• 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
https://doi.org/10.11606/T.55.2019.tde-12082019-103339
Document
Author
Full name
Mário César Monteiro do Prado
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2019
Supervisor
Committee
Gameiro, Márcio Fuzeto (President)
Bonotto, Everaldo de Mello
Castelo Filho, Antonio
Rodrigues, Savio Brochini
Title in Portuguese
Multiplicidade exata de soluções de equações diferenciais via um método assistido por computador
Keywords in Portuguese
Equações diferenciais
Métodos assistidos por computador.
Multiplicidade de soluções
Não-existência
Abstract in Portuguese
Neste trabalho, desenvolvemos um método assistido por computador para determinar todas as soluções de um determinado problema de valor de fronteira. Nossa abordagem combina estimativas de energia, validação rigorosa de soluções numéricas e um teste computacional rigoroso que verifica a inexistência de soluções nas regiões de interesse. O método obteve sucesso na obtenção da multiplicidade exata de soluções de equilíbrio das equações de SwiftHohenberg nas dimensões um e dois e na equação unidimensional de Cahn-Hilliard.
Title in English
Exact multiplicity of solutions of differential equations via computer-assisted methods.
Keywords in English
Computer-assisted methods.
Differential equations
Multiplicity of solutions
Non-existence
Abstract in English
In this work, we develope a computer-aided method to determine all solutions of a given boundary value problem. Our approach combines energy estimates, rigorous validation of numerical solutions and a rigorous computational test for verifying the non-existence of solutions in some regions of the solution space. The method was successful in obtaining the exact multiplicity of equilibria of a Swift-Hohenberg equation in dimensions one and two and of a one-dimensional Cahn-Hilliard equation, for some parameter values of these equations
 
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.
Publishing Date
2019-08-12
 
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 © 2001-2024. All rights reserved.