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

doi:10.1007/s11425-010-4139-8

CSpace > 系统科学研究所

	Almost all points on the real axis can be original points of shock waves
	Li Bang-He
	2011
发表期刊	SCIENCE CHINA-MATHEMATICS
ISSN	1674-7283
卷号	54 期号:1 页码:1-8
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.
关键词	conservation law shock wave original points on real axis
DOI	10.1007/s11425-010-4139-8
语种	英语
资助项目	National Natural Science Foundation of China[10771206]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000286201100001
出版者	SCIENCE PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/12007
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.