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

Abstract : 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.
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Cited literature [29 references]

https://hal.archives-ouvertes.fr/hal-01215944
Contributor : Francesco Rossi <>
Submitted on : Friday, October 16, 2015 - 11:49:16 AM
Last modification on : Wednesday, September 12, 2018 - 1:27:36 AM
Long-term archiving on : Thursday, April 27, 2017 - 4:43:21 AM

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### Citation

Paola Goatin, Francesco Rossi. A traffic flow model with non-smooth metric interaction: Well-posedness and micro-macro limit. Communications in Mathematical Sciences, International Press, 2017, 15 (1), pp.261 - 287. ⟨10.4310/CMS.2017.v15.n1.a12⟩. ⟨hal-01215944⟩

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