Research output: Contribution to journal › Article › peer-review
Journal | Journal of Differential Equations |
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Date | E-pub ahead of print - 5 Feb 2019 |
Date | Published (current) - 5 Jul 2019 |
Issue number | 2 |
Volume | 267 |
Number of pages | 50 |
Pages (from-to) | 776-825 |
Early online date | 5/02/19 |
Original language | English |
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.
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