almostallpointsontherealaxiscanbeoriginalpointsofshockwaves

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	almostallpointsontherealaxiscanbeoriginalpointsofshockwaves
	Li Banghe
	2011
发表期刊	sciencechinamathematics
ISSN	1674-7283
卷号	54 期号:1 页码:1
摘要	For a conservation law with convex condition and initial data in L∞(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∞(R) ∩ L∞(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) ∩ L∞ (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) ∩ L∞(R) with the property: almost all points on the real axis are original points of shock waves, is dense in C(R) ∩ L∞(R). All these results show that Oleinik's assertion on the countability of discontinuity lines is wrong
语种	英语
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/36446
专题	系统科学研究所
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. almostallpointsontherealaxiscanbeoriginalpointsofshockwaves[J]. sciencechinamathematics,2011,54(1):1.
APA	Li Banghe.(2011).almostallpointsontherealaxiscanbeoriginalpointsofshockwaves.sciencechinamathematics,54(1),1.
MLA	Li Banghe."almostallpointsontherealaxiscanbeoriginalpointsofshockwaves".sciencechinamathematics 54.1(2011):1.