Conservation Laws with Unilateral Constraints in Traffic Modeling

Rinaldo M. Colombo (1) , Paola Goatin (2) , Massimiliano D Rosini (3)

1 Dipartimento di Matematica [Universita di Brescia]
2 OPALE - Optimization and control, numerical algorithms and integration of complex multidiscipline systems governed by PDE
3 ICM

Macroscopic models for both vehicular and pedestrian traffic are based on conservation laws. The mathematical description of toll gates along roads or of the escape dynamics for crowds needs the introduction of unilateral constraints on the observable flow. This note presents a rigorous approach to these constraints, and numerical integrations of the resulting models are included to show their practical usability.

Domaines: Equations aux dérivées partielles [math.AP]

Rinaldo M. Colombo, Paola Goatin, Massimiliano D Rosini. Conservation Laws with Unilateral Constraints in Traffic Modeling. De Bernardis E. and Spigler R. and Valente V. Applied and Industrial Mathematics in Italy III, 82, Series on Advances in Mathematics for Applied Sciences, pp.244-255, 2009, ⟨10.1685/CSC09XXX⟩. ⟨hal-00765427⟩