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.

中文翻译：

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人群的动力学BGK模型：以平衡状态为特征的人群

本文重点关注基于Bhatnagar-Gross-Krook动力学模型的集体行人运动的动态描述。所提出的数学模型基于行人在一定松弛时间内达到平衡状态的趋势。确定代表该平衡状态的麦克斯韦函数的近似值。证明了离散速度模型存在性和唯一性的结果。因此，证明了对连续BGK方程解的收敛性。数值模拟被提出来验证所提出的数学模型。