A traffic flow model with non-smooth metric interaction: Well-posedness and micro-macro limit

We prove existence and uniqueness of solutions to a transport equation modelling vehicular traffic in which the velocity field depends non-locally on the downstream traffic density via a discontinuous anisotropic kernel. The result is obtained recasting the problem in the space of probability measures equipped with the $\infty$-Wasserstein distance. We also show convergence of solutions of a finite dimensional system, which provide a particle method to approximate the solutions to the original problem.

Keywords

transport equations, non-local velocity, Wasserstein distance, macroscopic traffic flow models, micro-macro limits

2010 Mathematics Subject Classification

Primary 35F25, 35L65. Secondary 65M12, 90B20.

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Published 10 January 2017