Hamilton-Jacobi 方程特征线的性质 II

journal6 ›› 2010, Vol. 31 ›› Issue (5): 22-25.

Hamilton-Jacobi 方程特征线的性质 II

(华北电力大学数理系，北京102206)

出版日期:2010-09-25 发布日期:2012-04-12

Properties of the Charactristics of Hamilton-Jacobi Equations II

(Department of Mathematics and Physics,North China Electric Power University,Beijing 102206,China)

Online:2010-09-25 Published:2012-04-12
About author:ZHAO Yin-chuan (1977-),male,was born in Shaoxing City,Zhejiang Province,instructor of Department of Mathematics and Physics,North China Electric Power University;research area is nonlinear partial equation.
Supported by:
National Natural Foundation of China (10926067;70901025)

摘要/Abstract

摘要：研究了带凸Hamiltonian的高维Hamilton-Jacobi (HJ)方程特征线的性质.证明了所有的特征线分2类，其中一类永远不会碰到奇异点，另一类将在有限的时间内碰到奇异点.

关键词： Hamilton-Jacobi 方程, 特征线, 非退化（退化）最小值点, Hopf-Lax公式

Abstract: Properties of the characteristics of the Hamilton-Jacobi (HJ) equations of multi-dimensional space variables with convex Hamiltonians are studied.It is proved 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.

Key words: Hamilton-Jacobi equation, characteristics, non-degenerate (degenerate) minimizing point, Hopf-Lax formula

赵引川. Hamilton-Jacobi 方程特征线的性质 II[J]. journal6, 2010, 31(5): 22-25.

ZHAO Yin-Chuan. Properties of the Charactristics of Hamilton-Jacobi Equations II[J]. journal6, 2010, 31(5): 22-25.

[1]	杜慧. Hamilton-Jacobi方程解的定性分析[J]. 吉首大学学报（自然科学版）, 2017, 38(2): 4-5.
[2]	赵引川. Hamilton-Jacobi 方程特征线的性质 I[J]. journal6, 2010, 31(1): 13-15.