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arXiv · 1304.6282

Crowd dynamics and conservation laws with non-local constraints

Boris Andreianov·Carlotta Donadello·Massimiliano D. Rosini
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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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Boris Andreianov, Carlotta Donadello, Massimiliano D. Rosini. 2013-04-23. Crowd dynamics and conservation laws with non-local constraints. https://arxiv.org/abs/1304.6282

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