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Abstract The stochastic Landau-Lifshitz-Gilbert equations (SLLGEs) describe the behaviour of the magnetisation under the influence of the randomly fluctuating effective field. In this work, we consider the SLLGEs in one… Click to show full abstract
Abstract The stochastic Landau-Lifshitz-Gilbert equations (SLLGEs) describe the behaviour of the magnetisation under the influence of the randomly fluctuating effective field. In this work, we consider the SLLGEs in one space dimension in the presence of both the exchange energy and anisotropy energy and prove the existence of strong solution taking values in a two-dimensional unit sphere S 2 in R 3 . The key ingredients for the construction of the solution and its corresponding convergence results are the Doss-Sussmann transformation, maximal regularity property, and the Wong-Zakai approximation.
Journal Title: Journal of Mathematical Analysis and Applications
Year Published: 2019
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