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Modeling and Simulation of Macroscopic Pedestrian Flow Models

  • Naveen Kumar MahatoEmail author
  • Axel Klar
  • Sudarshan Tiwari
Conference paper
Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 30)

Abstract

Mathematical modeling and numerical simulation of human crowd motion have become a major subject of research with a wide field of applications. A variety of models for pedestrian behavior have been proposed on different levels of description in recent years. Macroscopic pedestrian flow model involving equations for density and mean velocity of the flow is derived in Bellomo and Dogbe (Math. Models Methods Appl. Sci. 18:1317-1345, 2008), Burger et al. (Discrete Contin. Dynam. Systems Ser. B: J. Bridging Math. Sci. 19:1311-1333, 2014), Hughes (Transp. Res. B Methodol. 36:507-535, 2000) and Mahato et al. (Appl. Math. Model. 53:447-461, 2018; Int. J. Adv. Eng. Sci. Appl. Math. 10:41-53, 2018).

Notes

Acknowledgements

This work is supported by the German research foundation, DFG grant KL 1105/27-1, by RTG GrK 1932 “Stochastic Models for Innovations in the Engineering Sciences”, project area P1 and by the DAAD PhD program MIC “Mathematics in Industry and Commerce”.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Naveen Kumar Mahato
    • 1
    Email author
  • Axel Klar
    • 1
  • Sudarshan Tiwari
    • 1
  1. 1.Technische Universität KaiserslauternDepartment of MathematicsKaiserslauternGermany

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