On the Hughes model and numerical aspects
On the Hughes model and numerical aspects
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.
12 pages, 17 figures
- King Abdullah University of Science and Technology Saudi Arabia
Mathematics - Analysis of PDEs, Optimization and Control (math.OC), FOS: Mathematics, Mathematics - Optimization and Control, Analysis of PDEs (math.AP)
Mathematics - Analysis of PDEs, Optimization and Control (math.OC), FOS: Mathematics, Mathematics - Optimization and Control, Analysis of PDEs (math.AP)
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