Stability and hyperbolicity of equilibria for a nonlocal quasilinear Chafee-Infante equation

• Grant number: 21/01132-4
• Support Opportunities: Scholarships in Brazil - Master
• Start date: June 01, 2021
• End date: March 31, 2022
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Alexandre Nolasco de Carvalho
• Grantee: Rafael de Oliveira Moura
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

This project aims to study the topics of spectral theory of operators, theory of semigroups and their generators and geometric theory of parabolic semilinear differential equations, and then to apply such knowledge to analyze the semilinear Chafee-Infante equation. Finally, we seek to study stability and hyperbolicity of equilibria for a non-local quasilinear Chafee-Infante equation, making use of a method of linearization for quasilinear problems, which has been developed in [1], in order to conclude that the saddle-point property holds for the equilibria of this equation. (AU)

Academic Publications

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

MOURA, Rafael de Oliveira. Stability and hyperbolicity of equilibria for a nonlocal quasilinear Chafee-Infante equation. 2022. Master's Dissertation - Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB) São Carlos.