论文标题
抽象平滑歧管上langevin型动力学的低调
Hypocoercivity of Langevin-type dynamics on abstract smooth manifolds
论文作者
论文摘要
在本文中，我们研究了非线性平滑几何形状中Langevin型动力学的低调。主要结果将指数衰减呈现为平衡状态，并具有明确的可收敛速率，它植根于Dolbeault，Mouhot和Schmeiser的吸引人的希尔伯特空间策略。与双重Fokker-Planck框架相比，[GS14]中将此策略扩展到Kolmogorov向后的进化方程。我们使用这种数学上完整的详细说明来研究抽象的歧管设置中的Langevin型SDE，即（至少）（至少）位置变量遵守某些平滑的侧面条件。这种方程式发生，例如作为工业应用中的纤维放置过程。我们用（半）喷雾剂来贡献这种几何兰格文动力学的拉格朗日型公式，并指出了光纤束衡量空间的必要性以指定模型希尔伯特空间。
In this article we investigate hypocoercivity of Langevin-type dynamics in nonlinear smooth geometries. The main result stating exponential decay to an equilibrium state with explicitly computable rate of convergence is rooted in an appealing Hilbert space strategy by Dolbeault, Mouhot and Schmeiser. This strategy was extended in [GS14] to Kolmogorov backward evolution equations in contrast to the dual Fokker-Planck framework. We use this mathematically complete elaboration to investigate wide ranging classes of Langevin-type SDEs in an abstract manifold setting, i.e. (at least) the position variables obey certain smooth side conditions. Such equations occur e.g. as fibre lay-down processes in industrial applications. We contribute the Lagrangian-type formulation of such geometric Langevin dynamics in terms of (semi-)sprays and point to the necessity of fibre bundle measure spaces to specify the model Hilbert space.
