Spectrum analysis and optimal decay rates of the bipolar Vlasov-Poisson-Boltzmann equations

Hai-Liang Li Tong Yang Mingying Zhong

Analysis of PDEs mathscidoc:1912.43988

arXiv preprint arXiv:1411.5470, 2016.11
In the present paper, we consider the initial value problem for the bipolar Vlasov-Poisson-Boltzmann (bVPB) system and its corresponding modified Vlasov-Poisson-Boltzmann (mVPB). We give the spectrum analysis on the linearized bVPB and mVPB systems around their equilibrium state and show the optimal convergence rate of global solutions. It was showed that the electric field decays exponentially and the distribution function tends to the absolute Maxwellian at the optimal convergence rate (1+ t)^{-3/4} for the bVPB system, yet both the electric field and the distribution function converge to equilibrium state at the optimal rate (1+ t)^{-3/4} for the mVPB system.
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@inproceedings{hai-liang2016spectrum,
  title={Spectrum analysis and optimal decay rates of the bipolar Vlasov-Poisson-Boltzmann equations},
  author={Hai-Liang Li, Tong Yang, and Mingying Zhong},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224211100917258552},
  booktitle={arXiv preprint arXiv:1411.5470},
  year={2016},
}
Hai-Liang Li, Tong Yang, and Mingying Zhong. Spectrum analysis and optimal decay rates of the bipolar Vlasov-Poisson-Boltzmann equations. 2016. In arXiv preprint arXiv:1411.5470. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224211100917258552.
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