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# On the Hughes ’ model for pedestrian flow : The one-dimensional case

@inproceedings{Francesco2010OnTH, title={On the Hughes ’ model for pedestrian flow : The one-dimensional case}, author={Marco Di Francesco and Peter A. Markowich and Jan-Frederik Pietschmann and Marie-Therese Wolfram}, year={2010} }

- Published 2010

In this paper we investigate the mathematical theory of Hughes’ model for the flow of pedestrians (cf. [17]), consisting of a nonlinear conservation law for the density of pedestrians coupled with an eikonal equation for a potential modelling the common sense of the task. We first consider an approximation of the original model in which the eikonal equation is replaced by an elliptic approximation. For such an approximated system we prove existence and uniqueness of entropy solutions (in one… CONTINUE READING

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