A non-local macroscopic model for traffic flow

Ciotir, Ioana; Fayad, Rim; Forcadel, Nicolas; Tonnoir, Antoine

ESAIM: Mathematical Modelling and Numerical Analysis , Tome 55 (2021) no. 2, pp. 689-711

In this work, we propose a non-local Hamilton–Jacobi model for traffic flow and we prove the existence and uniqueness of the solution of this model. This model is justified as the limit of a rescaled microscopic model. We also propose a numerical scheme and we prove an estimate error between the continuous solution of this problem and the numerical one. Finally, we provide some numerical illustrations.

Classification : 76A30, 35B27, 35D40, 35F21
Keywords: Traffic flow, macroscopic models, non-local model, homogenization, viscosity solutions, Hamilton–Jacobi equations

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