The reason of Hopf's and Oleinik's proofs for countability of shocks being wrong

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	The reason of Hopf's and Oleinik's proofs for countability of shocks being wrong
其他题名	The reason of Hopf’s and Oleinik’s proofs for countability of shocks being wrong
	Li BangHe
	2012
发表期刊	SCIENCE CHINA-MATHEMATICS
ISSN	1674-7283
卷号	55 期号:4 页码:727-729
摘要	For the number of complete shock curves of a conservation law with one space variable, Hopf in 1950 for the Burger equation, and Oleinik in 1956 for the general, stated that it is at most countable. In 1979, the present author published an example to show that the statement of Hopf and Oleinik is wrong. But after so long time, the wrong statement for countability still appeared in some publications, which is at least partly due to that some ones felt difficult to understand Hopf and Oleinik's proofs being wrong. So, pointing out where they went wrong becomes very necessary.
其他摘要	For the number of complete shock curves of a conservation law with one space variable,Hopf in 1950 for the Burger equation,and Oleinik in 1956 for the general,stated that it is at most countable.In 1979,the present author published an example to show that the statement of Hopf and Oleinik is wrong.But after so long time,the wrong statement for countability still appeared in some publications,which is at least partly due to that some ones felt difficult to understand Hopf and Oleinik’s proofs being wrong.So,pointing out where they went wrong becomes very necessary.
关键词	ORIGINAL POINTS REAL AXIS WAVES countability of shocks uncountability of shocks conservation law
收录类别	CSCD
语种	英语
资助项目	[National Basic Research Program of China] ; [National Natural Science Foundation of China]
CSCD记录号	CSCD:4537869
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/52583
专题	中国科学院数学与系统科学研究院
作者单位	中国科学院数学与系统科学研究院
推荐引用方式 GB/T 7714	Li BangHe. The reason of Hopf's and Oleinik's proofs for countability of shocks being wrong[J]. SCIENCE CHINA-MATHEMATICS,2012,55(4):727-729.
APA	Li BangHe.(2012).The reason of Hopf's and Oleinik's proofs for countability of shocks being wrong.SCIENCE CHINA-MATHEMATICS,55(4),727-729.
MLA	Li BangHe."The reason of Hopf's and Oleinik's proofs for countability of shocks being wrong".SCIENCE CHINA-MATHEMATICS 55.4(2012):727-729.