Time decay rate of solutions toward the viscous shock waves to the Cauchy problem for the scalar conservation law with nonlinear viscosity and discontinuous initial data

doi:10.1016/j.na.2022.112945

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	Time decay rate of solutions toward the viscous shock waves to the Cauchy problem for the scalar conservation law with nonlinear viscosity and discontinuous initial data
	Liu, Yechi
	2022-09-01
发表期刊	NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
ISSN	0362-546X
卷号	222 页码:14
摘要	In this paper, it is shown that the weak solution to the Cauchy problem for the scalar viscous conservation law, with nonlinear viscosity and different far field states, exists globally in time. Especially, this existence holds with discontinuous initial data. Furthermore, when the corresponding Riemann problem for the hyperbolic part has a single shock wave solution, it is proved that the weak solution converges toward the viscous shock wave as time goes to infinity, and the decay rate is also obtained. The proof is given by a technical energy method. (c) 2022 Elsevier Ltd. All rights reserved.
关键词	Viscous conservation law Asymptotic behavior Time decay rate Viscous shock wave Discontinuous initial data
DOI	10.1016/j.na.2022.112945
收录类别	SCI
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000806759100008
出版者	PERGAMON-ELSEVIER SCIENCE LTD
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/61509
专题	中国科学院数学与系统科学研究院
通讯作者	Liu, Yechi
作者单位	Chinese Acad Sci, Inst Appl Math, AMSS, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Liu, Yechi. Time decay rate of solutions toward the viscous shock waves to the Cauchy problem for the scalar conservation law with nonlinear viscosity and discontinuous initial data[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS,2022,222:14.
APA	Liu, Yechi.(2022).Time decay rate of solutions toward the viscous shock waves to the Cauchy problem for the scalar conservation law with nonlinear viscosity and discontinuous initial data.NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS,222,14.
MLA	Liu, Yechi."Time decay rate of solutions toward the viscous shock waves to the Cauchy problem for the scalar conservation law with nonlinear viscosity and discontinuous initial data".NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS 222(2022):14.