Palestras e Seminários
22/09/2021
11:00
virtual/à distância
Palestrante: Arthur C. Cunha
https://sites.google.com/view/sdnl-icmc-usp/seminarios
Responsável: Estefani Moraes Moreira (Este endereço de email está sendo protegido de spambots. Você precisa do JavaScript ativado para vê-lo.)
Seminários em Dinâmica não Linear
In this talk we find an upper bound for the fractal dimension of uniform attractors in Banach spaces. The main technique we employ is essentially based on a compact embedding of some auxiliary Banach space into the phase space and a corresponding smoothing effect between these spaces. Our bounds on the fractal
dimension of uniform attractors are given in terms of the dimension of the symbol space and the Kolmogorov entropy number of the embedding. In addition, a dynamical analysis on the symbol space is also given, showing that the finite-dimensionality of the hull of a time-dependent function is fully determined by the tails of the function, which allows us to consider more general non-autonomous terms than quasi-periodic functions. As application we show that the uniform attractor of the reaction-diffusion equation is finite dimensional in L^2 and in L^p, with p > 2.
