A mixed system modeling two-directional pedestrian flows

Paola Goatin, Matthias Mimault
2014 Mathematical Biosciences and Engineering  
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 × 2 system of conservation laws of mixed hyperbolicelliptic 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
more » ... it of a subsequence of approximate solutions. 2010 Mathematics Subject Classification. Primary: 35L65 -35M30; Secondary: 90B20.
doi:10.3934/mbe.2015.12.375 pmid:25811441 fatcat:m5bpdpnwabcgxmcf72smyoymzm