Hamilton-Jacobi equations on networks

Yves Achdou; Fabio Camilli; Alessandra Cutri; Nicoletta Tchou

hal-00503910, version 2

Hamilton-Jacobi equations on networks

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

Résumé : 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.

1 : Laboratoire Jacques-Louis Lions (LJLL)
CNRS : UMR7598 – Université Pierre et Marie Curie [UPMC] - Paris VI
2 : Dipartimento di Metodi e Modelli Matematici per le Scienze Applicate (MeMoMat)
Universita di Roma "La Sapienza"
3 : Dipartimento di Matematica [Roma II] (DIPMAT)
Universita degli studi di Roma Tor Vergata
4 : Institut de Recherche Mathématique de Rennes (IRMAR)
CNRS : UMR6625 – Université de Rennes 1 – École normale supérieure de Cachan - ENS Cachan – Institut National des Sciences Appliquées (INSA) : - RENNES – Université de Rennes II - Haute Bretagne

hal-00503910, version 2
http://hal.archives-ouvertes.fr/hal-00503910
oai:hal.archives-ouvertes.fr:hal-00503910
Contributeur : Marie-Annick Guillemer <>
Soumis le : Mardi 19 Octobre 2010, 14:23:08
Dernière modification le : Mercredi 20 Octobre 2010, 10:11:48

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