Perturbation of boundary value problems

• Grant number: 24/14305-2
• Support Opportunities: Scholarships in Brazil - Support Program for Fixating Young Doctors
• Start date: September 01, 2024
• End date: August 31, 2025
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Agreement: CNPq
• Principal Investigator: Marcone Corrêa Pereira
• Grantee: Elaine Andressa Tavares de Lima
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated research grant: 24/01946-0 - Spectral Analysis of the Laplacian Operator in Two-Dimensional Strips, AP.R

Abstract

In this project we propose to study the behavior of the solutions of boundary value problems when the differential equation that defines it is perturbed. We will focus on the study of singular problems, motivated by areas as homogenization and asymptotic analysis of partial differential equations. We intend to study the existence of limit equations for the perturbed problems, the context in which such equations are well posed and the errors committed by the approximation. (AU)