Journal of Nonlinear Science

, Volume 25, Issue 4, pp 827–859 | Cite as

Differential Equations Modeling Crowd Interactions

  • Raul Borsche
  • Rinaldo M. ColomboEmail author
  • Mauro Garavello
  • Anne Meurer


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.


Nonlocal conservation laws Crowd dynamics Car traffic 

Mathematics Subject Classification

35L65 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”.


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Raul Borsche
    • 1
  • Rinaldo M. Colombo
    • 2
    Email author
  • Mauro Garavello
    • 3
  • Anne Meurer
    • 1
  1. 1.Fachbereich MathematikTechnische Universität KaiserslauternKaiserslauternGermany
  2. 2.Unità INdAM, c/o DIIUniversità degli studi di BresciaBresciaItaly
  3. 3.Dipartimento di Matematica e ApplicazioniUniversità di Milano BicoccaMilanItaly

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