Periodic solutions for the Landau-Lifshitz-Gilbert equation
Analysis of PDEs
2010-06-25 v1
Abstract
Ferromagnetic materials tend to develop very complex magnetization patterns whose time evolution is modeled by the so-called Landau-Lifshitz-Gilbert equation (LLG). In this paper, we construct time-periodic solutions for LLG in the regime of soft and small ferromagnetic particles which satisfy a certain shape condition. Roughly speaking, it is assumed that the length of the particle is greater than its hight and its width. The approach is based on a perturbation argument and the spectral analysis of the corresponding linearized problem as well as the theory of sectorial operators.
Keywords
Cite
@article{arxiv.1006.4765,
title = {Periodic solutions for the Landau-Lifshitz-Gilbert equation},
author = {Alexander Huber},
journal= {arXiv preprint arXiv:1006.4765},
year = {2010}
}