THE KINETIC FOKKER-PLANCK EQUATION WITH GENERAL FORCE

Chuqi Cao (1, 2, 3)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 Université Paris Dauphine-PSL
3 Mathematical Sciences Center [Tsinghua]

We consider the kinetic Fokker-Planck equation with a class of general force. We prove the existence and uniqueness of a positive nor- malized 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 improve the rate of convergence for the Fitzhugh-Nagumo equation from non-quantitative to quantitative explicit rate.

Domaines: Equations aux dérivées partielles [math.AP]

Chuqi Cao. THE KINETIC FOKKER-PLANCK EQUATION WITH GENERAL FORCE. 2020. ⟨hal-02127815v2⟩