Hamilton-Jacobi equations on networks

Abstract : 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.
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Submitted on : Monday, February 14, 2011 - 9:36:44 AM
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Yves Achdou, Fabio Camilli, Alessandra Cutri, Nicoletta Tchou. Hamilton-Jacobi equations on networks. IFAC Proceedings Volumes, Elsevier, 2011, 44 (1), pp.2577-2582. ⟨10.3182/20110828-6IT-1002.01084⟩. ⟨hal-00503910v4⟩

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