4] B. D. Cullity, Introduction to magnetic materials, Addison-Wesley Pub. Co., Reading, Mass., 1972.

[5] W. E., Selected problems in materials science, in Mathematics unlimited-2001 and beyond. Part I, II, 407-432. Edited by Bjorn Engquist and Wilfried Schmid. Springer-Verlag, Berlin, 2001. Part I: xvi+591 pp.; Part II: pp. i-xvi and 593-1237. | Zbl

[6] S. Gustafson - J. Shatah, The stability of localized solutions of Landau-Lifshitz equations, Comm. Pure Appl. Math., 55 (9) (2002), 1136-1159. | Zbl

[7] K. Hamdache, Homogenization of layered ferromagnetic media, Preprint CMAP495, 2002. http://www.cmap.polytechnique.fr/preprint/

[8] K. Hamdache - M. Tilioua, Interlayer exchange coupling for ferromagnets through spacers, SIAM J. Appl. Math., 64 (3) (2004), 1077-1097. | Zbl

[9] S. P. Ingvarsson, Magnetization dynamics in transition metal ferromagnets studied by magneto-tunneling and ferromagnetic resonance, PhD thesis, Brown University, 2001.

[10] S. Mizohata, The theory of partial differential equations, Cambridge University Press, New York, 1973. | Zbl

[11] R. Moser, 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] A. Pazy, Semigroups of linear operators and applications to partial differential equations, volume 44 of Applied Mathematical Sciences, Springer-Verlag, New York, 1983. | Zbl

[13] J. Shatah - M. Struwe, The Cauchy problem for wave maps, Int. Math. Res. Not., 11 ( 2002), 555-571. | Zbl

[14] M. Struwe, On the evolution of harmonic mappings of Riemannian surfaces, Comment. Math. Helv., 60 (4) (1985), 558-581. | fulltext EuDML | Zbl

[15] P.-L. Sulem - C. Sulem - C. Bardos, On the continuous limit for a system of classical spins, Comm. Math. Phys., 107 (3) (1986), 431-454. | Zbl

[16] A. Visintin, On Landau-Lifshitz equations for ferromagnetism, Japan J. Appl. Math., 2 (1) (1985) 69-84. | Zbl