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Preprint, Working Paper, ... |
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| Subject: |
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Mathematics/Optimization and Control
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| Title: |
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Hamilton-Jacobi equations on networks |
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| Author(s): |
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Yves Achdou ( ) 1, Fabio Camilli () 2, Alessandra Cutri 3, Nicoletta Tchou () 4 |
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| Laboratory: |
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| Research team: |
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Equations aux dérivées partielles |
| Abstract: |
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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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| Fulltext language: |
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English |
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| Keyword(s): |
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Optimal control – Graphs – Networks – Hamilton-Jacobi equations – Viscosity solutions |
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| Classification: |
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34H05, 49J15 |
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| Comment: |
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There is a more recent version of this preprint with the different title: Hamilton-Jacobi equation constrained on networks. The link for this version is hal-00656919, v1 |
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