About the Structure of Attractors for a Nonlocal Chafee-Infante Problem

Rubén Caballero, Alexandre N. Carvalho, Pedro Marín-Rubio and José Valero
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Rubén Caballero: Centro de Investigación Operativa, Universidad Miguel Hernández de Elche, Avenida Universidad s/n, 03202 Elche, Spain
Alexandre N. Carvalho: Instituto de Ciências Matemáticas e de Computaçao, Universidade de São Paulo, Campus de São Carlos, Caixa Postal 668, 13560-970 São Carlos, Brazil
Pedro Marín-Rubio: Departamento Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, C/Tarfia, 41012 Sevilla, Spain
José Valero: Centro de Investigación Operativa, Universidad Miguel Hernández de Elche, Avenida Universidad s/n, 03202 Elche, Spain

Mathematics, 2021, vol. 9, issue 4, 1-36

Abstract: In this paper, we study the structure of the global attractor for the multivalued semiflow generated by a nonlocal reaction-diffusion equation in which we cannot guarantee the uniqueness of the Cauchy problem. First, we analyse the existence and properties of stationary points, showing that the problem undergoes the same cascade of bifurcations as in the Chafee-Infante equation. Second, we study the stability of the fixed points and establish that the semiflow is a dynamic gradient. We prove that the attractor consists of the stationary points and their heteroclinic connections and analyse some of the possible connections.

Keywords: reaction-diffusion equations; nonlocal equations; global attractors; multivalued dynamical systems; structure of the attractor; stability; Morse decomposition (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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