CROWD DYNAMICS AND CONSERVATION LAWS WITH NON-LOCAL CONSTRAINTS

Boris Andreianov (1) , Carlotta Donadello (1) , Massimiliano D. Rosini (2)

1 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)
2 ICM

In this paper we model pedestrian flows evacuating a narrow corridor through an exit by a one-dimensional hyperbolic conservation law with a non-local constraint. Existence and stability results for the Cauchy problem with Lipschitz constraint are achieved by a procedure that combines the wave-front tracking algorithm with the operator splitting method. The Riemann problem with piecewise constant constraint is discussed in details, stressing the possible lack of uniqueness, self-similarity and $\Lloc1$-continuity. One explicit example of application is provided.

Mots clés: Crowd dynamics; constrained hyperbolic PDE's; non-local constraints

Domaines: Equations aux dérivées partielles [math.AP]

Boris Andreianov, Carlotta Donadello, Massimiliano D. Rosini. CROWD DYNAMICS AND CONSERVATION LAWS WITH NON-LOCAL CONSTRAINTS. 2013. ⟨hal-00816449v1⟩