On the modelling and management of traffic
Rinaldo M. Colombo, Paola Goatin, Massimiliano D. Rosini (2011)
ESAIM: Mathematical Modelling and Numerical Analysis
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Several realistic situations in vehicular traffic that give rise to queues can be modeled through conservation laws with boundary and unilateral constraints on the flux. This paper provides a rigorous analytical framework for these descriptions, comprising stability with respect to the initial data, to the boundary inflow and to the constraint. We present a framework to rigorously state optimal management problems and prove the existence of the corresponding optimal controls....