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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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Type
Article accepté pour publication ou publié
External document link
http://hal.archives-ouvertes.fr/hal-00569010/fr/
Date
2013
Journal name
ESAIM. COCV
Volume
19
Number
1
Publisher
Cambridge University Press
Pages
129-166
Publication identifier
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Author(s)
Zidani, Hasnaa
Monneau, Régis
Imbert, Cyril cc
Abstract (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.
Subjects / Keywords
Junctions; Traffic problems; Optimal control; Viscosity solutions; Discontinuous Hamiltonians; Hamilton-Jacobi equations