Math. Model. Nat. Phenom.
Volume 17, 2022
|Number of page(s)||37|
|Published online||11 July 2022|
Homogenization of a microscopic pedestrians model on a convergent junction
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
* Corresponding author: email@example.com
Accepted: 3 June 2022
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.
Mathematics Subject Classification: 35D40 / 90B20 / 35B27 / 35F20 / 45K05
Key words: Specified homogenization / Hamilton-Jacobi equations / pedestrians / non-local operators / Slepčev formulation / viscosity solutions / microscopic model on junction
© The authors. Published by EDP Sciences, 2022
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