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| Author(s): |
Camila Leão Cardozo
Total Authors: 1
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| Document type: | Doctoral Thesis |
| Press: | São Carlos. |
| Institution: | Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB) |
| Defense date: | 2017-11-01 |
| Examining board members: |
Ma To Fu;
Everaldo de Mello Bonotto;
Antonio Castelo Filho;
Luci Harue Fatori;
Marcelo José Dias Nascimento
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| Advisor: | Márcio Fuzeto Gameiro |
| Abstract | |
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. (AU) | |
| FAPESP's process: | 12/16218-2 - Rigorous Construction of Manifolds of Solutions of PDEs |
| Grantee: | Camila Leão Cardozo |
| Support Opportunities: | Scholarships in Brazil - Doctorate |