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Discrete and Continuous Dynamical Systems - Series B (DCDS-B)
 

Car-following and the macroscopic Aw-Rascle traffic flow model

Pages: 279 - 303, Volume 13, Issue 2, March 2010      doi:10.3934/dcdsb.2010.13.279

 
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Marte Godvik - Department of Mathematical Sciences, Norwegian University of Science and Technology, NO–7491 Trondheim, Norway (email)
Harald Hanche-Olsen - Department of Mathematical Sciences, Norwegian University of Science and Technology, NO–7491 Trondheim, Norway (email)

Abstract: We consider a semi-discrete car-following model and the macroscopic Aw-Rascle model for traffic flow given in Lagrangian form. The solution of the car-following model converges to a weak entropy solution of the system of hyperbolic balance laws with Cauchy initial data. For the homogeneous system, we allow vacuum in the initial data. By using properties of the semi-discrete model, we show that this solution of the hyperbolic system is stable in the $L^1$-norm.

Keywords:  Traffic flow, car-following, non--strictly hyperbolic system, vacuum.
Mathematics Subject Classification:  35L45, 35L65, 35L67, 35L80, 90B20.

Received: February 2008;      Revised: January 2009;      Available Online: December 2009.