Modeling of crowds in the regions with moving obstacles via measure\n sweeping processes

2020/07/09 by Nadezhda Maltugueva, Maltugueva, Nadezhda, Nikolay Pogodaev +1
Engineering · #Evacuation and Crowd Dynamics

paper · pdf · doi:10.48550/arxiv.2007.04605

Abstract

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

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