A Hamilton-Jacobi approach to junction problems and application to traffic flows - Centre de mathématiques appliquées (CMAP) Accéder directement au contenu
Article Dans Une Revue ESAIM: Control, Optimisation and Calculus of Variations Année : 2013

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

Résumé

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 result is a comparison principle. We also prove 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 new powerful tools for the analysis of such problems.
Fichier principal
Vignette du fichier
jonction-hal3.pdf (529.45 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-00569010 , version 1 (24-02-2011)
hal-00569010 , version 2 (16-07-2011)
hal-00569010 , version 3 (28-11-2011)

Identifiants

Citer

Cyril Imbert, Régis Monneau, Hasnaa Zidani. A Hamilton-Jacobi approach to junction problems and application to traffic flows. ESAIM: Control, Optimisation and Calculus of Variations, 2013, 19 (01), pp 129-166. ⟨10.1051/cocv/2012002⟩. ⟨hal-00569010v3⟩
629 Consultations
444 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More