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arXiv · 1603.06237

On the Hughes Model and Numerical Aspects

Diogo A. Gomes·Roberto M. Velho
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Abstract

We study a crowd model proposed by R. Hughes and we describe a numerical approach to solve it. The Hughes model comprises a Fokker-Planck equation coupled with an eikonal equation with Dirichlet or Neumann data. First, we establish a priori estimates for the solutions. Second, we study radial solutions and identify a shock formation mechanism. Third, we illustrate the existence of congestion, the breakdown of the model, and the trend to the equilibrium. Finally, we propose a new numerical method and consider two numerical examples.

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Diogo A. Gomes, Roberto M. Velho. 2016-03-20. On the Hughes Model and Numerical Aspects. https://arxiv.org/abs/1603.06237

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