The Boltzmann Equation with Time-periodic Boundary Temperature

doi:10.1007/s10255-019-0803-0

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	The Boltzmann Equation with Time-periodic Boundary Temperature
	Duan, Renjun 1; Wang, Yong2,3 ; Zhang, Zhu 1
	2019
发表期刊	ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES
ISSN	0168-9673
卷号	35 期号:1 页码:174-208
摘要	This paper is concerned with the boundary-value problem on the Boltzmann equation in bounded domains with diffuse-reflection boundary where the boundary temperature is time-periodic. We establish the existence of time-periodic solutions with the same period for both hard and soft potentials, provided that the time-periodic boundary temperature is sufficiently close to a stationary one which has small variations around a positive constant. The dynamical stability of time-periodic profiles is also proved under small perturbations, and this in turn yields the non-negativity of the profile. For the proof, we develop new estimates in the time-periodic setting.
关键词	Boltzmann equation time-periodic boundary time-periodic solutions existence dynamical stability a priori estimates
DOI	10.1007/s10255-019-0803-0
语种	英语
资助项目	RGC of Hong Kong[14302817] ; CUHK[4053286] ; NSFC[11771429] ; NSFC[11688101] ; NSFC[11671237]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000459979000008
出版者	SPRINGER HEIDELBERG
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/34174
专题	应用数学研究所
通讯作者	Duan, Renjun
作者单位	1.Chinese Univ Hong Kong, Dept Math, Hong Kong, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China 3.Univ Chinese Acad Sci, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Duan, Renjun,Wang, Yong,Zhang, Zhu. The Boltzmann Equation with Time-periodic Boundary Temperature[J]. ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES,2019,35(1):174-208.
APA	Duan, Renjun,Wang, Yong,&Zhang, Zhu.(2019).The Boltzmann Equation with Time-periodic Boundary Temperature.ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES,35(1),174-208.
MLA	Duan, Renjun,et al."The Boltzmann Equation with Time-periodic Boundary Temperature".ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES 35.1(2019):174-208.