Eikonal型方程粘性解的表达式  

A Note on Representation Formula for Solutions of Eikonal Type Equations

作　　者：郭云霞[1] 温海瑞[2] 

机构地区：[1]中国人民解放军空军工程大学理学院,西安710065 [2]北京理工大学数学系,北京100081

出　　处：《应用泛函分析学报》2014年第2期146-149,共4页Acta Analysis Functionalis Applicata

基　　金：国家自然科学基金(11272050)

摘　　要：对于圆锥型和棱锥型Hamiltonian的Eikonal型方程,本文给出了一种几何方法,得出其初值问题解的表达式并且说明由此式给出的解为原初值问题的粘性解.首先用一个凸函数序列逼近Eikonal型方程中的Hamiltonian,再由Hopf-Lax公式给出方程序列的粘性解,最后证明了该粘性解序列会收敛到Eikonal方程的粘性解.In this paper, a geometric method of representation formula to viscosity solution of Eikonal type equations with cone and pyramid Hamiltonians in gradient variables is derived. Using a sequence of convex functions to approximate particular Hamiltonian in Eikonal type equations, then with the help of Hopf-Lax formula, the viscosity solution of the Hamilton-Jacobi equation which approximating the Eikonal type equation is deduced, and show that these viscosity solutions form a sequence which will converge to that of Eikonal type equations.

关 键 词：HAMILTON-JACOBI方程 Eikonal型方程 Hopf-Lax公式 

分 类 号：O175.2[理学—数学]