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STABILITY OF THE SUPERPOSITION OF A VISCOUS CONTACT WAVE WITH TWO RAREFACTION WAVES TO THE BIPOLAR VLASOV POISSON BOLTZMANN SYSTEM
Li, Hai-Liang1; Wang, Teng2; Wang, Yi3,4
2018
Source PublicationSIAM JOURNAL ON MATHEMATICAL ANALYSIS
ISSN0036-1410
Volume50Issue:2Pages:1829-1876
AbstractWe 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.
Keywordbipolar Vlasov Poisson Boltzmann system rarefaction wave viscous contact wave time-asymptotic stability micro-macro decomposition
DOI10.1137/17M1150888
Language英语
Funding ProjectNSFC[11461161007] ; NSFC[11671384] ; NSFC[11231006] ; NSFC[11601031] ; NSFC[11671385] ; NSFC[11688101] ; Beijing New Century Baictianwan Talent Project ; Youth Innovation Promotion Association of CAS
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000431193200013
PublisherSIAM PUBLICATIONS
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/30186
Collection应用数学研究所
Affiliation1.Capital Normal Univ, Sch Math Sci, Beijing 100048, Peoples R China
2.Beijing Univ Technol, Coll Appl Sci, Beijing 100124, Peoples R China
3.Chinese Acad Sci, AMSS, Inst Appl Math, Beijing 100190, Peoples R China
4.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
Recommended Citation
GB/T 7714
Li, Hai-Liang,Wang, Teng,Wang, Yi. STABILITY OF THE SUPERPOSITION OF A VISCOUS CONTACT WAVE WITH TWO RAREFACTION WAVES TO THE BIPOLAR VLASOV POISSON BOLTZMANN SYSTEM[J]. SIAM JOURNAL ON MATHEMATICAL ANALYSIS,2018,50(2):1829-1876.
APA Li, Hai-Liang,Wang, Teng,&Wang, Yi.(2018).STABILITY OF THE SUPERPOSITION OF A VISCOUS CONTACT WAVE WITH TWO RAREFACTION WAVES TO THE BIPOLAR VLASOV POISSON BOLTZMANN SYSTEM.SIAM JOURNAL ON MATHEMATICAL ANALYSIS,50(2),1829-1876.
MLA Li, Hai-Liang,et al."STABILITY OF THE SUPERPOSITION OF A VISCOUS CONTACT WAVE WITH TWO RAREFACTION WAVES TO THE BIPOLAR VLASOV POISSON BOLTZMANN SYSTEM".SIAM JOURNAL ON MATHEMATICAL ANALYSIS 50.2(2018):1829-1876.
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