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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https://hal.archives-ouvertes.fr/hal-00503910
Contributor : Marie-Annick Guillemer <>
Submitted on : Tuesday, October 19, 2010 - 2:23:08 PM
Last modification on : Friday, January 4, 2019 - 5:32:29 PM
Long-term archiving on : Friday, December 2, 2016 - 12:52:08 AM

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  • HAL Id : hal-00503910, version 2

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Yves Achdou, Fabio Camilli, Alessandra Cutri, Nicoletta Tchou. Hamilton-Jacobi equations on networks. 2010. ⟨hal-00503910v2⟩

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