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

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Abstract : 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.
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Cited literature [33 references]

https://hal.archives-ouvertes.fr/hal-00816449
Submitted on : Tuesday, April 23, 2013 - 10:55:44 AM
Last modification on : Thursday, December 26, 2019 - 12:00:08 PM
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### Citation

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

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