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A piecewise linear solution of the Cauchy problem for the Hamilton-Jacobi equation. (English. Russian original) Zbl 0799.35039
Russ. Acad. Sci., Dokl., Math. 46, No. 1, 144-148 (1993); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 325, No. 5, 932-936 (1992).
The Cauchy problem for the Hamilton-Jacobi equation is considered, with Hamiltonian independent of time and the space variable. It is also assumed that both the Hamiltonian and the boundary functions are piecewise linear and the phase space is two-dimensional, the solution is understood in the generalized (minimax and/or viscosity) sense. Under these assumptions a finite algorithm for exact construction of a solution is outlined. A complete description and justification of the algorithm are given elsewhere.

35F25 Initial value problems for nonlinear first-order PDEs
49L25 Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games