Palestra 1
Titulo: Stabilization of a time delayed for a generalized dispersive system.
Palestrante: Fernando A. Gallego (Universidad Nacional de Colombia)
Data: 08/02/2023
Horário: 11:00
Local: sala C-119
Resumo: In this talk we study the asymptotic behavior of the solution of the time–delayed higher order dispersive systems posed in the real line. Under suitable assumptions on the time delay coefficients we prove that the system under consideration is exponentially stable in two different ways. First, if the coefficient of the delay term is bounded from below by a positive constant, we use the Lyapunov approach to prove that the energy associated to the solution of the higher order dispersive system decays exponentially. After that, we extend this result to the case in which the coefficient of the undelayed feedback is also indefinite. Both problems are investigated when the exponent p in the nonlinear term ranges over the interval [1, 2j) where 2j + 1 is the order of the dispersive system.

Palestra 2
Titulo: A coupling approach to quantify the transportation Wasserstein path-distance between heat equation and the Goldstein--Kac telegraph equation.
Palestrante: Gerardo Barrera (University of Helsinki)
Data: 08/02/2023
Horário: 12:00
Local: sala C-119
Resumo: In this talk, I will present a non-asymptotic process level control between the so-called telegraph process (a.k.a. Goldstein-Kac equation) and a diffusion process with suitable diffusivity constant (explicit) via a transportation Wasserstein path-distance with quadratic average cost.

We stress that the telegraph process solves a partial linear differential equation of the hyperbolic type for which explicit computations can be carried by in terms of Bessel functions. In the present talk, I will discuss the coupling approach, which is a robust technique that can be used for more general PDEs. The proof is done via the interplay of the following couplings: coin-flip coupling, synchronous coupling and the celebrated Komlós-Major-Tusnády coupling. In addition, non-asymptotic estimates for the corresponding L^p time average are given explicitly.

The talk is based on joint work with Jani Lukkarinen, University of Helsinki, Finland."