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Mathematical Biosciences and Engineering (MBE)
 

Many particle approximation of the Aw-Rascle-Zhang second order model for vehicular traffic

Pages: 127 - 141, Volume 14, Issue 1, February 2017      doi:10.3934/mbe.2017009

 
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Marco Di Francesco - DISIM, Università degli Studi dell’Aquila, via Vetoio 1 (Coppito), 67100 LAquila (AQ), Italy (email)
Simone Fagioli - DISIM, Università degli Studi dell’Aquila, via Vetoio 1 (Coppito), 67100 LAquila (AQ), Italy (email)
Massimiliano D. Rosini - Instytut Matematyki, Uniwersytet Marii Curie-Skłodowskiej, pl. Marii Curie-Skłodowskiej 1, 20-031 Lublin, Poland (email)

Abstract: We consider the follow-the-leader approximation of the Aw-Rascle-Zhang (ARZ) model for traffic flow in a multi population formulation. We prove rigorous convergence to weak solutions of the ARZ system in the many particle limit in presence of vacuum. The result is based on uniform ${\mathbf{BV}}$ estimates on the discrete particle velocity. We complement our result with numerical simulations of the particle method compared with some exact solutions to the Riemann problem of the ARZ system.

Keywords:  Aw-Rascle-Zhang model, second order models for vehicular traffics, many particle limit.
Mathematics Subject Classification:  Primary: 35L65, 90B20.

Received: October 2015;      Accepted: April 2016;      Available Online: October 2016.

 References