Rigorous Construction of Manifolds of Solutions of PDEs

• Grant number: 12/16218-2
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: January 01, 2013
• End date: July 31, 2015
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Marcio Fuzeto Gameiro
• Grantee: Camila Leão Cardozo
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

The goal of this research project 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.

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

CARDOZO, Camila Leão. Rigorous construction of manifolds of solutions of PDEs. 2017. Doctoral Thesis - Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB) São Carlos.