Séminaire de EDP - Physique Mathématique

Pas de séminaire

TBA

Pas de séminaire

In this talk, we describe and discuss elements of mathematical theory of the Hughes model for pedestrian evacuation. We present recent existence results obtained with M.D. Rosini, G. Stivaletta and with T. Girard for the one-dimensional case, either via convergence of the deterministic many-particle approximation or via the Schauder fixed-point approach, along with the limitations and the extensions of our approach. Some numerical simulations, in one and two directions, will also be presented and commented.

The Bismut hypoelliptic Laplacian, a geometric version of the Kramers-Fokker-Planck operator, is a two-parameter-dependent operator: $b$ (the inverse of the friction parameter) and $h$ (the temperature). I will discuss the high-friction limit ($b \to 0$) and the low-temperature limit ($h \to 0$) for the hypoelliptic Laplacian. In this limit, the hypoelliptic Laplacian converges to the Witten Laplacian, with a comparison of their spectra.