Crowd dynamics and conservation laws with non-local constraints

TL;DR

This paper models pedestrian evacuation flows using a one-dimensional hyperbolic conservation law with non-local constraints, establishing existence and stability results through advanced mathematical techniques.

Contribution

It introduces a novel approach combining wave-front tracking and operator splitting to analyze conservation laws with non-local constraints, including detailed Riemann problem analysis.

Findings

Existence and stability of solutions are proven.

The Riemann problem may lack uniqueness and self-similarity.

An explicit application example is provided.

Abstract

In this paper we model pedestrian flows evacuating a narrow corridor through an exit by a one-dimensional hyperbolic conservation law with a non-local constraint. Existence and stability results for the Cauchy problem with Lipschitz constraint are achieved by a procedure that combines the wave-front tracking algorithm with the operator splitting method. The Riemann problem with piecewise constant constraint is discussed in details, stressing the possible lack of uniqueness, self-similarity and $\Lloc1$-continuity. One explicit example of application is provided.