Optimal entropy solutions for conservation laws with discontinuous flux-functions, J. Hyperbolic Differ. Equ, vol.2, issue.04, p.118, 2005. ,
Nonlocal systems of conservation laws in several space dimensions, SIAM J. Numer. Anal, vol.53, issue.2, pp.963-983, 2015. ,
URL : https://hal.archives-ouvertes.fr/hal-01016784
An integro-differential conservation law arising in a model of granular flow, J. Hyperbolic Differ. Equ, vol.9, issue.1, pp.105-131, 2012. ,
On a nonlocal hyperbolic conservation law arising from a gradient constraint problem, Bull. Braz. Math. Soc. (N.S.), vol.43, issue.4, pp.599-614, 2012. ,
On the numerical integration of scalar nonlocal conservation laws, ESAIM, vol.2, issue.1, pp.19-37, 2015. ,
A theory of L 1 ?dissipative solvers for scalar conservation laws with discontinuous flux, Arch. Ration. Mech. Anal, vol.201, issue.1, p.118, 2011. ,
URL : https://hal.archives-ouvertes.fr/hal-00475840
Resurrection of "second order" models of traffic flow, SIAM J. Appl. Math, vol.60, issue.3, pp.916-938, 2000. ,
An n-populations model for traffic flow, European J. Appl. Math, vol.14, issue.5, pp.587-612, 2003. ,
Regularity results for the solutions of a non-local model of traffic flow. Discrete and Continuous Dynamical Systems A, vol.39, p.3197, 1078. ,
On nonlocal conservation laws modelling sedimentation, Nonlinearity, vol.24, issue.3, pp.855-885, 2011. ,
Well-posedness of a conservation law with non-local flux arising in traffic flow modeling, Numer. Math, vol.132, issue.2, pp.217-241, 2016. ,
URL : https://hal.archives-ouvertes.fr/hal-00954527
Anti-dissipative schemes for advection and application to Hamilton-Jacobi-Bellmann equations, J. Sci. Comput, vol.30, issue.1, p.80, 2007. ,
URL : https://hal.archives-ouvertes.fr/hal-00878221
Kru?kov's estimates for scalar conservation laws revisited, Trans. Amer. Math. Soc, vol.350, issue.7, p.37, 1998. ,
Improved accuracy of high-order weno finite volume methods on cartesian grids, J. Sci. Comput, vol.61, issue.2, p.99, 2014. ,
Antidiffusive and random-sampling lagrangianremap schemes for the multiclass Lighthill-Whitham-Richards traffic model, SIAM J. Sci. Comput, vol.35, issue.6, pp.1341-1368, 2013. ,
Antidiffusive Lagrangian-remap schemes for models of polydisperse sedimentation, Numer. Methods Partial Differential Equations, vol.32, issue.4, p.121, 2016. ,
A family of numerical schemes for kinematic flows with discontinuous flux, J. Engrg. Math, vol.60, issue.3-4, pp.387-425, 2008. ,
An Engquist-Osher-type scheme for conservation laws with discontinuous flux adapted to flux connections, SIAM J. Numer. Anal, vol.47, issue.3, p.118, 2009. ,
High-order numerical schemes for onedimensional nonlocal conservation laws, SIAM J. Sci. Comput, vol.40, issue.1, pp.288-305, 2018. ,
A non-local traffic flow model for 1-to-1 junctions, European J. Appl. Math, p.103, 2019. ,
URL : https://hal.archives-ouvertes.fr/hal-02142345
Global entropy weak solutions for general non-local traffic flow models with anisotropic kernel, vol.52, pp.163-180, 2018. ,
URL : https://hal.archives-ouvertes.fr/hal-01567575
Non-local multi-class traffic flow models, Netw. Heterog. Media, vol.14, issue.2, pp.371-387, 2019. ,
URL : https://hal.archives-ouvertes.fr/hal-01853260
Stability estimates for non-local scalar conservation laws, Nonlinear Anal. Real World Appl, vol.45, pp.668-687, 2019. ,
URL : https://hal.archives-ouvertes.fr/hal-01685806
High-order Finite Volume WENO schemes for non-local multi-class traffic flow models, Proc. XVII International Conference on Hyperbolic Problems Theory, Numerics, Applications, p.79, 2019. ,
URL : https://hal.archives-ouvertes.fr/hal-01979543
Lagrangian-antidiffusive remap schemes for non-local multi-class traffic flow models, Comput. Appl. Math, p.79, 2020. ,
URL : https://hal.archives-ouvertes.fr/hal-01952378
Recent results on the singular local limit for nonlocal conservation laws, vol.117, 2019. ,
On the singular local limit for conservation laws with nonlocal fluxes, 2017. ,
A class of nonlocal models for pedestrian traffic, Math. Models Methods Appl. Sci, vol.22, issue.04, p.1150023, 2012. ,
URL : https://hal.archives-ouvertes.fr/hal-00586008
On the modelling and management of traffic, ESAIM Math. Model. Numer. Anal, vol.45, issue.5, p.48, 2011. ,
Minimising stop and go waves to optimise traffic flow, Appl. Math. Lett, vol.17, issue.6, p.67, 2004. ,
Control of the continuity equation with a non local flow, ESAIM Control Optim. Calc. Var, vol.17, issue.2, pp.353-379, 2011. ,
URL : https://hal.archives-ouvertes.fr/hal-00361393
Nonlocal crowd dynamics models for several populations, Acta Math. Sci. Ser. B Engl. Ed, vol.32, issue.1, pp.177-196, 2012. ,
URL : https://hal.archives-ouvertes.fr/hal-00632755
Nonlocal systems of balance laws in several space dimensions with applications to laser technology, J. Differential Equations, vol.259, issue.11, pp.6749-6773, 2015. ,
Stability and total variation estimates on general scalar balance laws, Commun. Math. Sci, vol.7, issue.1, pp.37-65, 2009. ,
URL : https://hal.archives-ouvertes.fr/hal-00330543
Hyperbolic predators vs. parabolic prey, Commun. Math. Sci, vol.13, issue.2, pp.369-400, 2015. ,
Rigorous estimates on balance laws in bounded domains, Acta Math. Sci. Ser. B Engl. Ed, vol.35, issue.4, p.37, 2015. ,
IBVPs for scalar conservation laws with time discontinuous fluxes, Math. Methods Appl. Sci, vol.41, issue.4, pp.1463-1479, 2018. ,
Nonlocal conservation laws in bounded domains, SIAM J. Math. Anal, vol.50, issue.4, pp.4041-4065, 2018. ,
Existence and uniqueness of measure solutions for a system of continuity equations with non-local flow, NoDEA Nonlinear Differential Equations Appl, pp.1-15, 2012. ,
URL : https://hal.archives-ouvertes.fr/hal-00653053
The initial boundary value problem for general non-local scalar conservation laws in one space dimension, Nonlinear Analysis, vol.161, pp.131-156, 2017. ,
Contact discontinuity capturing schemes for linear advection and compressible gas dynamics, J. Sci. Comput, vol.16, issue.4, pp.479-524, 2001. ,
On scalar conservation laws with point source and discontinuous flux function, SIAM J. Math. Anal, vol.26, issue.6, p.118, 1995. ,
A uniqueness condition for nonlinear convection-diffusion equations with discontinuous coefficients, J. Hyperbolic Differ. Equ, vol.6, issue.01, p.118, 2009. ,
Finite volume methods, Handbook of numerical analysis, vol.VII, pp.713-1020, 2000. ,
URL : https://hal.archives-ouvertes.fr/hal-02100732
Maximum principle satisfying CWENO schemes for nonlocal conservation laws, SIAM J. Sci. Comput, vol.41, issue.2, pp.973-988, 2019. ,
A Godunov type scheme for a class of LWR traffic flow models with non-local flux, Netw. Heterog. Media, vol.13, issue.4, pp.531-547, 2018. ,
Well-posedness of IBVP for 1D scalar non-local conservation laws, ZAMM Z. Angew. Math. Mech, vol.0, issue.0, p.201800318, 2019. ,
URL : https://hal.archives-ouvertes.fr/hal-01929196
The Lighthill-Whitham-Richards traffic flow model with non-local velocity: analytical study and numerical results, vol.INRIA, 2015. ,
URL : https://hal.archives-ouvertes.fr/hal-01118734
Well-posedness and finite volume approximations of the LWR traffic flow model with non-local velocity, Netw. Heterog. Media, vol.11, issue.1, pp.107-121, 2016. ,
URL : https://hal.archives-ouvertes.fr/hal-01234584
Numerical approximation of hyperbolic systems of conservation laws, apl. Math. Sci, vol.118, 1996. ,
Modeling, simulation and validation of material flow on conveyor belts, Appl. Math. Model, vol.38, issue.13, pp.3295-3313, 2014. ,
On the uniqueness and stability of entropy solutions of nonlinear degenerate parabolic equations with rough coefficients, Discrete Contin. Dyn. Syst, vol.9, issue.5, pp.1081-1104, 2003. ,
L 1 stability for entropy solutions of nonlinear degenerate parabolic convection-diffusion equations with discontinuous coefficients, Skr. K. Nor. Vidensk. Selsk, issue.3, p.114, 2003. ,
Convergence of a Godunov scheme for conservation laws with a discontinuous flux lacking the crossing condition, J. Hyperbolic Differ. Equ, vol.14, issue.04, pp.671-701, 2017. ,
Existence, uniqueness and regularity results on nonlocal balance laws, J. Differential Equations, vol.263, issue.7, pp.4023-4069, 2017. ,
On approximation of local conservation laws by nonlocal conservation laws, J. Appl. Math. Anal. Appl, vol.475, issue.2, 1927. ,
Existence, uniqueness and regularity of multidimensional nonlocal balance laws with damping, J. Math. Anal. Appl, vol.466, issue.1, pp.18-55, 2018. ,
Nonlocal scalar conservation laws on bounded domains and applications in traffic flow, SIAM J. Math. Anal, vol.50, issue.6, pp.6271-6306, 2018. ,
First order quasilinear equations with several independent variables. Mat. Sb, vol.81, pp.228-255, 1970. ,
Non-oscillatory central schemes for a traffic flow model with arrehenius look-ahead dynamics, Netw. Heterog. Media, vol.4, issue.3, p.27, 2009. ,
The Godunov scheme and what it means for first order traffic flow models, Proc. 13th Intrn. Symp. Transportation and Traffic Theory, p.118, 1996. ,
Improved stability estimates for general scalar conservation laws, J. Hyperbolic Differ. Equ, vol.08, issue.04, pp.727-757, 2011. ,
Finite volume methods for hyperbolic problems, Cambridge Texts in Applied Mathematics, vol.63, p.558, 2002. ,
Shock formation in a traffic flow model with Arrhenius look-ahead dynamics, Netw. Heterog. Media, vol.6, issue.4, pp.681-694, 2011. ,
On kinematic waves. II. A theory of traffic flow on long crowded roads, Proc. Roy. Soc. London. Ser. A, vol.229, pp.317-345, 1955. ,
Models of Freeway Traffic and Control. Simulation Councils, Incorporated, 1971. ,
Shock waves on the highway, Oper. Res, vol.4, pp.42-51, 1956. ,
Traveling waves for nonlocal models of traffic flow, Discrete Contin. Dyn. Syst, vol.39, p.4001, 2019. ,
, Traveling Waves for Conservation Laws with Nonlocal Flux for Traffic Flow on Rough Roads. arXiv e-prints, 2018.
Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws, Advanced numerical approximation of nonlinear hyperbolic equations, p.99, 1998. ,
Efficient implementation of essentially non-oscillatory shockcapturing schemes, J. Comput. Phys, vol.77, issue.2, p.99, 1988. ,
Stochastic modeling and simulation of traffic flow: asymmetric single exclusion process with Arrhenius look-ahead dynamics, SIAM J. Appl. Math, vol.66, issue.3, pp.921-944, 2006. ,
High resolution schemes using flux limiters for hyperbolic conservation laws, SIAM J. Numer. Anal, vol.21, issue.5, p.89, 1984. ,
Towards the ultimate conservative difference scheme. v. a second-order sequel to Godunov's method, J. Comput. Phys, vol.32, issue.1, p.89, 1979. ,
Pure and applied mathematics, 1974. ,
A non-equilibrium traffic model devoid of gas-like behavior, Transportation Research Part B: Methodological, vol.36, issue.3, pp.275-290, 2002. ,
On a nonlocal dispersive equation modeling particle suspensions, Quart. Appl. Math, vol.57, issue.3, pp.573-600, 1999. ,