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| HAL: hal-00503910, version 1 |
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| Available versions: | v1 (2010-07-19) | v2 (2010-10-20) | v3 (2010-11-02) | v4 (2011-02-14) |
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| Hamilton-Jacobi equations on networks |
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| Yves Achdou 1Fabio Camilli 2 |
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| (2010-07-19) |
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| 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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| 1: | Laboratoire Jacques-Louis Lions (LJLL) |
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CNRS : UMR7598 – Université Pierre et Marie Curie (UPMC) - Paris VI |
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| 2: | Dipartimento di Metodi e Modelli Matematici per le Scienze Applicate (MeMoMat) |
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Universita di Roma "La Sapienza" |
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| 3: | Dipartimento di Matematica [Roma II] (DIPMAT) |
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Universita degli studi di Roma Tor Vergata |
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| 4: | Institut de Recherche Mathématique de Rennes (IRMAR) |
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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 |
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| Subject | : | Mathematics/Optimization and Control |
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| Optimal control – Graphs – Networks – Hamilton-Jacobi equations – Viscosity solutions |
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| hal-00503910, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00503910 | |
| oai:hal.archives-ouvertes.fr:hal-00503910 | |
| From: Marie-Annick Guillemer | |
| Submitted on: Monday, 19 July 2010 12:01:06 | |
| Updated on: Monday, 19 July 2010 13:06:52 | |
