The one-dimensional Hughes model for pedestrian flow: Riemann???type solutions, Acta Mathematica Scientia, vol.32, issue.1, pp.259-280, 2012. ,
DOI : 10.1016/S0252-9602(12)60016-2
First order quasilinear equations with boundary conditions, Communications in Partial Differential Equations, vol.2, issue.33, pp.1017-1034, 1979. ,
DOI : 10.1090/S0025-5718-1977-0478651-3
Hyperbolic systems of conservation laws, of Oxford Lecture Series in Mathematics and its Applications, 2000. ,
DOI : 10.5209/rev_REMA.1999.v12.n1.17204
On the Hughes' model for pedestrian flow: The one-dimensional case, Journal of Differential Equations, vol.250, issue.3, pp.1334-1362, 2011. ,
DOI : 10.1016/j.jde.2010.10.015
On entropy weak solutions of Hughes??? model for pedestrian motion, Zeitschrift f??r angewandte Mathematik und Physik, vol.160, issue.3, 2012. ,
DOI : 10.1007/s00033-012-0232-x
URL : https://hal.archives-ouvertes.fr/hal-00647798
A difference method for numerical calculation of discontinuous solutions of the equations of hydrodynamics, Mat. Sb, issue.89, pp.47-271, 1959. ,
Front tracking for hyperbolic conservation laws, of Applied Mathematical Sciences, 2002. ,
Revisiting Hughes' dynamic continuum model for pedestrian flow and the developement of an efficient solution algorithm, Transpn. Res.?B, pp.43-127, 2009. ,
A continuum theory for the flow of pedestrians The flow of human crowds, in Annual review of fluid mechanics, Transpn. Res.?B Annu. Rev. Fluid Mech., Annual Reviews, vol.3610, issue.35, pp.507-535, 2002. ,
A reactive dynamic continuum user equilibrium model for bidirectional pedestrian flows, Acta Math. Sci. Ser. B Engl. Ed, pp.29-1541, 2009. ,
Convergence of the Lax-Friedrichs scheme and stability for conservation laws with a discontinous space-time dependent flux, Chinese Ann, Math. Ser. B, vol.25, pp.287-318, 2004. ,
The calculation of the interaction of non-stationary shock waves with barriers, Z. Vy?isl. Mat. i Mat. Fiz, vol.1, pp.267-279, 1961. ,
Convergence of a Difference Scheme for Conservation Laws with a Discontinuous Flux, SIAM Journal on Numerical Analysis, vol.38, issue.2, pp.681-698, 2000. ,
DOI : 10.1137/S0036142999363668
A fast sweeping method for Eikonal equations, Mathematics of Computation, vol.74, issue.250, pp.603-627, 2005. ,
DOI : 10.1090/S0025-5718-04-01678-3