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Flux-limited solutions for quasi-convex Hamilton-Jacobi equations on networks

Abstract : We study Hamilton-Jacobi equations on networks in the case where Hamiltonians are quasi-convex with respect to the gradient variable and can be discontinuous with respect to the space variable at vertices. First, we prove that imposing a general vertex condition is equivalent to imposing a specific one which only depends on Hamiltonians and an additional free parameter, the flux limiter. Second, a general method for proving comparison principles is introduced. This method consists in constructing a vertex test function to be used in the doubling variable approach. With such a theory and such a method in hand, we present various applications, among which a very general existence and uniqueness result for quasi-convex Hamilton-Jacobi equations on networks.
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https://hal.archives-ouvertes.fr/hal-00832545
Contributor : Cyril Imbert <>
Submitted on : Saturday, July 29, 2017 - 4:05:40 PM
Last modification on : Thursday, March 26, 2020 - 2:52:06 PM

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  • HAL Id : hal-00832545, version 6
  • ARXIV : 1306.2428

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Cyril Imbert, R Monneau. Flux-limited solutions for quasi-convex Hamilton-Jacobi equations on networks. Annales scientifiques de l'Ecole normale supérieure, 2017, 50 (2), pp.357 à 448. ⟨hal-00832545v6⟩

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