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Doctoral Thesis
DOI
10.11606/T.55.2018.tde-31012018-113548
Document
Author
Full name
Camila Leão Cardozo
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2017
Supervisor
Committee
Fu, Ma To (President)
Bonotto, Everaldo de Mello
Castelo Filho, Antonio
Fatori, Luci Harue
Nascimento, Marcelo José Dias
Title in Portuguese
Construção rigorosa  de variedades de soluções de EDPs
Keywords in Portuguese
Bifurcação cúspide
Computação rigorosa
Equação de Chan- Hilliard
Polinômios radiais
Abstract in Portuguese
O objetivo deste trabalho é construir rigorosamente variedades de soluções definidas implicitamente por equações não-lineares em dimensão infinita. Usando um método de continuação a múltiplos parâmetros aplicado a uma projeção em dimensão finita, uma triangulação da variedade é construída e usada para construir localmente a variedade no espaço de dimensão infinita. Aplicamos este método para encontrar equilíbrio da equação de Cahn-Hilliard. Estudamos também bifurcações cúspides, com o objetivo de encontrar as condições necessárias para a existência das mesmas em qualquer dimensão finita.
Title in English
Rigorous construction of manifolds of solutions of PDEs
Keywords in English
Chan-Hilliard equation
Cusp bifurcation
Radii polinomios
Rigorous construction
Abstract in English
The goal of this research is to rigorously compute implicitly defined manifolds of solutions of infinite dimensional nonlinear equations. Using a multi-parameter continuation method on a finite dimensional projection, a triangulation of the manifold is computed and is then used to construct local charts of the global manifold in the infinite dimensional domain of the operator. We apply this method to find the equilibria of the Cahn-Hilliard equation. We also studied cusp bifurcations, in order to find the necessary conditions for the existence of the same in any finite dimension.
 
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Publishing Date
2018-01-31
 
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