从微观尺度到集体群体动力学
From the Micro-scale to Collective Crowd Dynamics
摘要：
本文研究了群体动力学的动力学理论模型，旨在说明微观尺度的动力学如何转化为集体行为的动力学。一个新的模型的推导其次是定性分析的初始值问题。解的存在性证明了任意大的时间，而模拟开发的计算方案的基础上分裂方法，其中的传输方程处理的双曲型方程的有限差分方法。一些初步的推理对恐慌条件的建模提出。
英文摘要：
This paper deals with the kinetic theory modeling of crowd dynamics with the aim of showing how the dynamics at the micro-scale is transferred to the dynamics of collective behaviors. The derivation of a new model is followed by a qualitative analysis of the initial value problem. Existence of solutions is proved for arbitrary large times, while simulations are developed by computational schemes based on splitting methods, where the transport equations treated by finite difference methods for hyperbolic equations. Some preliminary reasonings toward the modeling of panic conditions are proposed.
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