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Rigorous Derivation and Analysis on the Kinetic Equation of Pedestrian Flow Model

Speaker

Qitao Yin, University of Mannheim, Germany

Time

2018.01.10 14:00-15:00

Venue

601 Pao Yue-Kong Library

Abstract

In this talk, a rigorous proof of the mean field limit for a pedestrian flow model in two dimensions will be given by using a probabilistic method. The model under investigation is an interacting particle system coupled to the eikonal equation on the microscopic scale. For stochastic initial data, it is proved that the solution of the N-particle pedestrian flow system with properly chosen cut-off converges in the probability sense to the solution of the characteristics of the non-cut-off Vlasov equation. Furthermore, the global existence and uniqueness of the weak solution to the mean field kinetic equation can be obtained by using uniform estimates and compactness arguments while difficulties arising from the non-local non-linear interaction are tackled appropriately using the Aubin-Lions compact embedding theorem.