Existence of stationary solutions to the VlasovPoissonBoltzmann system

Renjun Duan Tong Yang Changjiang Zhu

Analysis of PDEs mathscidoc:1912.43980

Journal of mathematical analysis and applications, 327, (1), 425-434, 2007.3
In this paper, we study the existence of stationary solutions to the VlasovPoissonBoltzmann system when the background density function tends to a positive constant with a very mild decay rate as| x|. In fact, the stationary VlasovPoissonBoltzmann system can be written into an elliptic equation with exponential nonlinearity. Under the assumption on the decay rate being (ln (e+| x|)) for some > 0, it is shown that this elliptic equation has a unique solution. This result generalizes the previous work [R. Glassey, J. Schaeffer, Y. Zheng, Steady states of the VlasovPoissonFokkerPlanck system, J. Math. Anal. Appl. 202 (1996) 10581075] where the decay rate (1+| x|) 1 2 is assumed.
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@inproceedings{renjun2007existence,
  title={Existence of stationary solutions to the VlasovPoissonBoltzmann system},
  author={Renjun Duan, Tong Yang, and Changjiang Zhu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224211031913048544},
  booktitle={Journal of mathematical analysis and applications},
  volume={327},
  number={1},
  pages={425-434},
  year={2007},
}
Renjun Duan, Tong Yang, and Changjiang Zhu. Existence of stationary solutions to the VlasovPoissonBoltzmann system. 2007. Vol. 327. In Journal of mathematical analysis and applications. pp.425-434. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224211031913048544.
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