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Doctoral Thesis
DOI
https://doi.org/10.11606/T.45.2019.tde-30042019-150438
Document
Author
Full name
Ânderson da Silva Vieira
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2014
Supervisor
Committee
Pava, Jaime Angulo (President)
Fernández, Adan José Corcho
Natali, Fábio Matheus Amorin
Oliva Filho, Sergio Muniz
Oliveira, Luiz Augusto Fernandes de
Title in Portuguese
Dinâmica da equação de Schrödinger com potencial delta de Dirac em espaço com peso
Keywords in Portuguese
Equação de Schrödinger não-linear
Espaços Lp e de Sobolev com peso
Potencial delta de Dirac
Variedade invariante centro
Abstract in Portuguese
Nesse trabalho, estudamos a equação de Schrödinger não-linear com uma função potencial delta atrativa. As soluções para essa equação tem uma componente localizada e uma dispersiva. Além de estudar o comportamento das soluções dessa equação em espaços de Sobolev clássicos, mostramos algumas propriedades do grupo unitário em espaços Lp, L2 com peso, Sobolev com peso e assim obtemos alguns resultados de boa colocação local e global das soluções. O ponto central desta tese é mostrarmos a existência de uma variedade invariante centro que irá consistir de órbitas periódicas no tempo.
Title in English
Dynamics of Schrödinger equation with Dirac delta potential in weighted space
Keywords in English
Center invariant manifold
Delta Dirac potential
Nonlinear Schrödinger equation
Weighted Lp and Sobolev spaces
Abstract in English
In this work, we study the nonlinear Schrodinger equation with an attractive delta function potential.The solutions to this equation have a localized and a dispersive component. In addition to studying the behavior of solutions of this equation in classical Sobolev space, we show some properties for the unitary group in Lp, weighted L2 and Sobolev spaces and so we get some results of local and global well-posedness of solutions. The central theme this thesis is to show the existence of a center invariant manifold, which will consist of time-periodic orbits.
 
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Tese_versao_final.pdf (958.36 Kbytes)
Publishing Date
2019-04-30
 
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