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

• Autor: Moura, Rafael De Oliveira
• Orientador: Carvalho, Alexandre Nolasco de
  
• Assuntos: Análise Espectral; Semigrupos; Semigrupos Gradientes; Equações Diferenciais Parciais Semilineres; Equação De Chafee-Infante Quasilinear; Equação De Chafee-Infante Não-Local; Equação De Chafee-Infante; Atrator Global; Semilinear Partial Differential Equations; Semigroups; Quasilinear Chafee-Infante Equation; Nonlocal Chafee-Infante Equation; Gradient Semigroups; Global Attractor; Chafee-Infante Equation; Spectral Analysis
• Notas: Dissertação (Mestrado)
  
• Descrição: In this work we present the topics of spectral theory of operators, theory of semigroups and their generators and geometric theory of parabolic semilinear differential equations, and then apply these theories to analyze the qualitative aspects of 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 (CARVALHO; MOREIRA, 2021), in order to conclude that the equilibria of this complicated equation inherit some properties of stability and hyperbolicity from the classical semilinear equation.
  
• DOI: 10.11606/D.55.2022.tde-27052022-102622
  
• Editor: Biblioteca Digital de Teses e Dissertações da USP; Universidade de São Paulo; Instituto de Ciências Matemáticas e de Computação
  
• Data de criação/publicação: 2022-03-28
  
• Formato: Adobe PDF
  
• Idioma: Inglês