Geodesic
Le equazioni di evoluzione dei continui ferromagnetici
Bollettino della Unione matematica italiana, Série 8, 4B (2001) no. 1, pp. 31-44.

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

This expository paper is meant to be a faithful account the invited lecture I gave in Naples on September 14, 1999, during the 16th Congress of U.M.I., the Italian Mathematical Union. In Section 2, I consider the Gilbert equation, the parabolic equation that rules the evolution of the magnetization vector in a rigid ferromagnet. Among the issues I here discuss are the relations of the Gilbert equation to the harmonic map equation and its heat flow, the existence of global-in-time weak solutions, and some conjectures on the possible evolutions of singular solutions. Section 3 consists of an abridged presentation of dynamical micromagnetics, a general mathematical model for the dynamics of ferromagnetic bodies undergoing arbitrarily large deformations. In particular, I show how a generalized Gilbert equation can be arrived at, and I briefly discuss equilibria and dissipation mechanisms. 
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Podio-Guidugli, P. Le equazioni di evoluzione dei continui ferromagnetici. Bollettino della Unione matematica italiana, Série 8, 4B (2001) no. 1, pp. 31-44. http://geodesic.mathdoc.fr/item/BUMI_2001_8_4B_1_a9/

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