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One-Dimensional Conservation Laws with Nonlocal Point Constraints on the Flux

  • Boris Andreianov
  • Carlotta Donadello
  • Ulrich Razafison
  • Massimiliano Daniele RosiniEmail author
Chapter
Part of the Modeling and Simulation in Science, Engineering and Technology book series (MSSET)

Abstract

We review recent results and present new ones on one-dimensional conservation laws with point constraints on the flux. Their application is, for instance, the modeling of traffic flow through bottlenecks, such as exits in the context of pedestrians’ traffic and tollgates in vehicular traffic. In particular, we consider nonlocal constraints, which allow to model, e.g., the irrational behavior (“panic”) near the exits observed in dense crowds and the capacity drop at tollbooths in vehicular traffic. Numerical schemes for the considered applications, based on finite volume methods, are designed, their convergence is proved, and their validations are done with explicit solutions. Finally, we complement our results with numerical examples, which show that constrained models are able to reproduce important features in traffic flow, such as capacity drop and self-organization.

Notes

Acknowledgements

MDR acknowledges support from Università degli Studi di Ferrara Project 2017 “FIR: Modelli macroscopici per il traffico veicolare o pedonale”.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Boris Andreianov
    • 1
  • Carlotta Donadello
    • 2
  • Ulrich Razafison
    • 2
  • Massimiliano Daniele Rosini
    • 3
    Email author
  1. 1.LMPT, CNRS UMR 7350, Université de ToursToursFrance
  2. 2.Laboratoire de Mathématiques CNRS UMR 6623Université Bourgogne Franche-ComtéBesançonFrance
  3. 3.Department of Mathematics and Computer ScienceUniversity of FerraraFerraraItaly

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