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

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Wong–Zakai approximation for the stochastic Landau–Lifshitz–Gilbert equations. / Brzezniak, Zdzislaw; Manna, Utpal; Mukherjee, Debopriya.

In: Journal of Differential Equations, Vol. 267, No. 2, 05.07.2019, p. 776-825.

Research output: Contribution to journalArticlepeer-review

Harvard

Brzezniak, Z, Manna, U & Mukherjee, D 2019, 'Wong–Zakai approximation for the stochastic Landau–Lifshitz–Gilbert equations', Journal of Differential Equations, vol. 267, no. 2, pp. 776-825. https://doi.org/10.1016/j.jde.2019.01.025

APA

Brzezniak, Z., Manna, U., & Mukherjee, D. (2019). Wong–Zakai approximation for the stochastic Landau–Lifshitz–Gilbert equations. Journal of Differential Equations, 267(2), 776-825. https://doi.org/10.1016/j.jde.2019.01.025

Vancouver

Brzezniak Z, Manna U, Mukherjee D. Wong–Zakai approximation for the stochastic Landau–Lifshitz–Gilbert equations. Journal of Differential Equations. 2019 Jul 5;267(2):776-825. https://doi.org/10.1016/j.jde.2019.01.025

Author

Brzezniak, Zdzislaw ; Manna, Utpal ; Mukherjee, Debopriya. / Wong–Zakai approximation for the stochastic Landau–Lifshitz–Gilbert equations. In: Journal of Differential Equations. 2019 ; Vol. 267, No. 2. pp. 776-825.

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@article{200b6e75d22c49539ec3b2f17fd49a84,
title = "Wong–Zakai approximation for the stochastic Landau–Lifshitz–Gilbert equations",
abstract = " 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. ",
keywords = "Ferromagnetism, Maximal regularity, Stochastic Landau–Lifshitz–Gilbert equations, Wong–Zakai approximation",
author = "Zdzislaw Brzezniak and Utpal Manna and Debopriya Mukherjee",
year = "2019",
month = jul,
day = "5",
doi = "10.1016/j.jde.2019.01.025",
language = "English",
volume = "267",
pages = "776--825",
journal = "Journal of Differential Equations",
issn = "0022-0396",
publisher = "Academic Press Inc.",
number = "2",

}

RIS (suitable for import to EndNote) - Download

TY - JOUR

T1 - Wong–Zakai approximation for the stochastic Landau–Lifshitz–Gilbert equations

AU - Brzezniak, Zdzislaw

AU - Manna, Utpal

AU - Mukherjee, Debopriya

PY - 2019/7/5

Y1 - 2019/7/5

N2 - 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.

AB - 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.

KW - Ferromagnetism

KW - Maximal regularity

KW - Stochastic Landau–Lifshitz–Gilbert equations

KW - Wong–Zakai approximation

UR - http://www.scopus.com/inward/record.url?scp=85060757299&partnerID=8YFLogxK

U2 - 10.1016/j.jde.2019.01.025

DO - 10.1016/j.jde.2019.01.025

M3 - Article

AN - SCOPUS:85060757299

VL - 267

SP - 776

EP - 825

JO - Journal of Differential Equations

JF - Journal of Differential Equations

SN - 0022-0396

IS - 2

ER -