| Abstract: |
| We introduce a macroscopic crowd motion model inspired by Hughes (2002, 2003), coupling a nonlinear conservation law for pedestrian density with an Eikonal equation characterizing the shortest path. This approach modifies Hughes` original formulation and refines the prediction-correction framework recently proposed by Ennaji, Igbida and Jradi (2023). By incorporating anticipatory behavior and dynamic route adjustment, our model offers a realistic representation of crowd dynamics in complex environments. Finally, we present the mathematical formulation, discuss its well-posedness, and illustrate its qualitative behavior through numerical simulations. |
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