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

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