Homogenization of a microscopic pedestrians model on a convergent junction

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'ecole Normale Super. 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.

Automated summary

This paper establishes a rigorous connection between microscopic and macroscopic pedestrian models at a convergent junction. By injecting the microscopic model into a non-local PDE, the study demonstrates the local uniform convergence of the viscosity solution of the non-local PDE towards the solution of the macroscopic model.