Programa de Verão do IMEUFBA 2024
Semana Temática de Equações Diferenciais Parciais
 Terçafeira dia 05/03/2024

10h (Apertura)
Palestra: Smoothing and finitedimensionality of uniform attractors in banach spaces.
Palestrante: Prof. Arthur Cavalcante Cunha (IMEUFBA)
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 finitedimensionality of the hull of a timedependent function is fully determined by the tails of the function, which allows us to consider more general nonautonomous terms than quasiperiodic functions. As application, we show that the uniform attractor of a reactiondiffusion equation is finitedimensional 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 (IMEUFBA)
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. 
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 LumerPhillips theorem. Exponential stability is obtained due to the analyticity of the semigroup associated with the energy space. 
14h
Palestra: Wellposedness and exponential stability for TimoshenkoEhrenfest system with internal dissipation of fractional derivative type.
Palestrante: Rafael Oliveira de Jesus (UPE).
Resumo: We deal with the wellposedness, strong and exponential stability for TimoshenkoEhrenfest system with internal dissipation of fractional derivative type. We use semigroup theory. The existence and uniqueness of the solution are obtained by applying the LumerPhillips Theorem. We present two results for the asymptotic behavior: strong stability of the C0semigroup associated with the system using the ArendtBatty and LyubichVu'ss general criterion and the exponential stability applying the GearhartPrüssHuang's theorem.

16h (Encerramento)
Palestra: Ponte suspensa: Aspetos recentes em EDP
Palestrante: Carlos Alberto Raposo (IMEUFBA)
Resumo: Iremos apresentar alguns modelos de ponte suspensas, onde o deck é modelado não necessariamente por vigas de Timoshenko.
Quartafeira dia 06/03/2024
Todas as atividades serão presenciais e acontecerão na Sala 13 do IMEUFBA.