Conservation laws with a nonlocal flow, Application to pedestrian traffic

TL;DR

This paper introduces new models for pedestrian traffic flow incorporating nonlocal effects and establishes their mathematical well-posedness through proofs of existence and uniqueness.

Contribution

It presents novel pedestrian traffic models with nonlocal flow components and provides rigorous mathematical analysis of their solutions.

Findings

Models of pedestrian traffic with nonlocal flow are well-posed.

Existence and uniqueness of solutions are proven for these models.

The work advances the mathematical understanding of pedestrian flow dynamics.

Abstract

In this note, we introduce some models of pedestrian traffic and prove existence and uniqueness for these models.