行人流的时变测度与宏观建模
Time-evolving measures and macroscopic modeling of pedestrian flow
摘要：
本文论述了一个新的模型的行人流量的早期结果，设想在一个测量理论框架。建模方法包括在离散时间欧拉宏观表示的系统通过一个家庭的措施，推动了一些运动映射，提供了一个估计的空间占用行人在连续的时间步长。从建模的角度来看，该设置特别适合于处理行人、障碍物和墙边界条件之间的非局部交互。此外，分析和数值逼近所产生的数学结构，这是这项工作的主要目标，遵循更容易和直接的情况下，标准的双曲守恒律，也用于专业文献中的一些作者来解决类似的问题。
英文摘要：
This paper deals with the early results of a new model of pedestrian flow, conceived within a measure-theoretical framework. The modeling approach consists in a discrete-time Eulerian macroscopic representation of the system via a family of measures which, pushed forward by some motion mappings, provide an estimate of the space occupancy by pedestrians at successive time steps. From the modeling point of view, this setting is particularly suitable to treat nonlocal interactions among pedestrians, obstacles, and wall boundary conditions. In addition, analysis and numerical approximation of the resulting mathematical structures, which is the main target of this work, follow more easily and straightforwardly than in case of standard hyperbolic conservation laws, also used in the specialized literature by some Authors to address analogous problems.
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