Halvard O. Storbugt: The 1D Hughes model for pedestrian evacuation, and its deterministic particle approximation

Abstract:

The Hughes model is one of several PDE models for the evacuation of human crowds, a phenomenon which has gained significant attention in recent years. The model considers an evacuation domain with several exits, where pedestrians choose the exit they perceive to be closest, while avoiding crowded regions. Here, the possibility of pedestrians changing their preferred exit poses interesting technical challenges. I will present the one-dimensional variant of the model, which takes the form of a scalar conservation law with a discontinuous flux function. I discuss theoretical and numerical difficulties associated with the direction switching phenomenon.