Stochastic homogenization of the Landau–Lifshitz–Gilbert equation

François Alouges; Anne de Bouard; Benoît Merlet; Léa Nicolas

doi:10.1007/s40072-020-00185-4

Stochastic homogenization of the Landau–Lifshitz–Gilbert equation

François Alouges
, Anne de Bouard
, Benoît Merlet
, Léa Nicolas

Université de Lille
INRIA Institut National de Recherche en Informatique et en Automatique

Research output: Contribution to journal › Article › peer-review

Abstract

Following the ideas of Zhikov and Piatnitski (Izv Math 70(1):19–67, 2006), and more precisely the stochastic two-scale convergence, this paper establishes a homogenization theorem in a stochastic setting for two nonlinear equations: the equation of harmonic maps into the sphere and the Landau–Lifschitz–Gilbert equation. These equations have strong nonlinear features, and in general their solutions are not unique.

Original language	English
Pages (from-to)	789-818
Number of pages	30
Journal	Stochastics and Partial Differential Equations: Analysis and Computations
Volume	9
Issue number	4
DOIs	https://doi.org/10.1007/s40072-020-00185-4
Publication status	Published - 1 Dec 2021

Keywords

Harmonic maps
Homogenization
Landau-Lifshitz equations
Micromagnetics

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10.1007/s40072-020-00185-4

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title = "Stochastic homogenization of the Landau–Lifshitz–Gilbert equation",

abstract = "Following the ideas of Zhikov and Piatnitski (Izv Math 70(1):19–67, 2006), and more precisely the stochastic two-scale convergence, this paper establishes a homogenization theorem in a stochastic setting for two nonlinear equations: the equation of harmonic maps into the sphere and the Landau–Lifschitz–Gilbert equation. These equations have strong nonlinear features, and in general their solutions are not unique.",

keywords = "Harmonic maps, Homogenization, Landau-Lifshitz equations, Micromagnetics",

author = "Fran{\c c}ois Alouges and \{de Bouard\}, Anne and Beno{\^i}t Merlet and L{\'e}a Nicolas",

note = "Publisher Copyright: {\textcopyright} 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC part of Springer Nature.",

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T1 - Stochastic homogenization of the Landau–Lifshitz–Gilbert equation

AU - Alouges, François

AU - de Bouard, Anne

AU - Merlet, Benoît

AU - Nicolas, Léa

PY - 2021/12/1

Y1 - 2021/12/1

N2 - Following the ideas of Zhikov and Piatnitski (Izv Math 70(1):19–67, 2006), and more precisely the stochastic two-scale convergence, this paper establishes a homogenization theorem in a stochastic setting for two nonlinear equations: the equation of harmonic maps into the sphere and the Landau–Lifschitz–Gilbert equation. These equations have strong nonlinear features, and in general their solutions are not unique.

AB - Following the ideas of Zhikov and Piatnitski (Izv Math 70(1):19–67, 2006), and more precisely the stochastic two-scale convergence, this paper establishes a homogenization theorem in a stochastic setting for two nonlinear equations: the equation of harmonic maps into the sphere and the Landau–Lifschitz–Gilbert equation. These equations have strong nonlinear features, and in general their solutions are not unique.

KW - Harmonic maps

KW - Homogenization

KW - Landau-Lifshitz equations

KW - Micromagnetics

UR - https://www.scopus.com/pages/publications/85098690852

U2 - 10.1007/s40072-020-00185-4

DO - 10.1007/s40072-020-00185-4

M3 - Article

AN - SCOPUS:85098690852

SN - 2194-0401

VL - 9

SP - 789

EP - 818

JO - Stochastics and Partial Differential Equations: Analysis and Computations

JF - Stochastics and Partial Differential Equations: Analysis and Computations

IS - 4

ER -

Stochastic homogenization of the Landau–Lifshitz–Gilbert equation

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Keywords

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