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A Hamilton-Jacobi approach to junction problems and application to traffic flows

Zidani, Hasnaa; Monneau, Régis; Imbert, Cyril (2013), A Hamilton-Jacobi approach to junction problems and application to traffic flows, ESAIM. COCV, 19, 1, p. 129-166. http://dx.doi.org/10.1051/cocv/2012002

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Article accepté pour publication ou publié
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http://hal.archives-ouvertes.fr/hal-00569010/fr/
Date
2013
Nom de la revue
ESAIM. COCV
Volume
19
Numéro
1
Éditeur
Cambridge University Press
Pages
129-166
Identifiant publication
Métadonnées
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Auteur(s)
Zidani, Hasnaa
Monneau, Régis
Imbert, Cyril cc
Résumé (EN)
This paper is concerned with the study of a model case of first order Hamilton-Jacobi equations posed on a ``junction'', that is to say the union of a finite number of half-lines with a unique common point. The main results are a comparison principle, existence and stability of solutions. The two challenging difficulties are the singular geometry of the domain and the discontinuity of the Hamiltonian. As far as discontinuous Hamiltonians are concerned, these results seem to be new. They are applied to the study of some models arising in traffic flows. The techniques developed in the present article provide powerful new tools in the analysis of such traffic flow problems.
Mots-clés
Junctions; Traffic problems; Optimal control; Viscosity solutions; Discontinuous Hamiltonians; Hamilton-Jacobi equations