A Hamilton-Jacobi approach to junction problems and application to traffic flows
ESAIM: Control, Optimisation and Calculus of Variations, Tome 19 (2013) no. 1, pp. 129-166.

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.

DOI : https://doi.org/10.1051/cocv/2012002
Classification : 35F21,  35D40,  35Q93,  35R05,  35B51
Mots clés : Hamilton-Jacobi equations, discontinuous hamiltonians, viscosity solutions, optimal control, traffic problems, junctions
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author = {Imbert, Cyril and Monneau, R\'egis and Zidani, Hasnaa},
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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, Tome 19 (2013) no. 1, pp. 129-166. doi : 10.1051/cocv/2012002. http://www.numdam.org/articles/10.1051/cocv/2012002/

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