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

doi:10.1142/S0219891607001185

科研成果详情

发表状态	已发表Published
题名	On the piecewise smoothness of entropy solutions to scalar conservation laws for a large class of initial data
作者	Tang, Tao1,2 ; Wang, Jinghua 3; Zhao, Yinchuan 4
发表日期	2007
发表期刊	Journal of Hyperbolic Differential Equations
ISSN/eISSN	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
DOI	10.1142/S0219891607001185
URL	查看来源
收录类别	SCIE
语种	英语English
WOS研究方向	Mathematics ; Physics
WOS类目	Mathematics, Applied ; Physics, Mathematical
WOS记录号	WOS:000251175900001
引用统计	被引频次：5[WOS] [WOS记录] [WOS相关记录]
文献类型	期刊论文
条目标识符	https://repository.uic.edu.cn/handle/39GCC9TT/4798
专题	个人在本单位外知识产出
作者单位	1.Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong; 2.Institute of Computational Mathematics, Chinese Academy of Sciences, Beijing, China; 3.Institute of Systems Sciences, Academy of Mathematics and System Sciences, The Chinese Academy of Sciences, Beijing 100080, P. R. China; 4.Institute of Computational Mathematics, Academy of Mathematics and System Sciences, The Chinese Academy of Sciences, Beijing 100080, P. 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 large 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 large 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 large class of initial data". Journal of Hyperbolic Differential Equations 4.3(2007): 369-389.