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

Autor:	Maltugueva, Nadezhda, Pogodaev, Nikolay
Rok vydání:	2020
Předmět:	Mathematics - Analysis of PDEs 35F10 35R37 49J53 49Q20
Druh dokumentu:	Working Paper
Popis:	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 the environment optimization problems, and provide some results of numerical computations. Comment: 31 pages, 3 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2007.04605 Zobrazit plný text záznamu View this record from Arxiv