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Journal Articles Annales Scientifiques de l'École Normale Supérieure Year : 2017

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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Dates and versions

hal-00832545 , version 1 (10-06-2013)
hal-00832545 , version 2 (17-01-2014)
hal-00832545 , version 3 (24-06-2014)
hal-00832545 , version 4 (10-10-2014)
hal-00832545 , version 5 (10-02-2016)
hal-00832545 , version 6 (29-07-2017)

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Cite

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