离散Fokker-Planck方程的强制性、弱强制性、指数时间衰减及模拟
Coercivity, hypocoercivity, exponential time decay and simulations for discrete Fokker-Planck equations
AI总结：
该研究提出一维齐次与非齐次Fokker-Planck方程的多种离散形式，借助新型离散Poincaré不等式与适配的弱强制性方法，证明了时间连续与离散情形下解的指数收敛性。
摘要：
本文提出并研究了一维齐次与非齐次Fokker-Planck方程的若干离散形式。针对速度与空间的这类离散化方案，我们证明了时间连续方程与时间离散方程的解均指数收敛到平衡态。我们的方法针对速度导数的“双向”离散化，采用了新型离散Poincaré不等式；对于非齐次问题，我们将弱强制性方法适配到离散情形。
英文摘要：
In this article, we propose and study several discrete versions of homogeneous and inhomogeneous one-dimensional Fokker-Planck equations. In particular, for these discretizations of velocity and space, we prove the exponential convergence to the equilibrium of the solutions, for time-continuous equations as well as for time-discrete equations. Our method uses new types of discrete Poincaré inequalities for a "two-direction" discretization of the derivative in velocity. For the inhomogeneous problem, we adapt hypocoercive methods to the discrete cases.
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