Homogenization of a microscopic pedestrians model on a convergent junction

N. El Khatib¹ ; N. Forcadel^2, 3 ; M. Zaydan¹

¹ Lebanese American University, Department of computer science and mathematics, Byblos campus, P.O. Box 36, Byblos, Lebanon
² Normandie Univ, INSA de Rouen, LMI (EA 3226 – FR CNRS 3335), 76000 Rouen, France
³ 685 Avenue de 1’Université, 76801 St Etienne du Rouvray cedex, France

Mathematical modelling of natural phenomena, Tome 17 (2022), article no. 21

Résumé

In this paper, we establish a rigorous connection between a microscopic and a macroscopic pedestrians model on a convergent junction. At the microscopic level, we consider a “follow the leader” model far from the junction point and we assume that a rule to enter the junction point is imposed. At the macroscopic level, we obtain the Hamilton-Jacobi equation with a flux limiter condition at x = 0 introduced in Imbert and Monneau [Ann. Sci. l’École Normale Supér. 50 (2017) 357-414], To obtain our result, we inject using the “cumulative distribution functions” the microscopic model into a non-local PDE. Then, we show that the viscosity solution of the non-local PDE converges locally uniformly towards the solution of the macroscopic one.

Détail

DOI : 10.1051/mmnp/2022023

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