Tuesday, June 4, 2024 - 17:00 in ZiF
Stochastic Landau-Lifshitz-Gilbert equations (SLLGEs) driven by a rough path
A talk in the Harmonic and Stochastic Analysis of Dispersive PDEs series by
Erika Hausenblas from Montanuniversität Leoben
| Abstract: |
The stochastic Landau-Lifshitz-Gilbert equations (SLLGEs) describe the behaviour of the
magnetisation under the influence of the randomly fluctuating effective field.
In a joint work by Mukherjee and Fahim, we adapted Lyons’ rough paths theory to study Landau-
Lifshitz-Gilbert equations (LLGEs). Here, we considered the LLG equation driven by geometric
rough paths in one dimension, with non-zero exchange energy only. By proposing a suitable
transformation, we convert the LLGEs to a highly nonlinear time-dependent partial differential
equation without rough paths term. Our point of interest is the regular approximation of
the geometric rough path. We investigate the limit equation, the form of the correction term,
and its rate of convergence in controlled rough path spaces. The key ingredients for the
construction of the solution and its corresponding convergence results are the Doss-Sussmann
transformation, maximal regularity property, and the geometric rough path theory.
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