Oleinik-Lax formulas and multitime Hamilton-Jacobi systems (Q1849012)

In this paper two results for Hamilton-Jacobi equations with semicontinuous solutions are presented. The first result gives a representation formula for the solutions of such equations based on the reachable set of a suitably defined auxiliary differential inclusion. The second result concerns systems of Hamilton-Jacobi equations on different time scales (multitime Hamilton-Jacobi equations). Here a representation formula of the solution by commuting semigroups is developed. Again, reachable sets of suitable differential inclusion play an important role, here as a tool in the proof of the result.