Citation

Goatin P, Mimault M. Math. Biosci. Eng. 2015; 12(2): 375-392.

Affiliation

INRIA Sophia Antipolis - Méditerranée, EPI OPALE, 2004, route des Lucioles - BP 93, 06902 Sophia Antipolis Cedex, France. paola.goatin@inria.fr.

Copyright

(Copyright © 2015, American Institute of Mathematical Sciences)

DOI

unavailable

PMID

25811441

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.

Language: en