Preprint 2016-007
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 [9] 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 [9], existence of solution to the Cauchy problem was proved in [1].
References
[1] B. Andreianov, C. Donadello, and M. D. Rosini. A second order model for vehicular traffics with local point constraints on the flow. M3AS Math. Methods Models Appl. Sci., 26(4) 751–802, 2016. [MR3460622]
[9] M. Garavello and P. Goatin. The Aw–Rascle traffic model with locally constrained flow. J. Math. Anal. Appl., 378(2) 634–648, 2011. [MR2773272]
[1] B. Andreianov, C. Donadello, and M. D. Rosini. A second order model for vehicular traffics with local point constraints on the flow. M3AS Math. Methods Models Appl. Sci., 26(4) 751–802, 2016. [MR3460622]
[9] M. Garavello and P. Goatin. The Aw–Rascle traffic model with locally constrained flow. J. Math. Anal. Appl., 378(2) 634–648, 2011. [MR2773272]