We study a crowd model proposed by R. Hughes in  and we describe a numerical approach to solve it. This 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 examples.
|Original language||English (US)|
|Title of host publication||2016 IEEE 55th Conference on Decision and Control (CDC)|
|Publisher||Institute of Electrical and Electronics Engineers (IEEE)|
|Number of pages||6|
|State||Published - Jan 5 2017|