Hamilton-Jacobi equations on networks

Yves Achdou (1) , Fabio Camilli (2) , Alessandra Cutri (3) , Nicoletta Tchou (4)

1 LJLL - Laboratoire Jacques-Louis Lions
2 MeMoMat - Dipartimento di Metodi e Modelli Matematici per le Scienze Applicate
3 DIPMAT - Dipartimento di Matematica [Roma II]
4 IRMAR - Institut de Recherche Mathématique de Rennes

We 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.

Mots clés: Optimal control; Graphs; Networks; Hamilton-Jacobi equations; Viscosity solutions

Domaines: Optimisation et contrôle [math.OC]

Yves Achdou, Fabio Camilli, Alessandra Cutri, Nicoletta Tchou. Hamilton-Jacobi equations on networks. 2010. ⟨hal-00503910v3⟩