Self-similar shrinkers of the one-dimensional Landau-Lifshitz-Gilbert equation

Susana Gutiérrez, André de Laire

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)
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Abstract

The main purpose of this paper is the analytical study of self-shrinker solutions of the one-dimensional Landau–Lifshitz–Gilbert equation (LLG), a model describing the dynamics for the spin in ferromagnetic materials. We show that there is a unique smooth family of backward self-similar solutions to the LLG equation, up to symmetries, and we establish their asymptotics. Moreover, we obtain that in the presence of damping, the trajectories of the self-similar profiles converge to great circles on the sphere S 2, at an exponential rate. In particular, the results presented in this paper provide examples of blow-up in finite time, where the singularity develops due to rapid oscillations forming limit circles.

Original languageEnglish
JournalJournal of Evolution Equations
DOIs
Publication statusPublished - 11 Jun 2020

Bibliographical note

4 figures

Keywords

  • Asymptotics
  • Backward self-similar solutions
  • Blow up
  • Ferromagnetic spin chain
  • Heat flow for harmonic maps
  • Landau–Lifshitz–Gilbert equation
  • Quasi-harmonic sphere
  • Self-similar expanders

ASJC Scopus subject areas

  • Mathematics (miscellaneous)

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