THE LARGE TIME GENERIC FORM OF THE SOLUTION TO HAMILTON-JACOBI EQUATIONS

doi:10.1016/S0252-9602(11)60398-6

数学物理学报(英文版) ›› 2011, Vol. 31 ›› Issue (6): 2265-2277.doi: 10.1016/S0252-9602(11)60398-6

THE LARGE TIME GENERIC FORM OF THE SOLUTION TO HAMILTON-JACOBI EQUATIONS

王靖华¹, 温海瑞²,赵引川³

1.Academy of Mathematics and System Sciences, The Chinese Academy of Sciences, Beijing 100190, China；2.Department of Mathematics, Beijing Institute of Technology, Beijing 100081, China；3.Department of Mathematics and Physics, North China Electric Power University, Beijing 102206, China

收稿日期:2011-09-20 出版日期:2011-11-20 发布日期:2011-11-20
通讯作者: 温海瑞,wenhr@bit.edu.cn E-mail:jwang@amss.ac.cn；wenhr@bit.edu.cn；zyc747250@hotmail.com
基金资助:
This research was supported by National Natural Science Foundation of China (10871133, 11071246 and 11101143), Fundamental Research Funds of the Central Universities (09QL48). †Corresponding author: Wen Hairui.

THE LARGE TIME GENERIC FORM OF THE SOLUTION TO HAMILTON-JACOBI EQUATIONS

Wang Jinghua¹, Wen Hairui², Zhao Yinchuan³

1.Academy of Mathematics and System Sciences, The Chinese Academy of Sciences, Beijing 100190, China；2.Department of Mathematics, Beijing Institute of Technology, Beijing 100081, China；3.Department of Mathematics and Physics, North China Electric Power University, Beijing 102206, China

Received:2011-09-20 Online:2011-11-20 Published:2011-11-20
Contact: Wen Hairui,wenhr@bit.edu.cn E-mail:jwang@amss.ac.cn；wenhr@bit.edu.cn；zyc747250@hotmail.com
Supported by:
This research was supported by National Natural Science Foundation of China (10871133, 11071246 and 11101143), Fundamental Research Funds of the Central Universities (09QL48). †Corresponding author: Wen Hairui.

摘要/Abstract

摘要：

We use Hopf-Lax formula to study local regularity of solution to Hamilton-Jacobi (HJ) equations of multi-dimensional space variables with convex Hamiltonian. Then we give the large time generic form of the solution to HJ equation, i.e. for most initial data there exists a constant T > 0, which depends only on the Hamiltonian and initial datum, for t > T the solution of the IVP (1.1) is smooth except for a smooth n-dimensional hypersurface, across which Du(x, t) is discontinuous. And we show that the hypersurface tends asymptotically to a given hypersurface with rate t^−1/4 .

关键词: Hopf-Lax formula, Hamilton-Jacobi equations, local regularity, large time generic form

Abstract:

Key words: Hopf-Lax formula, Hamilton-Jacobi equations, local regularity, large time generic form

中图分类号:

49L25

王靖华, 温海瑞, 赵引川. THE LARGE TIME GENERIC FORM OF THE SOLUTION TO HAMILTON-JACOBI EQUATIONS[J]. 数学物理学报(英文版), 2011, 31(6): 2265-2277.

Wang Jinghua, Wen Hairui, Zhao Yinchuan. THE LARGE TIME GENERIC FORM OF THE SOLUTION TO HAMILTON-JACOBI EQUATIONS[J]. Acta mathematica scientia,Series B, 2011, 31(6): 2265-2277.

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THE LARGE TIME GENERIC FORM OF THE SOLUTION TO HAMILTON-JACOBI EQUATIONS

THE LARGE TIME GENERIC FORM OF THE SOLUTION TO HAMILTON-JACOBI EQUATIONS

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