Full text
| |
| Author(s): |
Rafael de Oliveira Moura
Total Authors: 1
|
| Document type: | Master's Dissertation |
| Press: | São Carlos. |
| Institution: | Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB) |
| Defense date: | 2022-03-28 |
| Examining board members: |
Alexandre Nolasco de Carvalho;
Flank David Morais Bezerra;
Everaldo de Mello Bonotto;
Juliana Fernandes da Silva Pimentel
|
| Advisor: | Alexandre Nolasco de Carvalho |
| Abstract | |
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. (AU) | |
| FAPESP's process: | 21/01132-4 - Stability and hyperbolicity of equilibria for a nonlocal quasilinear Chafee-Infante equation |
| Grantee: | Rafael de Oliveira Moura |
| Support Opportunities: | Scholarships in Brazil - Master |