Modeling of crowds in regions with moving obstacles

<p style='text-indent:20px;'>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 <inline-formula><tex-math id="M1">\begin{document}$ r $\end{document}</tex-math></inline-formula>-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.</p>