Asymptotic Stability of Shock Profiles and Rarefaction Waves under Periodic Perturbations for 1-D Convex Scalar Viscous Conservation Laws

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	Asymptotic Stability of Shock Profiles and Rarefaction Waves under Periodic Perturbations for 1-D Convex Scalar Viscous Conservation Laws
	Xin, Zhouping 1,2; Yuan, Qian3 ; Yuan, Yuan 4
	2021
发表期刊	INDIANA UNIVERSITY MATHEMATICS JOURNAL
ISSN	0022-2518
卷号	70 期号:6 页码:2295-2349
摘要	This paper studies the asymptotic stability of shock profiles and rarefaction waves under space-periodic perturbations for one-dimensional convex scalar viscous conservation laws. For the shock profile, we show that the solution approaches the background shock profile with a constant shift in the L-infinity (R) norm at exponential rates. The new phenomena contrasting to the case of localized perturbations is that the constant shift cannot be determined by the initial excessive mass in general, which indicates that the periodic oscillations at infinities make contributions to this shift. And the vanishing viscosity limit for the shift is also shown. The key elements of the proof consist of the construction of an ansatz which carries periodic oscillations of the solution as vertical bar X vertical bar -> +infinity, the anti-derivative variable argument, and an elaborate use of the maximum principle. For the rarefaction wave, we also show the stability in the L-infinity (R) norm.
收录类别	SCI
语种	英语
资助项目	Zheng Ge Ru Foundation through Hong Kong RGC Earmarked Research Grants[CUHK-14300917] ; Zheng Ge Ru Foundation through Hong Kong RGC Earmarked Research Grants[CUHK-14305315] ; Zheng Ge Ru Foundation through Hong Kong RGC Earmarked Research Grants[CUHK-14300819] ; Zheng Ge Ru Foundation through Hong Kong RGC Earmarked Research Grants[CUHK-14302819] ; Zheng Ge Ru Foundation through Hong Kong RGC Earmarked Research Grants[CUHK-14302917] ; Guangdong Province Basic and Applied Basic Research Foundation[2020B1515310002] ; China Postdoctoral Science Founda-tion[2019M660831] ; China Postdoctoral Science Founda-tion[2020TQ0345] ; Natural Science Founda-tion of China[11901208] ; Natural Science Founda-tion of China[11971009] ; Natural Science Foun-dation of Guangdong Province[2021A1515010247] ; National Key Research and Development Program of China[2021YFA1002900]
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000733338700003
出版者	INDIANA UNIV MATH JOURNAL
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/59803
专题	博士后
通讯作者	Yuan, Qian
作者单位	1.Chinese Univ Hong Kong, Inst Math Sci, Shatin, Hong Kong, Peoples R China 2.Chinese Univ Hong Kong, Dept Math, Shatin, Hong Kong, Peoples R China 3.Chinese Acad Sci, Acad Math & Syst Sci, Inst Appl Math, Beijing, Peoples R China 4.South China Normal Univ, Sch Math Sci, Guangzhou, Guangdong, Peoples R China
推荐引用方式 GB/T 7714	Xin, Zhouping,Yuan, Qian,Yuan, Yuan. Asymptotic Stability of Shock Profiles and Rarefaction Waves under Periodic Perturbations for 1-D Convex Scalar Viscous Conservation Laws[J]. INDIANA UNIVERSITY MATHEMATICS JOURNAL,2021,70(6):2295-2349.
APA	Xin, Zhouping,Yuan, Qian,&Yuan, Yuan.(2021).Asymptotic Stability of Shock Profiles and Rarefaction Waves under Periodic Perturbations for 1-D Convex Scalar Viscous Conservation Laws.INDIANA UNIVERSITY MATHEMATICS JOURNAL,70(6),2295-2349.
MLA	Xin, Zhouping,et al."Asymptotic Stability of Shock Profiles and Rarefaction Waves under Periodic Perturbations for 1-D Convex Scalar Viscous Conservation Laws".INDIANA UNIVERSITY MATHEMATICS JOURNAL 70.6(2021):2295-2349.