论文标题
landau-lifshitz-gilbert方程：低模式的可控性强迫确定性版本并支持随机版本的定理
Landau-Lifshitz-Gilbert equations: Controllability by Low Modes Forcing for deterministic version and Support Theorems for Stochastic version
论文作者
论文摘要
在本文中，我们仅在一个空间维度的一个空间维度和Neumann边界条件下，研究了Landau-Lifshitz-Gilbert方程（LLGES）的可控性问题。该纸是双重的。在本文的第一部分中，我们研究了LLGE的可控性问题。在这里作用的控制力是退化的，即它通过几个低模式频率作用。我们利用溶液的傅立叶系列扩展。我们借用差异几何控制理论（Like Bracket生成属性）来建立LLGE的有限维盖尔金近似值的全局可控性。我们显示了完整系统的$ l^2 $近似可控性。在第二部分中，我们考虑具有较低维度的随机强迫（有限维度布朗尼运动）的LLGE，并研究了支持定理。
In this article, we study the controllability issues of the Landau-Lifshitz-Gilbert Equations (LLGEs), accompanied with non-zero exchange energy only, in an interval in one spatial dimension with Neumann boundary conditions. The paper is of twofold. In the first part of the paper, we study the controllability issues of the LLGEs. The control force acting here is degenerate i.e., it acts through a few numbers of low mode frequencies. We exploit the Fourier series expansion of the solution. We borrow methods of differential geometric control theory (Lie bracket generating property) to establish the global controllability of the finite-dimensional Galerkin approximations of LLGEs. We show $L^2$ approximate controllability of the full system. In the second part, we consider the LLGEs with lower-dimensional degenerate random forcing (finite-dimensional Brownian motions) and study support theorems.
