Open AccessModeling of crowds in regions with moving obstacles
Author(s) -
Nadezhda Maltugueva,
Nikolay Pogodaev
Publication year - 2021
Publication title -
discrete and continuous dynamical systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.289
H-Index - 70
eISSN - 1553-5231
pISSN - 1078-0947
DOI - 10.3934/dcds.2021066
Subject(s) - obstacle , crowds , motion (physics) , measure (data warehouse) , computation , boundary (topology) , set (abstract data type) , computer science , mathematics , process (computing) , obstacle problem , mathematical analysis , algorithm , artificial intelligence , law , programming language , computer security , database , political science , operating system
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 \begin{document}$ r $\end{document} -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.