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Mathematical Biosciences and Engineering

2015, Volume 12, Issue 2: 375-392. doi: 10.3934/mbe.2015.12.375
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A mixed system modeling two-directional pedestrian flows

  • 1.
    INRIA Sophia Antipolis - Méditerranée, EPI OPALE, 2004, route des Lucioles - BP 93, 06902 Sophia Antipolis Cedex
  • 2.
    INRIA Sophia Antipolis - Méditerranée, 2004, route des Lucioles - BP 93, 06902 Sophia Antipolis Cedex
  • Received: 01 April 2014 Accepted: 29 June 2018 Published: 01 December 2014

  • MSC : Primary: 35L65, 35M30; Secondary: 90B20.

  • In this article, we present a simplified model to describe the dynamics of two groups of pedestrians moving in opposite directions in a corridor.The model consists of a $2\times 2$ system of conservation laws of mixed hyperbolic-elliptic type.We study the basic properties of the system to understand why and how bounded oscillations in numerical simulations arise.We show that Lax-Friedrichs scheme ensures the invariance of the domain and we investigate the existence of measure-valued solutionsas limit of a subsequence of approximate solutions.

    Citation: Paola Goatin, Matthias Mimault. A mixed system modeling two-directional pedestrian flows[J]. Mathematical Biosciences and Engineering, 2015, 12(2): 375-392. doi: 10.3934/mbe.2015.12.375

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  • In this article, we present a simplified model to describe the dynamics of two groups of pedestrians moving in opposite directions in a corridor.The model consists of a $2\times 2$ system of conservation laws of mixed hyperbolic-elliptic type.We study the basic properties of the system to understand why and how bounded oscillations in numerical simulations arise.We show that Lax-Friedrichs scheme ensures the invariance of the domain and we investigate the existence of measure-valued solutionsas limit of a subsequence of approximate solutions.


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    3. S. Roy, A. Borzì, A. Habbal, Pedestrian motion modelled by Fokker–Planck Nash games, 2017, 4, 2054-5703, 170648, 10.1098/rsos.170648
    4. Susana N. Gomes, Andrew M. Stuart, Marie-Therese Wolfram, Parameter Estimation for Macroscopic Pedestrian Dynamics Models from Microscopic Data, 2019, 79, 0036-1399, 1475, 10.1137/18M1215980
    5. Stephane Mollier, Maria Laura Delle Monache, Carlos Canudas-de-Wit, 2019, A decision support and planning mobility method for large scale traffic networks, 978-3-907144-00-8, 1, 10.23919/ECC.2019.8795881
    6. Nicola Bellomo, Livio Gibelli, Annalisa Quaini, Alessandro Reali, Towards a mathematical theory of behavioral human crowds, 2022, 32, 0218-2025, 321, 10.1142/S0218202522500087
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