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On the Well Posedness of the Initial Value Problem in a Kinetic Traffic Flow Model

ABSTRACT A traffic flow model is discussed in the framework of the Kinetic Theory of Active Particles (KTAP). Each active particle is a vehicle-driver pair characterized by a discrete velocity and by a driving ability. The system evolves through non-linear interactions which are modeled by the so-called Tables of Games. An evolution equation is derived and a theorem of existence and uniqueness of the solution for a finite time is proved. The results of numerical simulations which are consistent with the results of experimental evidence, are also shown.