2013/04/23 by Boris Andreïanov, Andreianov, Boris, Carlotta Donadello +3
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Evacuation and Crowd Dynamics #FOS: Mathematics #Navier-Stokes equation solutions
paper · pdf · doi:10.48550/arxiv.1304.6282
openalex publication_date 2013/04/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.