Programa de Verão do IME-UFBA 2024

Semana Temática de Equações Diferenciais Parciais

Terça-feira dia 05/03/2024


• 10h (Apertura)
  Palestra: Smoothing and finite-dimensionality of uniform attractors in banach spaces.
  Palestrante: Prof. Arthur Cavalcante Cunha (IME-UFBA)
  Resumo: The aim of this talk is to find an upper bound for the fractal dimension of uniform attractors in Banach spaces. The main technique 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. 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 a reaction-diffusion equation is finite-dimensional in L^2 and in L^p, with p > 2.
  


• 14h
  Palestra: Exponential stability of the von Kármán system with internal damping.
  Palestrante: Prof.a Roseane Martins (IME-UFBA)
  Resumo: This work deals with a von Kármán system with internal damping. For the solution's existence, we use nonlinear semigroup theory tools. We construct an evolution system by nonlinear Lipschitz perturbation of a semigroup of contractions. We apply the energy method for the asymptotic behavior, which uses suitable multipliers to construct a Lyapunov functional that leads to exponential decay.

Quarta-feira dia 06/03/2024


• 10h
  Palestra: Suspension bridge with internal damping.
  Palestrante: Prof. Leandro Correia de Araájo (UESB)
  Resumo: This work deals with a suspension bridge model with internal damping. We use semigroup theory. The existence of solution is proved by applying the Lumer-Phillips theorem. Exponential stability is obtained due to the analyticity of the semigroup associated with the energy space.


• 14h
  Palestra: Well-posedness and exponential stability for Timoshenko-Ehrenfest system with internal dissipation of fractional derivative type.
  Palestrante: Rafael Oliveira de Jesus (UPE).
  Resumo: We deal with the well-posedness, strong and exponential stability for Timoshenko-Ehrenfest system with internal dissipation of fractional derivative type. We use semigroup theory. The existence and uniqueness of the solution are obtained by applying the Lumer-Phillips Theorem. We present two results for the asymptotic behavior: strong stability of the C0-semigroup associated with the system using the Arendt-Batty and Lyubich-Vu'ss general criterion and the exponential stability applying the Gearhart-Prüss-Huang's theorem.
  


• 16h (Encerramento)
  Palestra: Ponte suspensa: Aspetos recentes em EDP
  Palestrante: Carlos Alberto Raposo (IME-UFBA)
  Resumo: Iremos apresentar alguns modelos de ponte suspensas, onde o deck é modelado não necessariamente por vigas de Timoshenko.
  

Todas as atividades serão presenciais e acontecerão na Sala 13 do IME-UFBA.