Kinetic BGK Model for a Crowd: Crowd Characterized By a State of Equilibrium


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Output type: Journal article

UM6P affiliated Publication?: Yes

Author list: El Mousaoui, Abdelghani; Argoul, Pierre; El Rhabi, Mohammed; Hakim, Abdelilah

Publisher: Springer Verlag (Germany) / Akademie věd České republiky, Matematický ústav

Publication year: 2020

Journal: Applications of Mathematics (0862-7940)

Volume number: 66

Issue number: 1

ISSN: 0862-7940

eISSN: 1572-9109

Languages: English (EN-GB)


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Abstract

This article focuses on dynamic description of the collective pedestrian motion based on the kinetic model of Bhatnagar-Gross-Krook. The proposed mathematical model is based on a tendency of pedestrians to reach a state of equilibrium within a certain time of relaxation. An approximation of the Maxwellian function representing this equilibrium state is determined. A result of the existence and uniqueness of the discrete velocity model is demonstrated. Thus, the convergence of the solution to that of the continuous BGK equation is proven. Numerical simulations are presented to validate the proposed mathematical model.


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Last updated on 2021-26-11 at 23:16