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

• Volume: 19, Issue: 1, page 129-166
• ISSN: 1292-8119

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## Abstract

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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.

## How to cite

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Imbert, Cyril, Monneau, Régis, and Zidani, Hasnaa. "A Hamilton-Jacobi approach to junction problems and application to traffic flows." ESAIM: Control, Optimisation and Calculus of Variations 19.1 (2013): 129-166. <http://eudml.org/doc/272814>.

@article{Imbert2013,
abstract = {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.},
author = {Imbert, Cyril, Monneau, Régis, Zidani, Hasnaa},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Hamilton-Jacobi equations; discontinuous hamiltonians; viscosity solutions; optimal control; traffic problems; junctions; discontinuous Hamiltonians},
language = {eng},
number = {1},
pages = {129-166},
publisher = {EDP-Sciences},
title = {A Hamilton-Jacobi approach to junction problems and application to traffic flows},
url = {http://eudml.org/doc/272814},
volume = {19},
year = {2013},
}

TY - JOUR
AU - Imbert, Cyril
AU - Monneau, Régis
AU - Zidani, Hasnaa
TI - A Hamilton-Jacobi approach to junction problems and application to traffic flows
JO - ESAIM: Control, Optimisation and Calculus of Variations
PY - 2013
PB - EDP-Sciences
VL - 19
IS - 1
SP - 129
EP - 166
AB - 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.
LA - eng
KW - Hamilton-Jacobi equations; discontinuous hamiltonians; viscosity solutions; optimal control; traffic problems; junctions; discontinuous Hamiltonians
UR - http://eudml.org/doc/272814
ER -

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