Hamilton-Jacobi equations on networks

There is a more recent version of this preprint with the different title: Hamilton-Jacobi equation constrained on networks. The link for this version is hal-00656919, v1International audienceWe consider continuous-state and continuous-time control problem where the admissible trajectories of the system are constrained to remain on a network. Under suitable assumptions, we prove that the value function is continuous. We define a notion of viscosity solution of Hamilton-Jacobi equations on the network for which we prove a comparison principle. The value function is thus the unique viscosity solution of the Hamilton-Jacobi equation on the network