D. Amadori, P. Goatin, and M. D. Rosini, Existence results for Hughes'model for pedestrian flows, J. Math. Anal. Appl, vol.420, issue.1, pp.387-406, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00872851

C. Bardos, J. C. Nédélec, and A. Y. Le-roux, First order quasilinear equations with boundary conditions, Comm. Partial Differential Equations, vol.4, issue.9, pp.1017-1034, 1979.

P. Bénilan and S. N. Kru?kov, First-order quasilinear equations with continuous nonlinearities, Dokl. Akad. Nauk, vol.339, issue.2, pp.151-154, 1994.

P. Bénilan and S. N. Kru?kov, Conservation laws with continuous flux functions, NoDEA Nonlinear Differential Equations Appl, vol.3, issue.4, pp.395-419, 1996.

I. , C. Dolcetta, and B. Perthame, On some analogy between different approaches to first order PDE's with nonsmooth coefficients, Adv. Math. Sci. Appl, vol.6, issue.2, pp.689-703, 1996.

G. Chavent and J. Jaffre, Mathematical models and finite elements for reservoir simulation : single phase, multiphase and multicomponent flows through porous media, Oxford Lecture Series in Mathematics and its Applications. North Holland, vol.17, 1986.

G. M. Coclite, M. Garavello, and B. Piccoli, Traffic flow on a road network, SIAM J. Math. Anal, vol.36, issue.6, pp.1862-1886, 2005.

M. G. Crandall and P. L. Lions, Viscosity solutions of Hamilton-Jacobi equations, Trans. Amer. Math. Soc, vol.277, issue.1, pp.1-42, 1983.

C. M. Dafermos, Hyperbolic conservation laws in continuum physics, Grundlehren der Mathematischen Wissenschaften [Fund. Princ. of Math. Sc, vol.325

. Springer-verlag, , 2016.

R. J. Diperna and P. L. Lions, Ordinary differential equations, transport theory and Sobolev spaces, Invent. Math, vol.98, issue.3, pp.511-547, 1989.

F. Dubois and P. Lefloch, Boundary conditions for nonlinear hyperbolic systems of conservation laws, J. Differential Equations, vol.71, issue.1, pp.93-122, 1988.

N. El-khatib, P. Goatin, and M. D. Rosini, On entropy weak solutions of Hughes'model for pedestrian motion, Z. Angew. Math. Phys, vol.64, issue.2, pp.223-251, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00647798

L. C. Evans, Partial differential equations, Graduate Studies in Mathematics, vol.19, 2010.

E. Gagliardo, Caratterizzazioni delle tracce sulla frontiera relative ad alcune classi di funzioni in n variabili, Rend. Sem. Mat. Univ. Padova, vol.27, pp.284-305, 1957.

S. N. Kruzhkov, Generalized solutions of the Cauchy problem in the large for first order nonlinear equations, Dokl. Akad. Nauk. SSSR, vol.187, pp.29-32, 1969.

S. N. Kruzhkov, First order quasilinear equations with several independent variables. Mat. Sb, vol.81, pp.228-255, 1970.

T. Laforce, K. Jessen, and F. M. Orr, Four-component gas/water/oil displacements in one dimension. I. Structure of the conservation law, Transp. Porous Media, vol.71, issue.2, pp.199-216, 2008.

P. Lions, Du nouveau sur les lois de conservation scalaires? Seminar at College de France, 2016.

P. Lions and P. , Well-posedness for multi-dimensional junction problems with Kirchofftype conditions, Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl, vol.28, issue.4, pp.807-816, 2017.

P. Lions and P. Souganidis, Viscosity solutions for junctions: well posedness and stability, Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl, vol.27, issue.4, pp.535-545, 2016.

F. Otto, Initial-boundary value problem for a scalar conservation law, C. R. Acad. Sci. Paris Sér. I Math, vol.322, issue.8, pp.729-734, 1996.

I. Roulstone and J. Norbury, Invisible in the storm, The role of mathematics in understanding weather, 2013.

H. M. Soner, Optimal control with state-space constraint, I. SIAM J. Control Optim, vol.24, issue.3, pp.552-561, 1986.

H. M. Soner, Optimal control with state-space constraint, II. SIAM J. Control Optim, vol.24, issue.6, pp.1110-1122, 1986.

P. R. Sperb, Maximum principles and their applications, Mathematics in Science and Engineering, vol.157, 1981.

J. Vovelle, Convergence of finite volume monotone schemes for scalar conservation laws on bounded domains, Numer. Math, vol.90, issue.3, pp.563-596, 2002.

G. B. Whitham, Linear and nonlinear waves, Pure and Applied Mathematics, 1974.