Representation Formula for Solutions of Eikonal Type Equations

Nonlinear Analysis

Gintautas Gudynas¹ 

[1] Klaipėda University, Lithuania;

关键词: Eikonal;    Hamilton – Jacobi;    semiconcave solution;   

DOI  :  10.15388/NA.2001.6.1.15225

来源: DOAJ

【 摘 要 】

Equations of an eikonal type ones arise in many areas of applications, including optics, fluid mechanics, material sciences, and control theory. This article investigates the representation formula for semiconcave solutions of the boundary problem for eikonal type equation. The formula is given by forming envelope of some fundamental solutions of the equation. Using these fundamental solutions we obtain the representation formula for solutions of Cauchy problem for appropriate Hamilton – Jacobi equation.

【 授权许可】

Unknown