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

Grant number: 21/01132-4
Support type:Scholarships in Brazil - Master
Effective date (Start): June 01, 2021
Effective date (End): March 31, 2022
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Analysis
Principal researcher:Alexandre Nolasco de Carvalho
Grantee:Rafael de Oliveira Moura
Home 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)

News published in Agência FAPESP Newsletter about the scholarship: