ON REPRESENTATION FORMULA FOR SOLUTIONS OF HAMILTON‐JACOBI EQUATION FOR SOME TYPES OF INITIAL CONDITIONS

G. Gudynas
2001 Mathematical Modelling and Analysis  
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.
doi:10.3846/13926292.2001.9637163 fatcat:i52p6kdi25f7vaz4cgaslj2w6q