Le equazioni di evoluzione dei continui ferromagnetici

P. Podio-Guidugli

Bollettino dell'Unione Matematica Italiana (2001)

  • Volume: 4-B, Issue: 1, page 31-44
  • ISSN: 0392-4041

Abstract

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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.

How to cite

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Podio-Guidugli, P.. "Le equazioni di evoluzione dei continui ferromagnetici." Bollettino dell'Unione Matematica Italiana 4-B.1 (2001): 31-44. <http://eudml.org/doc/194812>.

@article{Podio2001,
author = {Podio-Guidugli, P.},
journal = {Bollettino dell'Unione Matematica Italiana},
keywords = {Gilbert equation; parabolic equation; magnetization vector; harmonic map equation; existence; weak solutions},
language = {ita},
month = {2},
number = {1},
pages = {31-44},
publisher = {Unione Matematica Italiana},
title = {Le equazioni di evoluzione dei continui ferromagnetici},
url = {http://eudml.org/doc/194812},
volume = {4-B},
year = {2001},
}

TY - JOUR
AU - Podio-Guidugli, P.
TI - Le equazioni di evoluzione dei continui ferromagnetici
JO - Bollettino dell'Unione Matematica Italiana
DA - 2001/2//
PB - Unione Matematica Italiana
VL - 4-B
IS - 1
SP - 31
EP - 44
LA - ita
KW - Gilbert equation; parabolic equation; magnetization vector; harmonic map equation; existence; weak solutions
UR - http://eudml.org/doc/194812
ER -

References

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