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Stability of the Superposition of a Viscous Contact Wave with Two Rarefaction Waves to the Bipolar Vlasov--Poisson--Boltzmann System

Hai-liang Li Teng Wang Yi Wang

Analysis of PDEs mathscidoc:1912.43766

SIAM Journal on Mathematical Analysis, 50, (2), 1829-1876, 2018.4
We investigate the nonlinear stability of the superposition of a viscous contact wave and two rarefaction waves for a one-dimensional (1D) bipolar Vlasov--Poisson--Boltzmann (VPB) system, which can be used to describe the transportation of charged particles under the additional electrostatic potential force. Based on a new micro-macro type of decomposition around the local Maxwellian related to the bipolar VPB system in the previous work [H.-L. Li, Y. Wang, T. Yang, and M.-Y. Zhong, <i>Arch. Ration. Mech. Anal.</i>, 228 (2018), pp. 39--127], we prove that the superposition of a viscous contact wave and two rarefaction waves is time-asymptotically stable to the 1D bipolar VPB system under some smallness conditions on the initial perturbations and wave strength, which implies that this typical superposition wave pattern is nonlinearly stable under the combined effects of the binary collisions, the electrostatic potential
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@inproceedings{hai-liang2018stability,
  title={Stability of the Superposition of a Viscous Contact Wave with Two Rarefaction Waves to the Bipolar Vlasov--Poisson--Boltzmann System},
  author={Hai-liang Li, Teng Wang, and Yi Wang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224205644203199330},
  booktitle={SIAM Journal on Mathematical Analysis},
  volume={50},
  number={2},
  pages={1829-1876},
  year={2018},
}
Hai-liang Li, Teng Wang, and Yi Wang. Stability of the Superposition of a Viscous Contact Wave with Two Rarefaction Waves to the Bipolar Vlasov--Poisson--Boltzmann System. 2018. Vol. 50. In SIAM Journal on Mathematical Analysis. pp.1829-1876. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224205644203199330.
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