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

By C. Imbert, Régis Monneau, Hasnaa Zidani. 2011

131 citations recorded by the source corpus.

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.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/6d67dd8231c9268d8fc28fb715e1689ce08ac110

How researchers see this paper

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In Computational Theory and Mathematics

1. Régis Monneau
2. C. Imbert
3. Luis Silvestre
4. Russell W. Schwab
5. Enrico Valdinoci
6. Adina Ciomaga
7. Panagiotis E. Souganidis
8. Xavier Ros-Oton

In Control and Systems Engineering

1. Régis Monneau
2. C. Imbert
3. Panagiotis E. Souganidis
4. Pierre-Louis Lions

In Statistical and Nonlinear Physics

1. Régis Monneau
2. C. Imbert

Citations in the corpus

• Flux-limited solutions for quasi-convex Hamilton-Jacobi equations on networks (2013, methodology): “In [19], the comparison principle was a consequence of a super-optimality principle (in the spirit of [24] or [30, 31]) and the comparison of sub-solutions with the value function of the optimal control problem.”