论文标题
一维Landau-lifshitz-gilbert方程的自相似收缩器
Self-similar shrinkers of the one-dimensional Landau-Lifshitz-Gilbert equation
论文作者
论文摘要
本文的主要目的是对一维Landau-Lifshitz-Gilbert方程（LLG）的自我脱离溶液的分析研究，该模型描述了铁磁材料中旋转的动力学。我们表明，有一个独特的平稳的向后自相似解决方案，最直至对称性，我们建立了它们的渐近性。此外，我们获得了在阻尼的存在下，自相似轮廓的轨迹会以指数速率收敛到球体上的大圆圈$ \ mathbb {s}^2 $。特别是，本文中介绍的结果提供了有限时间的爆炸示例，其中奇异性由于迅速形成极限圆而形成。
The main purpose of this paper is the analytical study of self-shrinker solutions of the one-dimensional Landau-Lifshitz-Gilbert equation (LLG), a model describing the dynamics for the spin in ferromagnetic materials. We show that there is a unique smooth family of backward self-similar solutions to the LLG equation, up to symmetries, and we establish their asymptotics. Moreover, we obtain that in the presence of damping, the trajectories of the self-similar profiles converge to great circles on the sphere $\mathbb{S}^2$, at an exponential rate. In particular, the results presented in this paper provide examples of blow-up in finite time, where the singularity develops due to rapid oscillations forming limit circles.
