Minimal time problem for crowd models with localized vector fields

Abstract : In this work, we study a minimal time problem for a Partial Differential Equation of transport type, that arises in crowd models. The control is a Lipschitz vector field localized on a fixed control set ω. We provide a complete answer for the minimal time problem. After considering the discrete case, we show that the minimal time to steer one initial configuration to another is related to the condition of having enough mass in ω to feed the desired final configuration. We also give a numerical method to compute the minimal time and to build the corresponding control. These results are illustrated by some numerical simulations.
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https://hal.archives-ouvertes.fr/hal-01493143
Contributeur : Michel Duprez <>
Soumis le : lundi 13 novembre 2017 - 15:49:19
Dernière modification le : samedi 18 novembre 2017 - 01:07:09

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  • HAL Id : hal-01493143, version 4
  • ARXIV : 1703.08049

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Michel Duprez, Morgan Morancey, Francesco Rossi. Minimal time problem for crowd models with localized vector fields. 2017. 〈hal-01493143v4〉

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