• JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
 
  Bookmark and Share
 
 
Master's Dissertation
DOI
10.11606/D.55.2012.tde-11042012-155404
Document
Author
Full name
Cesar Augusto Esteves das Neves Cardoso
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2012
Supervisor
Committee
Carvalho, Alexandre Nolasco de (President)
Bruschi, Simone Mazzini
Paiva, Francisco Odair Vieira de
Title in Portuguese
Convergência compacta de resolvente e o teorema de Trotter Kato para perturbações singulares
Keywords in Portuguese
Convergência compacta
Homogeneização
Semigrupos
Abstract in Portuguese
Nesta dissertação estudamos uma versão do Teorema de Trotter-Kato que estabelece uma equivalência entre a continuidade, relativamente a um parâmetro, de operadores resolvente e a continuidade dos semigrupos lineares associados. Os operadores ilimitados envolvidos (geradores de semigrupos analíticos) estão definidos em espaços que variam com o parâmetro e isto nos leva a ter que comparar elementos de espaços de Banach diferentes. Este resultado é aplicado a um problema de Neumann em um domínio fino com fronteira altamente oscilante e que se degenera a um intervalo quando o parâmetro varia. Nesta aplicação, utilizamos o método das múltiplas escalas (comum em teoria de homogeneização) para obter formalmente o problema limite (veja [17]) e, em seguida, provamos a convergência compacta dos operadores resolventes utilizando as funções teste oscilantes de Tartar [15], [16] (veja também Cioranescu e Saint Jean Paulin [12]), obtidas através de um problema auxiliar, juntamente com operadores de extensão
Title in English
Compact convergence of resolvent and Trotter-Kato's Theorem for singular pertubations
Keywords in English
Compact convergence
Homogeneization
Semigroups
Abstract in English
In this work we study a version of Trotter-Katos Theorem that establishes an equivalence between the continuity, with respect to a parameter, of the resolvent operators and the continuity of the associated linear semigroups. The unbounded operators involved (generators of analytic semigroups) are defined spaces that vary with the parameter leading us to introduce methods to compare vectors in different Banach spaces. We apply this theorem to an elliptic boundary value problem with Neumann boundary condition in a highly oscillating thin domain that degenerates to a line segment as the parameter varies. In this application we use the multiple scale method (frequently used in the homogenization theory) to obtain, formally, the limiting problem (see [17]) and, in the sequel, we prove the compact convergence of resolvent operators using the oscillating test functions of Tartar [15] (see also [16] and Cioranescu and Saint Jean Paulin [12]) defined with the aid of an auxiliary problem as well as extension operators
 
WARNING - Viewing this document is conditioned on your acceptance of the following terms of use:
This document is only for private use for research and teaching activities. Reproduction for commercial use is forbidden. This rights cover the whole data about this document as well as its contents. Any uses or copies of this document in whole or in part must include the author's name.
cesarrev.pdf (699.57 Kbytes)
Publishing Date
2012-04-11
 
WARNING: Learn what derived works are clicking here.
All rights of the thesis/dissertation are from the authors
Centro de Informática de São Carlos
Digital Library of Theses and Dissertations of USP. Copyright © 2001-2020. All rights reserved.