中文摘要：

在现代社会中，公共场所拥挤人群现象常常发生，人们对拥挤人群的机理研究较少，在公共场所因对拥挤人群的疏导或管理不当频频发生而伤亡事故。针对公共场所拥挤人群的安全管理需求，根据波动理论，特别是激波理论，来研究拥挤人群的基本特性，如密度、速度与激波的关系等。在人群拥挤时，可将其视为一连续介质，人群中产生的任何扰动（直接表现为密度的变化）都将以波的形式在人群中传播，同时由于人群中个体间的差异，导致波发生非线性畸变，最后可能导致激波的产生，即拥挤事故。通过特征值解法及Madab软件，求解了对于不同的初始密度分布曲线、不同的速度，预测激波将在何时何处发生，即揭示激波产生的规律，总结了消除激波的一些措施，如改变边界条件、控制初始密度、设置畸点等，以避免拥挤事故的出现。

英文摘要：

In response to the growing concern for the control and safety of crowds in public areas from the public and the govemment, the management and control of crowds should be focused on the mechanism of overcrowding. The nature of crowds based on the wave theory is studied. All perturbations produced firm the crowds present directly the variation of crowd density propagating through the crowds by pedestrian wave. The difference among the individuals could result in the nonlinear aberration of wave. Some would gradually produce pedestrian shock wave which is the overcrowding catastrophe. With the feature value solution and Matlab software, the shock wave could be predicated as when and where to occur at different initial distribution of density and speed. The roles of pedestrian shock wave could be revealed. Some measures for avoiding the shock wave are proposed, such as changing the boundary condition and controlling initial density.