date
-
modality
In person
description
- Seminario de jóvenes investigadores
- Fecha y hora: martes 9 de diciembre, 10:00
- Lugar: Seminario 2, IMAG
- Ponente: Niccolô Tassi (Universidad de Granada)
- Title: Asymptotic behaviour of Nonlocal and Kinetic equations
- Abstract: Understanding the long-time dynamics of partial differential equations is essential for predicting how these models evolve, assessing their stability, and detecting critical phenomena such as blow-up or bifurcations. In this talk, I will discuss the asymptotic behaviour of certain nonlocal and kinetic equations, which can roughly be divided into confining and non-confining types. In the confining case, where a stationary state exists, various analytical techniques allow one to establish quantitative convergence results. I will present some recent results obtained with José Cañizo (Granada), where we apply Harris’s theorem to prove a uniform spectral gap for a family of nonlocal approximations of classical and fractional Fokker–Planck equations, and consequently proving uniform-in-time convergence with respect to the approximation parameter. In contrast, the long-time behavior of non-confining equations is still poorly understood. I will also discuss some results and ongoing work with José Cañizo and Stéphane Mischler (Paris Dauphine), where we extend some of the previous idea to this more challenging unconfined setting.
activity type