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(In-)stability of singular equivariant solutions to the Landau–Lifshitz–Gilbert equation

Published online by Cambridge University Press:  09 August 2013

JAN BOUWE VAN DEN BERG  and
J. F. WILLIAMS
JAN BOUWE VAN DEN BERG
Affiliation:
Department of Mathematics, VU University Amsterdam, de Boelelaan 1081, 1081 HV Amsterdam, the Netherlands email: janbouwe@math.vu.nl
J. F. WILLIAMS
Affiliation:
Department of Mathematics, Simon Fraser University, Burnaby, British Columbia, Canada email: jfw@math.sfu.ca
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Abstract

In this paper, we use formal asymptotic arguments to understand the stability properties of equivariant solutions to the Landau–Lifshitz–Gilbert model for ferromagnets. We also analyse both the harmonic map heatflow and Schrödinger map flow limit cases. All asymptotic results are verified by detailed numerical experiments, as well as a robust topological argument. The key result of this paper is that blowup solutions to these problems are co-dimension one and hence both unstable and non-generic.

Keywords

Landau–Lifshitz–GilbertHarmonic map heatflowSchrödinger map flowAsymptotic analysisBlowupNumerical simulationsAdaptive numerical methods
Type
Papers
Information
European Journal of Applied Mathematics , Volume 24 , Issue 6 , December 2013 , pp. 921 - 948
Copyright
Copyright © Cambridge University Press 2013 

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