Structure of the attractor for a non-local Chafee-Infante problem

TL;DR

This paper analyzes the global attractor structure of a non-local one-dimensional quasilinear problem related to the Chafee-Infante problem, using Conley index and connection matrix theories to identify heteroclinic connections.

Contribution

It provides a complete description of the attractor's structure for a non-local Chafee-Infante type problem, employing topological methods.

Findings

Identification of heteroclinic connections between equilibria

Complete characterization of the attractor's geometric structure

Application of Conley index and connection matrix theories

Abstract

In this article, we study the structure of the global attractor for a non-local one-dimensional quasilinear problem. The strong relation of our problem with a non-local version of the Chafee-Infante problem allows us to describe the structure of its attractor. For that, we made use of the Conley index and the connection matrix theories in order to find geometric information such as the existence of heteroclinic connections between the equilibria. In this way, the structure of the attractor is completely described.