论文标题
轨迹低调和控制理论的应用
Trajectorial hypocoercivity and application to control theory
论文作者
论文摘要
我们在简单的环境中介绍了最近工作ARXIV：2209.09340的定量方法，以及不包含在Arxiv：2209.09340中的紧凑性参数，本身具有关注。我们关注的是具有简并热化的线性动力学方程的指数稳定（光谱差距），即碰撞操作员在空间结构域的部分地区消失时。 ARXIV中的方法：2209.09340涵盖了散射和Fokker-Planck型操作员，并处理外部潜力和边界条件，但是在这些注释中，我们仅介绍其核心论点，并将自己限制在具有单位速度和热量变性的周期性圆环中。 Bernard and Salvarani（2013），Han-Kwan和Léautaud（2015），Evans和Moyano（Arxiv：1907.12836）的先前结果不涵盖该方程式。
We present the quantitative method of the recent work arXiv:2209.09340 in a simple setting, together with a compactness argument that was not included in arXiv:2209.09340 and has interest per se. We are concerned with the exponential stabilization (spectral gap) for linear kinetic equations with degenerate thermalization, i.e. when the collision operator vanishes on parts of the spatial domain. The method in arXiv:2209.09340 covers both scattering and Fokker-Planck type operators, and deals with external potential and boundary conditions, but in these notes we present only its core argument and restrict ourselves to the kinetic Fokker-Planck in the periodic torus with unit velocities and a thermalization degeneracy. This equation is not covered by the previous results of Bernard and Salvarani (2013), Han-Kwan and Léautaud (2015), Evans and Moyano (arXiv:1907.12836).
