Almost all points on the real axis can be original points of shock waves

doi:10.1007/s11425-010-4139-8

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	Almost all points on the real axis can be original points of shock waves
	Li Bang-He
刊名	SCIENCE CHINA-MATHEMATICS
	2011
卷号	54 期号:1 页码:1-8
关键词	conservation law shock wave original points on real axis
ISSN号	1674-7283
DOI	10.1007/s11425-010-4139-8
英文摘要	For a conservation law with convex condition and initial data in L (a)(R), it had been commonly believed that the number of discontinuity lines (or shock waves) of the solution is at most countable since Theorem 1 in Oleinik's seminal paper published in 1956 asserted this fact. In 1977, the author gave an example to show that there is an initial data in C (a)(R) a (c) L (a)(R) such that the number of shock waves is uncountable. And in 1980, he gave an example to show that there is an initial data in C(R)a (c) L (a)(R) such that the measure of original points of shock waves on the real axis is positive. In this paper, he proves further that the set consisting of initial data in C(R) a (c) L (a)(R) with the property: almost all points on the real axis are original points of shock waves, is dense in C(R) a (c) L (a)(R). All these results show that Oleinik's assertion on the countability of discontinuity lines is wrong.
语种	英语
出版者	SCIENCE PRESS
WOS记录号	WOS:000286201100001
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/12006]
专题	系统科学研究所
通讯作者	Li Bang-He
作者单位	Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Li Bang-He. Almost all points on the real axis can be original points of shock waves[J]. SCIENCE CHINA-MATHEMATICS,2011,54(1):1-8.
APA	Li Bang-He.(2011).Almost all points on the real axis can be original points of shock waves.SCIENCE CHINA-MATHEMATICS,54(1),1-8.
MLA	Li Bang-He."Almost all points on the real axis can be original points of shock waves".SCIENCE CHINA-MATHEMATICS 54.1(2011):1-8.