论文标题
弗拉索夫的边界控制 - 弗朗克方程
Boundary Control of Vlasov--Fokker--Planck Equations
论文作者
论文摘要
我们引入了一种新型的Lyapunov函数，用于稳定线性vlasov--fokker- planck类型方程，具有硬源项。与依赖运输特性获得稳定的现有结果相反，我们根据Fokker-Planck运营商的低核心分析提出了结果。现有估计值扩展以得出合适的反馈边界控制，以确保指数稳定。此外，我们研究了相关的宏观极限，并在反馈边界控制上得出条件，因此在形式极限中不存在边界层。
We introduce a novel Lyapunov function for stabilization of linear Vlasov--Fokker--Planck type equations with stiff source term. Contrary to existing results relying on transport properties to obtain stabilization, we present results based on hypocoercivity analysis for the Fokker--Planck operator. The existing estimates are extended to derive suitable feedback boundary control to guarantee the exponential stabilization. Further, we study the associated macroscopic limit and derive conditions on the feedback boundary control such that in the formal limit no boundary layer exists.
