Podio-Guidugli, P.:
Le equazioni di evoluzione dei continui ferromagnetici
Bollettino dell'Unione Matematica Italiana Serie 8 4-B (2001), fasc. n.1, p. 31-44, Unione Matematica Italiana (Italian)
pdf (456 Kb), djvu (184 Kb). | MR1821396 | Zbl 1039.74014
Sunto
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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Con il contributo del Ministero per i Beni e le Attività Culturali