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

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	On the piecewise smoothness of entropy solutions to scalar conservation laws for a larger class of initial data
	Tang, Tao ; Wang, Jinghua ; Zhao, Yinchuan
	2007-09-01
发表期刊	JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS
ISSN	0219-8916
卷号	4 期号:3 页码:369-389
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.
关键词	piecewise smooth solutions conservation laws a set of first category
语种	英语
WOS研究方向	Mathematics ; Physics
WOS类目	Mathematics, Applied ; Physics, Mathematical
WOS记录号	WOS:000251175900001
出版者	WORLD SCIENTIFIC PUBL CO PTE 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/3969
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.