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

G.J.B. van den Berg; J.F. Williams

doi:10.1017/S0956792513000247

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

G.J.B. van den Berg, J.F. Williams

Mathematics

Research output: Contribution to Journal › Article › Academic › peer-review

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. Copyright © Cambridge University Press 2013.

Original language	English
Pages (from-to)	921-948
Journal	European Journal of Applied Mathematics
Volume	24
DOIs	https://doi.org/10.1017/S0956792513000247
Publication status	Published - 2013

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@article{d9cddfdc84ec45aca6e2a1604609d439,

title = "(In-)Stability of singular equivariant solutions to the Landau-Lifshitz-Gilbert equation",

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 Schr{\"o}dinger 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. Copyright {\textcopyright} Cambridge University Press 2013.",

author = "{van den Berg}, G.J.B. and J.F. Williams",

year = "2013",

doi = "10.1017/S0956792513000247",

language = "English",

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pages = "921--948",

journal = "European Journal of Applied Mathematics",

issn = "0956-7925",

publisher = "Cambridge University Press",

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AU - van den Berg, G.J.B.

AU - Williams, J.F.

PY - 2013

Y1 - 2013

N2 - 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. Copyright © Cambridge University Press 2013.

AB - 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. Copyright © Cambridge University Press 2013.

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DO - 10.1017/S0956792513000247

M3 - Article

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EP - 948

JO - European Journal of Applied Mathematics

JF - European Journal of Applied Mathematics

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