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arXiv · 2606.02899

A coupled prediction-correction Hughes' model for congested crowd motion

Hamza Ennaji·Noureddine Igbida·Ghadir Jradi·José Miguel Urbano
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Abstract

In this work, we introduce a new macroscopic model for crowd motion inspired by the celebrated Hughes' model \cite{Hughes2002, Hughes2003}, which couples a nonlinear conservation law for the pedestrian density with an Eikonal equation describing the shortest path to the target. Our approach can be viewed both as a modification of Hughes' original formulation and as a refinement of the prediction-correction framework proposed in the recent work \cite{ennaji2023prediction}. The resulting model incorporates anticipatory behavior and dynamic route adjustment, offering a more realistic representation of crowd dynamics in complex environments. We present the mathematical formulation of the model, discuss its well-posedness properties, and illustrate its qualitative behavior through numerical simulations. Ultimately, we show, at least from a numerical perspective, that this variant provides a promising avenue towards establishing the well-posedness of the classical Hughes' model, which has remained a challenging open problem for a long time.

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Hamza Ennaji, Noureddine Igbida, Ghadir Jradi, José Miguel Urbano. 2026-06-01. A coupled prediction-correction Hughes' model for congested crowd motion. https://arxiv.org/abs/2606.02899

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