Stochastic homogenization of the Landau–Lifshitz–Gilbert equation

Stochastic homogenization of the Landau–Lifshitz–Gilbert equation

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–Lifsch...

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Veröffentlicht in:Stochastic partial differential equations : analysis and computations 2021-12, Vol.9 (4), p.789-818
Hauptverfasser: Alouges, François, de Bouard, Anne, Merlet, Benoît, Nicolas, Léa
Format: Artikel
Sprache:eng
Schlagworte:
Analysis of PDEs
Computational Mathematics and Numerical Analysis
Computational Science and Engineering
Homogenization
Mathematical analysis
Mathematics
Mathematics and Statistics
Nonlinear equations
Numerical Analysis
Partial Differential Equations
Probability
Probability Theory and Stochastic Processes
Statistical Theory and Methods
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Beschreibung
Zusammenfassung: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.
ISSN:2194-0401
2194-041X
DOI:10.1007/s40072-020-00185-4