| Abstract: |
| In this talk, we investigate several macroscopic PDE models for pedestrian dynamics describing the spatio-temporal evolution of a population under stress (panic) in dangerous situations. We first present a first-order model for the evacuation of a stressed population from a room with an exit, incorporating different interacting human behaviors. For this model, we establish the local existence, uniqueness, and regularity of solutions using semigroup theory, together with their positivity and \(L^1\)-boundedness. To illustrate the propagation of stress (panic) and its impact on evacuation dynamics, we provide numerical simulations of several evacuation scenarios, with particular emphasis on populations with a low-risk culture in emergency situations. We then introduce a second-order model to better capture stress effects within the population and compare its dynamics with those of the first-order model. |
|