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*Discrete and Continuous Dynamical Systems -- Series S*is devoted to

*Traffic Modeling and Management*. This subject dramatically developed in recent years. On one hand, the successes of the analytical theory of conservation laws have provided new tools to traffic researchers while, on the other hand, the requirements coming from the applications have grown dramatically. Remarkably, two of the papers that opened the way to this decades long development date the same year. In 1995

*``The Unique Limit of the Glimm Scheme''*by A. Bressan (Archive for Rational Mechanics and Analysis, 130, 3, 205--230) gave a basis for several well posedness results for 1D systems of conservation laws. In the same year,

*``Requiem for High-Order Fluid Approximations of Traffic Flow''*by C. Daganzo (Transportation Research Part B: Methodological, 29B, 4, 277--287) posed serious criticisms to models studied at that time and started to fix minimal requirements for a traffic model to be seriously considered.

For more information please click the “Full Text” above.

We study well-posedness of scalar conservation laws with moving flux constraints. In particular, we show the Lipschitz continuous dependence of BV solutions with respect to the initial data and the constraint trajectory. Applications to traffic flow theory are detailed.

We introduce a second order model for traffic flow with moving bottlenecks. The model consists of the × 2$ Aw-Rascle-Zhang system with a point-wise flow constraint whose trajectory is governed by an ordinary differential equation. We define two Riemann solvers, characterize the corresponding invariant domains and propose numerical strategies, which are effective in capturing the non-classical shocks due to the constraint activation.

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