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problems on hyperbolic PDEs
Car-following and the macroscopic Aw-Rascle traffic flow model
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.