On the piecewise smoothness of entropy solutions to scalar conservation laws for a larger class of initial data

	On the piecewise smoothness of entropy solutions to scalar conservation laws for a larger class of initial data
	Tang, Tao ; Wang, Jinghua ; Zhao, Yinchuan
刊名	JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS
	2007-09-01
卷号	4 期号:3 页码:369-389
关键词	piecewise smooth solutions conservation laws a set of first category
ISSN号	0219-8916
英文摘要	We prove that if the initial data do not belong to a certain subset of C-k, then the solutions of scalar conservation laws are piecewise C-k smooth. In particular, our initial data allow centered compression waves, which was the case not covered by Dafermos (1974) and Schaeffer (1973). More precisely, we are concerned with the structure of the solutions in some neighborhood of the point at which only a Ck+1 shock is generated. It is also shown that there are finitely many shocks for smooth initial data (in the Schwartz space) except for a certain subset of S(R) of the first category. It should be pointed out that this subset is smaller than those used in previous works. We point out that Thom's theory of catastrophes, which plays a key role in Schaeffer (1973), cannot be used to analyze the larger class of initial data considered in this paper.
WOS研究方向	Mathematics ; Physics
语种	英语
出版者	WORLD SCIENTIFIC PUBL CO PTE LTD
WOS记录号	WOS:000251175900001
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/3968]
专题	中国科学院数学与系统科学研究院
通讯作者	Tang, Tao
作者单位	1.Hong Kong Baptist Univ, Dept Math, Kowloon, Peoples R China 2.Chinese Acad Sci, Inst Computat Math, Beijing, Peoples R China 3.Chinese Acad Sci, Acad Math & Syst Sci, Inst Syst Sci, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Tang, Tao,Wang, Jinghua,Zhao, Yinchuan. On the piecewise smoothness of entropy solutions to scalar conservation laws for a larger class of initial data[J]. JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS,2007,4(3):369-389.
APA	Tang, Tao,Wang, Jinghua,&Zhao, Yinchuan.(2007).On the piecewise smoothness of entropy solutions to scalar conservation laws for a larger class of initial data.JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS,4(3),369-389.
MLA	Tang, Tao,et al."On the piecewise smoothness of entropy solutions to scalar conservation laws for a larger class of initial data".JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS 4.3(2007):369-389.