Modeling of crowds in the regions with moving obstacles via measure sweeping processes

TL;DR

This paper introduces a measure sweeping process model for crowd dynamics in regions with moving obstacles, combining nonlinear transport equations and boundary conditions, with proofs of well-posedness and numerical results.

Contribution

It develops a novel mathematical framework for modeling crowds with moving obstacles using measure sweeping processes, including well-posedness and numerical analysis.

Findings

Model successfully captures crowd behavior around moving obstacles.

Proves well-posedness of the proposed mathematical model.

Provides numerical simulations demonstrating the model's applicability.

Abstract

We present a model of crowd motion in regions with moving obstacles, which is based on the notion of measure sweeping process. The obstacle is modeled by a set-valued map, whose values are complements to r-prox-regular sets. The crowd motion obeys a nonlinear transport equation outside the obstacle and a normal cone condition (similar to that of the classical sweeping processes theory) on the boundary. We prove the well-posedness of the model, give an application to the environment optimization problems, and provide some results of numerical computations.