Almost all points on the real axis can be original points of shock waves
文献类型：期刊论文
| 作者 | Li Bang-He
|
| 刊名 | SCIENCE CHINA-MATHEMATICS
 |
| 出版日期 | 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 |
| WOS记录号 | WOS:000286201100001 |
| 出版者 | SCIENCE PRESS |
| 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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