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

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 pro...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2019-12, Vol.480 (1), p.123384, Article 123384
Main Authors: Manna, Utpal, Mukherjee, Debopriya, Panda, Akash A.
Format: Article
Language:English
Subjects:
Ferromagnetism
Maximal regularity
Stochastic Landau-Lifshitz-Gilbert equations
Wong-Zakai approximation
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Summary: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 S2 in R3. 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.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2019.123384