• 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
 
 
Doctoral Thesis
DOI
10.11606/T.45.2016.tde-20052016-141417
Document
Author
Full name
Hector Jose Cabarcas Urriola
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2015
Supervisor
Committee
Pava, Jaime Angulo (President)
Fernández, Adan José Corcho
Goloshchapova, Nataliia
Panthee, Mahendra Prasad
Petronilho, Gerson
Title in Portuguese
Propriedades de continuação única para soluções de equações de Schrödinger com ponto de interação
Keywords in Portuguese
Delta de Dirac
Equação de Schrödinger
Propriedade de continuação única
Abstract in Portuguese
Neste trabalho, estudamos propriedades de continuação única para as soluções da equação tipo Schrödinger com um ponto interação centrado em x=0, \partial_tu=i(\Delta_Z+V)u, onde V=V(x,t) é uma função de valor real e -\Delta_Z é o operador escrito formalmente como \[-\Delta_Z=-\frac\frac{d^2}{dx^2}+Z\delta_0,\] sendo \delta_0 a delta de Dirac centrada em zero e Z qualquer número real. Logo, usamos estes resultados para ver o possível fenômeno de concentração das soluções, que explodem, da equação de tipo Schrödinger não linear com um ponto de interação em x=0, \[\partial_tu=i(\Delta_Zu+|u|^u),\] com ho>5. Também, mostramos que para certas condições sobre o potencial dependente do tempo V, a equação linear em cima tem soluções não triviais.
Title in English
Unique continuation properties for solutions of Schrödinger equations with point interaction
Keywords in English
Dirac's delta
Schrödinger equations
Unique continuation
Abstract in English
In this work, we study unique continuation properties for solutions of the Schrödinger equations with an point interaction centered at $x=0$, \begin\label \partial_tu=i(\Delta_Z+V)u, \end where $V=V(x,t)$ is real value function and $-\Delta_Z$ is the operator formally written \[-\Delta_Z=-\frac\frac{d^2}{dx^2}+Z\delta_0,\] and $\delta_0$ is Dirac's delta centered at zero and $Z$ is a real number. Next, we use these results in order to study the possible profile of the concentration of blow up solutions for the non linear Schrödinger equation with a point interaction at $x=0$, \[\partial_tu=i(\Delta_Zu+|u|^u),\] with $ho>5$. Besides, we show that the equation above has non trivial solutions for some conditions on the time dependent potencial $V$.
 
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.
Tese.pdf (664.99 Kbytes)
Publishing Date
2016-05-23
 
WARNING: Learn what derived works are clicking here.
All rights of the thesis/dissertation are from the authors
CeTI-SC/STI
Digital Library of Theses and Dissertations of USP. Copyright © 2001-2020. All rights reserved.