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

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:267

Article

Brzezniak, Zdzislaw¹  Manna, Utpal²  Mukherjee, Debopriya² 

[1] Univ York, Dept Math, York YO10 5DD, N Yorkshire, England

[2] Indian Inst Sci Educ & Res IISER Thiruvananthapur, Sch Math, Thiruvananthapuram 695551, Kerala, India

关键词: Stochastic Landau-Lifshitz-Gilbert equations;    Wong-Zakai approximation;    Maximal regularity;    Ferromagnetism;   

DOI  :  10.1016/j.jde.2019.01.025

来源: Elsevier

【 摘 要 】

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. (c) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free