The Cauchy problem for the Aw–Rascle–Zhang traffic model with locally constrained flow
Mauro Garavello and Stefano Villa
Abstract: We study the Cauchy problem for the Aw–Rascle–Zhang model for traffic flow with a flux constraint at $x=0$. More precisely we consider the Riemann solver, conserving the number of cars at $x=0$ but not the generalized momentum, introduced in  for the problem with flux constrained. For such a Riemann solver, we prove existence of a solution for the Cauchy problem. The proof is based on the wave-front tracking method. For the other Riemann solver in , existence of solution to the Cauchy problem was proved in .
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