Hamilton-Jacobi 方程特征线的性质 I

journal6 ›› 2010, Vol. 31 ›› Issue (1): 13-15.

Hamilton-Jacobi 方程特征线的性质 I

(华北电力大学数理系，北京102206)

出版日期:2010-01-25 发布日期:2012-04-19

Properties of the Charactristic of Hamilton-Jacobi Equations I

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

Online:2010-01-25 Published:2012-04-19
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：研究带凸Hamiltonian的高维Hamilton-Jacobi (HJ)方程特征线的性质.证明了HJ方程解的表达式中的极值曲线是特征线，对上半空间中任一点，都存在1条有效特征线段经过它.

关键词： Hamilton-Jacobi 方程, 特征线, Hopf-Lax公式

Abstract: This paper is concerned with the Hamilton-Jacobi (HJ) equations of multidimensional space variables with convex Hamiltonians.The author proves the extreme curve in the formula of the solution to the HJ equation is a characteristic and for each point in upper half-space,there exists a valid characteristic segment passing through it.

Key words: Hamilton-Jacobi equation, characteristic, Hopf-Lax formula

赵引川. Hamilton-Jacobi 方程特征线的性质 I[J]. journal6, 2010, 31(1): 13-15.

ZHAO Yin-Chuan. Properties of the Charactristic of Hamilton-Jacobi Equations I[J]. journal6, 2010, 31(1): 13-15.

[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 II[J]. journal6, 2010, 31(5): 22-25.