Y. Achdou, F. Camilli, A. Cutr-`-cutr-`-i, and N. Tchou, Hamilton???Jacobi equations constrained on networks, ?Jacobi equations constrained on networks, pp.413-445, 2013.
DOI : 10.1007/BF01396221

URL : https://hal.archives-ouvertes.fr/hal-00656919

Y. Achdou, S. Oudet, and N. Tchou, Hamilton?Jacobi equations for optimal control on junctions and networks, ESAIM: Control, Optimisation and Calculus of Variations, vol.21, issue.3, pp.876-899, 2015.
DOI : 10.1051/cocv/2014054

URL : https://hal.archives-ouvertes.fr/hal-00847210

Y. Achdou and N. Tchou, Hamilton-Jacobi Equations on Networks as Limits of Singularly Perturbed Problems in Optimal Control: Dimension Reduction, Communications in Partial Differential Equations, vol.268, issue.4, pp.652-693, 2015.
DOI : 10.1016/j.jde.2011.08.036

URL : https://hal.archives-ouvertes.fr/hal-00961015

O. Alvarez, M. Bardi, and C. Marchi, Multiscale problems and homogenization for second-order Hamilton-Jacobi equations Multiscale singular perturbations and homogenization of optimal control problems, Geometric control and nonsmooth analysis, J. Differential Equations Adv. Math. Appl. Sci. World Sci. Publ, vol.243, issue.76, pp.349-387, 2007.

M. Bardi and I. Capuzzo-dolcetta, Optimal control and viscosity solutions of Hamilton-Jacobi- Bellman equations, Systems & Control: Foundations & Applications, With appendices by Maurizio Falcone and Pierpaolo Soravia, 1997.

G. Barles, A. Briani, E. Chasseigne, and C. Imbert, Flux-limited and classical viscosity solutions for regional control problems, ArXiv e-prints, 2016.

G. Barles, A. Briani, E. Chasseigne, and N. Tchou, Homogenization results for a deterministic multi-domains periodic control problem, Asymptotic Analysis, vol.9, issue.1, pp.3-4, 2015.
DOI : 10.4171/IFB/29

URL : https://hal.archives-ouvertes.fr/hal-01024602

I. Capuzzo-dolcetta and P. Lions, Hamilton-Jacobi equations with state constraints, Transactions of the American Mathematical Society, vol.318, issue.2, pp.318-643, 1990.
DOI : 10.1090/S0002-9947-1990-0951880-0

L. C. Evans, Synopsis, Proceedings of the Royal Society of Edinburgh: Section A Mathematics, vol.1248, issue.3-4, pp.3-4, 1989.
DOI : 10.1137/0326063

N. Forcadel and W. Salazar, A junction condition by specified homogenization of a discrete model with a local perturbation and application to traffic flow, working paper or preprint, 2016.

N. Forcadel and W. Salazar, Homogenization of a discrete model for a bifurcation and application to traffic flow, working paper or preprint, 2016.

N. Forcadel, W. Salazar, and M. Zaydan, Homogenization of second order discrete model with local perturbation and application to traffic flow, Discrete Contin, Dyn. Syst, vol.37, issue.3, pp.1437-1487, 2017.

G. Galise, C. Imbert, and R. Monneau, A junction condition by specified homogenization and application to traffic lights, Analysis & PDE, vol.8, issue.8, pp.1891-1929, 2015.
DOI : 10.2140/apde.2015.8.1891

URL : https://hal.archives-ouvertes.fr/hal-01010512

C. Imbert and R. Monneau, Quasi-convex Hamilton-Jacobi equations posed on junctions: the multidimensional case, 28 pages. Second version, 2016.

C. Imbert and R. Monneau, Flux-limited solutions for quasi-convex Hamilton-Jacobi equations on networks, Annales scientifiques de l'?cole normale sup?rieure, vol.50, issue.2, pp.357-448, 2017.
DOI : 10.24033/asens.2323

URL : https://hal.archives-ouvertes.fr/hal-00832545

C. Imbert, R. Monneau, H. Zidani, and . Hamilton, A Hamilton-Jacobi approach to junction problems and application to traffic flows, ESAIM: Control, Optimisation and Calculus of Variations, vol.19, issue.1, pp.129-166, 2013.
DOI : 10.1051/cocv/2012002

URL : https://hal.archives-ouvertes.fr/hal-00569010

P. Lions, G. Papanicolaou, and S. Varadhan, Homogenization of Hamilton-Jacobi equations, unpublished, 1988.

P. Lions and P. Souganidis, Viscosity solutions for junctions: well posedness and stability, Rendiconti Lincei - Matematica e Applicazioni, vol.27, issue.4, pp.535-545, 2016.
DOI : 10.4171/RLM/747

URL : http://arxiv.org/abs/1608.03682

P. Lions and P. Souganidis, Well posedness for multi-dimensional junction problems with Kirchofftype conditions, ArXiv e-prints, 2017.

S. Oudet, Hamilton-Jacobi equations for optimal control on multidimensional junctions, ArXiv eprints, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01093112

H. M. Soner, Optimal Control with State-Space Constraint I, SIAM Journal on Control and Optimization, vol.24, issue.3, pp.552-561, 1986.
DOI : 10.1137/0324032