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

Kistosil Fahim; Erika Hausenblas; Debopriya Mukherjee

doi:10.1007/s00245-021-09808-1

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

Kistosil Fahim, Erika Hausenblas, Debopriya Mukherjee

Lehrstuhl für Angewandte Mathematik (170)

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Begutachtung

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.

Originalsprache	Englisch
Seiten (von - bis)	1685-1730
Seitenumfang	46
Fachzeitschrift	Applied mathematics & optimization
Jahrgang	84.2021
Ausgabenummer	December, Suppl.2
DOIs	https://doi.org/10.1007/s00245-021-09808-1
Publikationsstatus	Veröffentlicht - 6 Aug. 2021

Bibliographische Notiz

Funding Information:
The first author of this paper is partially supported by Austrian Agency for International Cooperation in Education and Research (OeAD), Centre for International Cooperation and Mobility (ICM): ICM-2019-13458. The second author is supported by Austrian Science Foundation, project number P 32295 and the third author is supported by Marie Skłodowska-Curie Individual Fellowships H2020-MSCA-IF-2020, P 888255

Publisher Copyright:
© 2021, The Author(s).

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10.1007/s00245-021-09808-1

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