Wong–Zakai Approximation for Landau–Lifshitz–Gilbert Equation Driven by Geometric Rough Paths

Kistosil Fahim, Erika Hausenblas*, Debopriya Mukherjee

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

We adapt Lyon’s rough path theory to study Landau–Lifshitz–Gilbert equations (LLGEs) driven by geometric rough paths in one dimension, with non-zero exchange energy only. We convert the LLGEs to a fully nonlinear time-dependent partial differential equation without rough paths term by a suitable transformation. Our point of interest is the regular approximation of the geometric rough path. We investigate the limit equation, the form of the correction term, and its convergence rate in controlled rough path spaces. The key ingredients for constructing the solution and its corresponding convergence results are the Doss–Sussmann transformation, maximal regularity property, and the geometric rough path theory.

Original languageEnglish
Pages (from-to)1685-1730
Number of pages46
JournalApplied Mathematics and Optimization
Volume84
DOIs
Publication statusPublished - Dec 2021

Keywords

  • Ferromagnetism
  • Landau–Lifshitz–Gilbert equations
  • Partial differential equation
  • Rough paths theory
  • Wong–Zakai approximation

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