We present a model of crowd motion in regions with moving obstacles, which is based on the notion of measure sweeping process. The obstacle is modeled by a set-valued map, whose values are complements to $ r $-prox-regular sets. The crowd motion obeys a nonlinear transport equation outside the obstacle and a normal cone condition (similar to that of the classical sweeping processes theory) on the boundary. We prove the well-posedness of the model, give an application to environment optimization problems, and provide some results of numerical computations.

中文翻译：

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具有移动障碍物的区域中的人群建模

我们提出了一个具有移动障碍物的区域中的人群运动模型，该模型基于测量扫描过程的概念。障碍物由集合值映射建模，其值是 $ r $-prox-regular 集合的补充。人群运动服从障碍物外的非线性传输方程和边界上的法向锥条件（类似于经典扫掠过程理论的条件）。我们证明了模型的适定性，将其应用于环境优化问题，并提供了一些数值计算结果。