REGULARITY AND GLOBAL STRUCTURE OF SOLUTIONS TO HAMILTON-JACOBI EQUATIONS II. CONVEX INITIAL DATA
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 | 2009-12-01 |
| 卷号 | 6期号:4页码:709-723 |
| 关键词 | Hamilton-Jacobi equations Hopf's formula (II) global structure singularity point |
| ISSN号 | 0219-8916 |
| DOI | 10.1142/S0219891609001976 |
| 英文摘要 | The paper is concerned with the Hamilton-Jacobi (HJ) equations of multidimensional space variables with convex initial data and general Hamiltonians. Using Hopf's formula (II), we will study the differentiability of the HJ solutions. For any given point, we give a sufficient and necessary condition such that the solutions are C(k) smooth in some neighborhood of this point. We also study the characteristics of the equations which play important roles in our analysis. It is shown that there are only two kinds of characteristics, one never touches the singularity point, but the other one touches the singularity point in a finite time. Based on these results, we study the global structure of the set of singularity points for the solutions. It is shown that there exists a one-to-one correspondence between the path connected components of the set of singularity points and path connected component of the set {(Dg(y), H(Dg(y)))vertical bar y is an element of R(n)}\{(Dg(y), conv H (Dg(y)))vertical bar y is an element of R(n)}, where conv H is the convex hull of H. A path connected component of the set of singularity points never terminates as t increases. Moreover, our results depend only on H and its domain of definition. |
| 资助项目 | China Postdoctoral Science Foundation[148028] ; National Natural Foundation of China[70901025] ; National Natural Foundation of China[10671116] ; National Natural Foundation of China[10871133] ; CERG Grants of Hong Kong Research Grant Council ; FRG grants of Hong Kong Baptist University ; International Research Team of Complex Systems of Chinese Academy of Sciences |
| WOS研究方向 | Mathematics ; Physics |
| 语种 | 英语 |
| WOS记录号 | WOS:000273712400002 |
| 出版者 | WORLD SCIENTIFIC PUBL CO PTE LTD |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/7929]  |
| 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, Acad Math & Syst Sci, Inst 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 II. CONVEX INITIAL DATA[J]. JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS,2009,6(4):709-723. |
| APA | Zhao, Yinchuan,Tang, Tao,&Wang, Jinghua.(2009).REGULARITY AND GLOBAL STRUCTURE OF SOLUTIONS TO HAMILTON-JACOBI EQUATIONS II. CONVEX INITIAL DATA.JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS,6(4),709-723. |
| MLA | Zhao, Yinchuan,et al."REGULARITY AND GLOBAL STRUCTURE OF SOLUTIONS TO HAMILTON-JACOBI EQUATIONS II. CONVEX INITIAL DATA".JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS 6.4(2009):709-723. |
入库方式： OAI收割
来源：数学与系统科学研究院
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