Sharp critical thresholds for a class of nonlocal traffic flow models

TL;DR

This paper identifies precise initial conditions in nonlocal traffic flow models that determine whether solutions remain smooth or develop shocks, highlighting how look-ahead interactions can prevent traffic jams.

Contribution

It establishes sharp critical threshold conditions for nonlocal traffic models, revealing how initial data influences solution regularity and shock formation.

Findings

Subcritical initial data lead to global smooth solutions.

Supercritical data cause finite-time shocks.

Nonlocal interactions can prevent traffic jams.

Abstract

We study a class of traffic flow models with nonlocal look-ahead interactions. The global regularity of solutions depend on the initial data. We obtain sharp critical threshold conditions that distinguish the initial data into a trichotomy: subcritical initial conditions lead to global smooth solutions, while two types of supercritical initial conditions lead to two kinds of finite time shock formations. The existence of non-trivial subcritical initial data indicates that the nonlocal look-ahead interactions can help avoid shock formations, and hence prevent the creation of traffic jams.