We consider the kinetic Fokker–Planck equation with a class of general force. We prove the existence and uniqueness of a positive normalized equilibrium (in the case of a general force) and establish some exponential rate of convergence to the equilibrium (and the rate can be explicitly computed). Our results improve results about classical force to general force case. Our result also improves the rate of convergence for the Fitzhugh–Nagumo equation from non-quantitative to quantitative explicit rate.

中文翻译：

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具有一般力的动力学Fokker-Planck方程

我们考虑具有一类普通力的动力学Fokker-Planck方程。我们证明了正归一化均衡的存在性和唯一性（在一般力的情况下），并建立了到该均衡的一些指数收敛速度（并且可以明确地计算出该速度）。我们的结果改进了关于经典力到一般力情况的结果。我们的结果也将Fitzhugh-Nagumo方程的收敛速度从非定量的显式速率提高到定量的显式速率。