A SPACE-TIME NONLOCAL TRAFFIC FLOW MODEL: RELAXATION REPRESENTATION AND LOCAL LIMIT

摘要

We propose and study a nonlocal conservation law modelling traf- ?c ?ow in the existence of inter-vehicle communication. It is assumed that the nonlocal information travels at a ?nite speed and the model involves a space- time nonlocal integral of weighted tra?c density. The well-posedness of the model is established under suitable conditions on the model parameters and by a suitably-de?ned initial condition. In a special case where the weight kernel in the nonlocal integral is an exponential function, the nonlocal model can be reformulated as a 2 × 2 hyperbolic system with relaxation. With the help of this relaxation representation, we show that the Lighthill-Whitham-Richards model is recovered in the equilibrium approximation limit.