Event Details

  • 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.