STABILITY OF THE SUPERPOSITION OF A VISCOUS CONTACT WAVE WITH TWO RAREFACTION WAVES TO THE BIPOLAR VLASOV POISSON BOLTZMANN SYSTEM

doi:10.1137/17M1150888

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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-Liang 1; Wang, Teng 2; Wang, Yi3,4
	2018
发表期刊	SIAM JOURNAL ON MATHEMATICAL ANALYSIS
ISSN	0036-1410
卷号	50 期号:2 页码:1829-1876
摘要	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.
关键词	bipolar Vlasov Poisson Boltzmann system rarefaction wave viscous contact wave time-asymptotic stability micro-macro decomposition
DOI	10.1137/17M1150888
语种	英语
资助项目	NSFC[11461161007] ; NSFC[11671384] ; NSFC[11231006] ; NSFC[11601031] ; NSFC[11671385] ; NSFC[11688101] ; Beijing New Century Baictianwan Talent Project ; Youth Innovation Promotion Association of CAS
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000431193200013
出版者	SIAM PUBLICATIONS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/30186
专题	应用数学研究所
通讯作者	Wang, Yi
作者单位	1.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
推荐引用方式 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.