On the piecewise smoothness of entropy solutions to scalar conservation laws for a larger class of initial data
文献类型：期刊论文
| 作者 | Tang, Tao; Wang, Jinghua; Zhao, Yinchuan |
| 刊名 | JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS
 |
| 出版日期 | 2007-09-01 |
| 卷号 | 4期号:3页码:369-389 |
| 关键词 | piecewise smooth solutions conservation laws a set of first category |
| ISSN号 | 0219-8916 |
| 英文摘要 | We prove that if the initial data do not belong to a certain subset of C-k, then the solutions of scalar conservation laws are piecewise C-k smooth. In particular, our initial data allow centered compression waves, which was the case not covered by Dafermos (1974) and Schaeffer (1973). More precisely, we are concerned with the structure of the solutions in some neighborhood of the point at which only a Ck+1 shock is generated. It is also shown that there are finitely many shocks for smooth initial data (in the Schwartz space) except for a certain subset of S(R) of the first category. It should be pointed out that this subset is smaller than those used in previous works. We point out that Thom's theory of catastrophes, which plays a key role in Schaeffer (1973), cannot be used to analyze the larger class of initial data considered in this paper. |
| WOS研究方向 | Mathematics ; Physics |
| 语种 | 英语 |
| WOS记录号 | WOS:000251175900001 |
| 出版者 | WORLD SCIENTIFIC PUBL CO PTE LTD |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/3968]  |
| 专题 | 中国科学院数学与系统科学研究院 |
| 通讯作者 | Tang, Tao |
| 作者单位 | 1.Hong Kong Baptist Univ, Dept Math, Kowloon, Peoples R China 2.Chinese Acad Sci, Inst Computat Math, Beijing, Peoples R China 3.Chinese Acad Sci, Acad Math & Syst Sci, Inst Syst Sci, Beijing 100080, Peoples R China |
| 推荐引用方式 GB/T 7714 | Tang, Tao,Wang, Jinghua,Zhao, Yinchuan. On the piecewise smoothness of entropy solutions to scalar conservation laws for a larger class of initial data[J]. JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS,2007,4(3):369-389. |
| APA | Tang, Tao,Wang, Jinghua,&Zhao, Yinchuan.(2007).On the piecewise smoothness of entropy solutions to scalar conservation laws for a larger class of initial data.JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS,4(3),369-389. |
| MLA | Tang, Tao,et al."On the piecewise smoothness of entropy solutions to scalar conservation laws for a larger class of initial data".JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS 4.3(2007):369-389. |
入库方式： OAI收割
来源：数学与系统科学研究院
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