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The Kinetic Fokker Planck equation with General Force

Chuqi Cao Yau Mathematical Science Center, Tsinghua University

Analysis of PDEs mathscidoc:2205.03004

Journal of Evolution Equations, 21, 2021.5
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 gen- eral 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.
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@inproceedings{chuqi2021the,
  title={The Kinetic Fokker Planck equation with General Force},
  author={Chuqi Cao},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220518151450302702269},
  booktitle={Journal of Evolution Equations},
  volume={21},
  year={2021},
}
Chuqi Cao. The Kinetic Fokker Planck equation with General Force. 2021. Vol. 21. In Journal of Evolution Equations. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220518151450302702269.
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