AUTONOMOUS VEHICLES DRIVING TRAFFIC: THE CAUCHY PROBLEM*

This paper deals with the Cauchy problem for a PDE-ODE model, where a system of two conservation laws, namely the Two-Phase macroscopic model proposed in [Rinaldo M. Colombo, Francesca Marcellini, and Michel Rascle, SIAM J. Appl. Math., 70(7):2652–2666, 2010], is coupled with an ordinary differential equation describing the trajectory of an autonomous vehicle (AV), which aims to control the traffic flow. Under suitable assumptions, we prove a global-in-time existence result.