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.

Keywords: Hamilton-Jacobi equations, discontinuous hamiltonians, viscosity solutions, optimal control, traffic problems, junctions

@article{COCV_2013__19_1_129_0, author = {Imbert, Cyril and Monneau, R\'egis and Zidani, Hasnaa}, title = {A {Hamilton-Jacobi} approach to junction problems and application to traffic flows}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {129--166}, publisher = {EDP-Sciences}, volume = {19}, number = {1}, year = {2013}, doi = {10.1051/cocv/2012002}, mrnumber = {3023064}, zbl = {1262.35080}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/cocv/2012002/} }

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 SP - 129 EP - 166 VL - 19 IS - 1 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2012002/ DO - 10.1051/cocv/2012002 LA - en ID - COCV_2013__19_1_129_0 ER -

%0 Journal Article %A Imbert, Cyril %A Monneau, Régis %A Zidani, Hasnaa %T A Hamilton-Jacobi approach to junction problems and application to traffic flows %J ESAIM: Control, Optimisation and Calculus of Variations %D 2013 %P 129-166 %V 19 %N 1 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2012002/ %R 10.1051/cocv/2012002 %G en %F COCV_2013__19_1_129_0

Imbert, Cyril; Monneau, Régis; Zidani, Hasnaa. A Hamilton-Jacobi approach to junction problems and application to traffic flows. ESAIM: Control, Optimisation and Calculus of Variations, Volume 19 (2013) no. 1, pp. 129-166. doi : 10.1051/cocv/2012002. http://archive.numdam.org/articles/10.1051/cocv/2012002/

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