A mixed system modeling two-directional pedestrian flows

  • 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

    Related Papers:

  • 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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