一类非局部行人交通模型
A Class of Non-Local Models for Pedestrian Traffic
摘要：
我们提出了一类新的宏观模型的行人流。假设每个人都朝着一个固定的目标，偏离最佳路径根据瞬时人群分布。所得方程是一个具有非局部通量的守恒律。这类方程中的每一个方程都生成一个Lipschitz解半群，并且关于定义它的函数和参数是稳定的，并且证明了关键的定性性质，如拥挤密度的有界性.具体的模型，并通过数值积分显示其定性性质。
英文摘要：
We present a new class of macroscopic models for pedestrian flows. Each individual is assumed to move towards a fixed target, deviating from the best path according to the instantaneous crowd distribution. The resulting equation is a conservation law with a nonlocal flux. Each equation in this class generates a Lipschitz semigroup of solutions and is stable with respect to the functions and parameters defining it. Moreover, key qualitative properties such as the boundedness of the crowd density are proved. Specific models are presented and their qualitative properties are shown through numerical integrations.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
