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Wong–Zakai approximation for the stochastic Landau–Lifshitz–Gilbert equations

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Publication details

JournalJournal of Differential Equations
DateE-pub ahead of print - 5 Feb 2019
DatePublished (current) - 5 Jul 2019
Issue number2
Number of pages50
Pages (from-to)776-825
Early online date5/02/19
Original languageEnglish


In this work we study stochastic Landau–Lifshitz–Gilbert equations (SLLGEs) in one dimension, with non-zero exchange energy only. Firstly, by introducing a suitable transformation, we convert the SLLGEs to a highly nonlinear time dependent partial differential equation with random coefficients, which is not fully parabolic. We then prove that there exists a pathwise unique solution to this equation and that this solution enjoys the maximal regularity property. Following regular approximation of the Brownian motion and using reverse transformation, we show existence of strong solution of SLLGEs taking values in a two-dimensional unit sphere S 2 in R 3 . The construction of the solution and its corresponding convergence results are based on Wong–Zakai approximation.

    Research areas

  • Ferromagnetism, Maximal regularity, Stochastic Landau–Lifshitz–Gilbert equations, Wong–Zakai approximation

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