# American Institute of Mathematical Sciences

March  2010, 13(2): 279-303. doi: 10.3934/dcdsb.2010.13.279

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

 1 Department of Mathematical Sciences, Norwegian University of Science and Technology, NO–7491 Trondheim, Norway, Norway

Received  February 2008 Revised  January 2009 Published  December 2009

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.
Citation: Marte Godvik, Harald Hanche-Olsen. Car-following and the macroscopic Aw-Rascle traffic flow model. Discrete & Continuous Dynamical Systems - B, 2010, 13 (2) : 279-303. doi: 10.3934/dcdsb.2010.13.279
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