A mixed system modeling two-directional pedestrian flows

Abstract : 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 2x2 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 solutions as limit of a subsequence of approximate solutions.
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Paola Goatin, Matthias Mimault. A mixed system modeling two-directional pedestrian flows. Mathematical Biosciences and Engineering, AIMS Press, 2015, 12 (2), pp.375-392. ⟨hal-00968396⟩

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