REGULARITY AND GLOBAL STRUCTURE OF SOLUTIONS TO HAMILTON-JACOBI EQUATIONS II. CONVEX INITIAL DATA

doi:10.1142/S0219891609001976

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	REGULARITY AND GLOBAL STRUCTURE OF SOLUTIONS TO HAMILTON-JACOBI EQUATIONS II. CONVEX INITIAL DATA
	Zhao, Yinchuan 1,2; Tang, Tao 3,4; Wang, Jinghua 5
	2009-12-01
发表期刊	JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS
ISSN	0219-8916
卷号	6 期号:4 页码:709-723
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.
关键词	Hamilton-Jacobi equations Hopf's formula (II) global structure singularity point
DOI	10.1142/S0219891609001976
语种	英语
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
WOS类目	Mathematics, Applied ; Physics, Mathematical
WOS记录号	WOS:000273712400002
出版者	WORLD SCIENTIFIC PUBL CO PTE LTD
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/7930
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.