Regularity and global structure of solutions to Hamilton-Jacobi equations I. Convex Hamiltonians
文献类型：期刊论文
| 作者 | Zhao, Yinchuan1,2; Tang, Tao3,4; Wang, Jinghua5 |
| 刊名 | JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS
 |
| 出版日期 | 2008-09-01 |
| 卷号 | 5期号:3页码:663-680 |
| 关键词 | Hamilton-Jacobi equations Hopf's formula (I) global structure singularity point |
| ISSN号 | 0219-8916 |
| 英文摘要 | This paper is concerned with the Hamilton-Jacobi (HJ) equations of multidimensional space variables with convex Hamiltonians. Using Hopf's formula (I), we will study the differentiability of the HJ solutions. For any given point, we give a sufficient and necessary condition under which the solutions are C-k smooth in some neighborhood of the point. We also study the characteristics of the HJ equations. It is shown that there are only two kinds of characteristics, one never touches the singularity point, and the other touches the singularity point in a finite time. The sufficient and necessary condition under which the characteristic never touches the singularity point is given. Based on these results, we study the global structure of the set of singularity points for the HJ solutions. It is shown that there exists a one-to-one correspondence between the path connected components of the set of singularity points and the path connected components of a set on which the initial function does not attain its minimum. A path connected component of the set of singularity points never terminates at a finite time. Our results are independent of the particular forms of the equations as long as the Hamiltonians are convex. |
| WOS研究方向 | Mathematics ; Physics |
| 语种 | 英语 |
| WOS记录号 | WOS:000259233300008 |
| 出版者 | WORLD SCIENTIFIC PUBL CO PTE LTD |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/6801]  |
| 专题 | 中国科学院数学与系统科学研究院 |
| 通讯作者 | Zhao, Yinchuan |
| 作者单位 | 1.Peking Univ, LMAM, Beijing 100871, Peoples R China 2.Peking Univ, Sch Math Sci, Beijing 100871, Peoples R China 3.Hong Kong Baptist Univ, Dept Math, Kowloon Tong, Hong Kong, Peoples R China 4.Chinese Acad Sci, Inst Computat Math, Beijing, Peoples R China 5.Chinese Acad Sci, Inst Syst Sci, Acad Math & Syst Sci, Beijing 100080, Peoples R China |
| 推荐引用方式 GB/T 7714 | Zhao, Yinchuan,Tang, Tao,Wang, Jinghua. Regularity and global structure of solutions to Hamilton-Jacobi equations I. Convex Hamiltonians[J]. JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS,2008,5(3):663-680. |
| APA | Zhao, Yinchuan,Tang, Tao,&Wang, Jinghua.(2008).Regularity and global structure of solutions to Hamilton-Jacobi equations I. Convex Hamiltonians.JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS,5(3),663-680. |
| MLA | Zhao, Yinchuan,et al."Regularity and global structure of solutions to Hamilton-Jacobi equations I. Convex Hamiltonians".JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS 5.3(2008):663-680. |
入库方式： OAI收割
来源：数学与系统科学研究院
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