Coexisting Automated and Human-Driven Vehicles: Well-Posedness of a Mixed Nonlocal-Local Traffic Model

TL;DR

This paper introduces a macroscopic traffic flow model combining automated and human-driven vehicles, proving well-posedness of the resulting mixed nonlocal-local PDE system with unique solutions.

Contribution

It develops a novel mathematical framework for mixed traffic models, establishing existence, uniqueness, and continuous dependence of solutions for the first time.

Findings

The model generates a locally Lipschitz continuous semigroup.

Solutions are uniquely characterized within the chosen function spaces.

The approach handles the intrinsic differences between nonlocal and local equations.

Abstract

We present a macroscopic traffic flow model where standard vehicles coexist with vehicles informed on the traffic distribution. The resulting mixed nonlocal-local integro-differential PDEs is proved to generate a locally Lipschitz continuous semigroup whose orbits are uniquely characterized as solutions to the system, according to a natural definition of solution. The norms and function spaces adopted are intrinsic to the different nature of the equations.