We provide an overview of the results on Hughes' model for pedestrian movements available in the literature. The model consists of a nonlinear conservation law coupled with an eikonal equation. The main difficulty in developing a proper mathematical theory lies in the lack of regularity of the flux in the conservation law, which yields the possibility of non-classical shocks that are generated non-locally by the whole distribution of pedestrians. This is a possible reason behind the availability of existence results only on one-dimensional spatial domains, despite the model having a more natural setting in two spatial dimensions.
The Mathematical Theory of Hughes' Model: A Survey of Results
M. D. Rosini;
2023-01-01
Abstract
We provide an overview of the results on Hughes' model for pedestrian movements available in the literature. The model consists of a nonlinear conservation law coupled with an eikonal equation. The main difficulty in developing a proper mathematical theory lies in the lack of regularity of the flux in the conservation law, which yields the possibility of non-classical shocks that are generated non-locally by the whole distribution of pedestrians. This is a possible reason behind the availability of existence results only on one-dimensional spatial domains, despite the model having a more natural setting in two spatial dimensions.File in questo prodotto:
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