Crowd dynamics and conservation laws with non-local constraints and capacity drop

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; capacity drop

Domaines: Equations aux dérivées partielles [math.AP]

Boris Andreianov, Carlotta Donadello, Massimiliano D. Rosini. Crowd dynamics and conservation laws with non-local constraints and capacity drop. Mathematical Models and Methods in Applied Sciences, 2014, 24 (13), pp. 2685-2722. ⟨10.1142/S0218202514500341⟩. ⟨hal-00816449v2⟩