Nonlocal traffic flow models and the prevention of traffic jams

In this talk, I will discuss a family of traffic flow models. The classical Lighthill-Whitham-Richards model is known to have a finite time blowup for all generic initial data, which represents the creation of traffic jams. I will introduce a family of nonlocal traffic flow models, with look-ahead interactions. Such models can be derived from discrete cellular automata models. We show an intriguing phenomenon that the nonlocal slowdown interaction prevents traffic jams, under suitable settings. This talk is based on joint works with Yongki Lee and Yi Sun.