Wong–Zakai Approximation for Landau–Lifshitz–Gilbert Equation Driven by Geometric Rough Paths
Research output: Contribution to journal › Article › Research › peer-review
Standard
In: Applied mathematics & optimization, Vol. 84.2021, No. December, Suppl.2, 06.08.2021, p. 1685-1730.
Research output: Contribution to journal › Article › Research › peer-review
Harvard
APA
Vancouver
Author
Bibtex - Download
}
RIS (suitable for import to EndNote) - Download
TY - JOUR
T1 - Wong–Zakai Approximation for Landau–Lifshitz–Gilbert Equation Driven by Geometric Rough Paths
AU - Fahim, Kistosil
AU - Hausenblas, Erika
AU - Mukherjee, Debopriya
N1 - Publisher Copyright: © 2021, The Author(s).
PY - 2021/8/6
Y1 - 2021/8/6
N2 - We adapt Lyon’s rough path theory to study Landau–Lifshitz–Gilbert equations (LLGEs) driven by geometric rough paths in one dimension, with non-zero exchange energy only. We convert the LLGEs to a fully nonlinear time-dependent partial differential equation without rough paths term by a suitable transformation. 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 convergence rate in controlled rough path spaces. The key ingredients for constructing the solution and its corresponding convergence results are the Doss–Sussmann transformation, maximal regularity property, and the geometric rough path theory.
AB - We adapt Lyon’s rough path theory to study Landau–Lifshitz–Gilbert equations (LLGEs) driven by geometric rough paths in one dimension, with non-zero exchange energy only. We convert the LLGEs to a fully nonlinear time-dependent partial differential equation without rough paths term by a suitable transformation. 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 convergence rate in controlled rough path spaces. The key ingredients for constructing the solution and its corresponding convergence results are the Doss–Sussmann transformation, maximal regularity property, and the geometric rough path theory.
U2 - 10.1007/s00245-021-09808-1
DO - 10.1007/s00245-021-09808-1
M3 - Article
VL - 84.2021
SP - 1685
EP - 1730
JO - Applied mathematics & optimization
JF - Applied mathematics & optimization
SN - 1432-0606
IS - December, Suppl.2
ER -