Kinetic and Related Models (KRM)

Deterministic particle approximation of the Hughes model in one space dimension

Pages: 215 - 237, Volume 10, Issue 1, March 2017      doi:10.3934/krm.2017009

       Abstract        References        Full Text (1637.2K)       Related Articles       

Marco Di Francesco - DISIM, Università degli Studi dell’Aquila, via Vetoio 1 (Coppito), 67100 LAquila (AQ), Italy (email)
Simone Fagioli - DISIM, Universita degli Studi dell'Aquila, via Vetoio 1 (Coppito), 67100 L'Aquila (AQ), Italy (email)
Massimiliano Daniele Rosini - Instytut Matematyki, Uniwersytet Marii Curie-Sk lodowskiej, plac Marii Curie-Sk lodowskiej 1, 20-031 Lublin, Poland (email)
Giovanni Russo - Dipartimento di Matematica ed Informatica, Università di Catania, Viale Andrea Doria 6, 95125 Catania, Italy (email)

Abstract: In this paper we present a new approach to the solution to a generalized version of Hughes' models for pedestrian movements based on a follow-the-leader many particle approximation. In particular, we provide a rigorous global existence result under a smallness assumption on the initial data ensuring that the trace of the solution along the turning curve is zero for all positive times. We also focus briefly on the approximation procedure for symmetric data and Riemann type data. Two different numerical approaches are adopted for the simulation of the model, namely the proposed particle method and a Godunov type scheme. Several numerical tests are presented, which are in agreement with the theoretical prediction.

Keywords:  Crowd dynamics, conservation laws, eikonal equation, Hughes' model for pedestrian flows, particle approximation.
Mathematics Subject Classification:  Primary: 35L65; Secondary: 90B20.

Received: March 2016;      Revised: July 2016;      Available Online: November 2016.