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

• Ano de defesa: 2022
• Autor(a) principal: Moura, Rafael de Oliveira
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Biblioteca Digitais de Teses e Dissertações da USP
• Palavras-chave em Português: Análise espectral; Atrator global; Chafee-Infante equation; Equação de Chafee-Infante; Equação de Chafee-Infante não-local; Equação de Chafee-Infante quasilinear; Equações diferenciais parciais semilineres; Global attractor; Gradient semigroups; Nonlocal Chafee-Infante equation; Quasilinear Chafee-Infante equation; Semigroups; Semigrupos; Semigrupos gradientes; Semilinear partial differential equations; Spectral analysis
• Link de acesso: https://www.teses.usp.br/teses/disponiveis/55/55135/tde-27052022-102622/

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.