Differential Equations Modeling Crowd Interactions
- 360 Downloads
Nonlocal conservation laws are used to describe various realistic instances of crowd behaviors. First, a basic analytic framework is established through an ad hoc well-posedness theorem for systems of nonlocal conservation laws in several space dimensions interacting nonlocally with a system of ODEs. Numerical integrations show possible applications to the interaction of different groups of pedestrians and also with other agents.
KeywordsNonlocal conservation laws Crowd dynamics Car traffic
Mathematics Subject Classification35L65 90B20
This work was partially supported by the INDAM–GNAMPA project Conservation Laws: Theory and Applications, by the Graduiertenkolleg 1932 “Stochastic Models for Innovations in the Engineering Sciences” and by the Deutsche Forschungsgemeinschaft (DFG) project “Stochastic Models for Innovations in the Engineering Sciences”.
- Bressan, A., Piccoli, B.: Introduction to the Mathematical Theory of Control, Volume 2 of AIMS Series on Applied Mathematics. American Institute of Mathematical Sciences (AIMS), Springfield, MO (2007)Google Scholar
- Etikyala, R., Göttlich, S., Klar, A., Tiwari, S.: Particle methods for pedestrian flow models: from microscopic to nonlocal continuum models. Math. Models Methods Appl. Sci. 24(12), 2503–2523 (2014)Google Scholar
- Lécureux-Mercier, M.: Improved stability estimates on general scalar balance laws. ArXiv e-prints (2010)Google Scholar
- Piccoli, B., Tosin, A.: Time-evolving measures and macroscopic modeling of pedestrian flow. Arch. Ration. Mech. Anal. (2010). doi: 10.1007/s00205-010-0366-y