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

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Type: Preprint
National /International: International
Title: A coupled prediction-correction Hughes' model for congested crowd motion
Publication Date: 2026-06-05
Authors: - Hamza Ennaji
- Noureddine Igbida
- Ghadir Jradi
- José Miguel Urbano
Abstract:

In this work, we introduce a new macroscopic model for crowd motion inspired by the celebrated Hughes' model [32, 33], 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 [23]. 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 wellposedness 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.

Institution: DMUC 26-24
Online version: http://www.mat.uc.pt...prints/eng_2026.html
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© Centre for Mathematics, University of Coimbra, funded by
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Financiado total ou parcialmente pela FCT, Fundação para a Ciência e a Tecnologia, I.P., sob o Financiamento de:
UID/00324/2025 Projeto Estratégico com a referência DOI https://doi.org/10.54499/UID/00324/2025.
https://doi.org/10.54499/UID/PRR/00324/2025     UID/PRR/00324/2025   https://doi.org/10.54499/UID/PRR2/00324/2025   UID/PRR2/00324/2025
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