Mathematical Biosciences and Engineering, 2015, 12(2): 375-392. doi: 10.3934/mbe.2015.12.375.

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

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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

   

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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Keywords macroscopic models for pedestrian flows; Systems of conservation laws; finite volume schemes; mixed hyperbolic-elliptic systems; Young measures.

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

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This article has been cited by

  • 1. S. Roy, A. Borzì, A. Habbal, Pedestrian motion modelled by Fokker–Planck Nash games, Royal Society Open Science, 2017, 4, 9, 170648, 10.1098/rsos.170648
  • 2. Susana N. Gomes, Andrew M. Stuart, Marie-Therese Wolfram, Parameter Estimation for Macroscopic Pedestrian Dynamics Models from Microscopic Data, SIAM Journal on Applied Mathematics, 2019, 79, 4, 1475, 10.1137/18M1215980

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Copyright Info: 2015, Paola Goatin, et al., licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

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