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Author:

Li, Hai-Liang (Li, Hai-Liang.) | Wang, Teng (Wang, Teng.) (Scholars:王腾) | Wang, Yi (Wang, Yi.)

Indexed by:

EI Scopus SCIE

Abstract:

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, Arch. Ration. Mech. Anal., 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 force, and the mutual interactions of different charged particles. This is the first result about the nonlinear stability of the combination of two different wave patterns for the VPB system.

Keyword:

time-asymptotic stability micro-macro decomposition bipolar Vlasov Poisson Boltzmann system viscous contact wave rarefaction wave

Author Community:

  • [ 1 ] [Li, Hai-Liang]Capital Normal Univ, Sch Math Sci, Beijing 100048, Peoples R China
  • [ 2 ] [Wang, Teng]Beijing Univ Technol, Coll Appl Sci, Beijing 100124, Peoples R China
  • [ 3 ] [Wang, Yi]Chinese Acad Sci, AMSS, Inst Appl Math, Beijing 100190, Peoples R China
  • [ 4 ] [Wang, Yi]Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China

Reprint Author's Address:

  • [Wang, Yi]Chinese Acad Sci, AMSS, Inst Appl Math, Beijing 100190, Peoples R China;;[Wang, Yi]Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China

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Source :

SIAM JOURNAL ON MATHEMATICAL ANALYSIS

ISSN: 0036-1410

Year: 2018

Issue: 2

Volume: 50

Page: 1829-1876

2 . 0 0 0

JCR@2022

ESI Discipline: MATHEMATICS;

ESI HC Threshold:63

Cited Count:

WoS CC Cited Count: 6

SCOPUS Cited Count: 5

ESI Highly Cited Papers on the List: 0 Unfold All

WanFang Cited Count:

Chinese Cited Count:

30 Days PV: 6

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