Wong-Zakai approximation for the stochastic Landau-Lifshitz-Gilbert equations with anisotropy energy

[摘要] 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. (C) 2019 Elsevier Inc. All rights reserved.

[发布日期] 2019-12-01

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