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Abstract
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.
Nagrinejami Kosi uždaviniai lygtims su pradine salyga Iškiliu hamiltonianu atveju yra užduotos formules Koši uždaviniu sprendiniams: pirmosios lygties atveju, kai ϕ(x) yra pusiau tolydi iš apačios ir antrosios lygties atveju pradine funkcija tolydi Lipšico prasme ir yra laužte, trečiosios lygties atveju pradine funkcija aprežta ir dalimis pastovi.