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.
Apie Hamiltono-Jakobo sprendinių išraiškas tam tikroms pradinėms sąlygoms
Santrauka. Nagrinėjami Kosi uždaviniai lygtims
su pradine sąlyga
Iškilių hamiltonianų atveju yra užduotos formules Koši uždavinių sprendiniams: pirmosios lygties atveju, kai ϕ(x) yra pusiau tolydi iš apačios ir
antrosios lygties atveju pradinė funkcija tolydi Lipšico prasme ir yra laužtė, trečiosios lygties atveju pradinė funkcija aprėžta ir dalimis pastovi.
Gudynas, G. (2001). On representation formula for solutions of Hamilton‐Jacobi equation for some types of initial conditions. Mathematical Modelling and Analysis, 6(2), 241-250. https://doi.org/10.3846/13926292.2001.9637163
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