Open AccessON REPRESENTATION FORMULA FOR SOLUTIONS OF HAMILTON‐JACOBI EQUATION FOR SOME TYPES OF INITIAL CONDITIONS
Author(s) -
Gintautas Gudynas
Publication year - 2001
Publication title -
mathematical modelling and analysis/mathematical modeling and analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.491
H-Index - 25
eISSN - 1648-3510
pISSN - 1392-6292
DOI - 10.3846/13926292.2001.9637163
Subject(s) - mathematics , hamilton–jacobi equation , hamiltonian (control theory) , mathematical analysis , representation (politics) , regular polygon , initial value problem , pure mathematics , cauchy distribution , mathematical optimization , geometry , politics , political science , law
This article investigates the representation formula for the semiconcave solutions of the Cauchy problem for Hamilton‐Jacobi equation with the convex Hamiltonian and the unbounded lower semicontinous initial function. The formula like Hopf ‘s formula is given by forming envelope of some fundamental solutions of the equation.