Macroscopic traffic flow models with non-local velocity*

Abstract: Non-local traffic flow models consisting of conservation laws with integral dependent flux functions have been recently introduced to account for the reaction of drivers to the downstream traffic density, assigning a greater importance to closer vehicles. In this talk, we will recall some well-posedness results for this type of models and illustrate the solution behaviour with numerical simulations. S. Blandin and P. Goatin, Well-posedness of a conservation law with non-local flux arising in traffic flow modeling, Numer. Math.,132(2) (2016), 217-241. P. Goatin and S. Scialanga, Well-posedness and finite volume approximations of the LWR traffic flow model with non-local velocity, Netw. Heterog. Media, 11(1) (2016), 107-121. P. Goatin and F. Rossi, A traffic flow model with non-smooth metric interaction: well-posedness and micro-macro limit, Comm. Math. Sci., 15(1) (2017), 261-287. F.A. Chiarello and P. Goatin, Global entropy weak solutions for general non-local traffic flow models with anisotropic kernel, ESAIM: M2AN, 52 (2018), 163-180. F.A. Chiarello, P. Goatin and E. Rossi, Stability estimates for non-local scalar conservation laws, Nonlinear Anal. Real World Appl., 45 (2019), 668-687. F. Berthelin and P. Goatin, Regularity results for the solutions of a non-local model of traffic, Discrete Contin. Dyn. Syst. Ser. A, 39(6) (2019), 3197-3213. F.A. Chiarello and P. Goatin, Non-local multi-class traffic flow models, Netw. Heterog. Media, 14(2) (2019), 371-387. F.A. Chiarello, J. Friedrich, P. Goatin, S. Göttlich and O. Kolb, A non-local traffic flow model for 1-to-1 junctions, European J. Appl. Math., 31(6) (2020), 1029-1049.

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