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arXiv · 2602.23451

About the structure of attractors for a nonlocal Chafee-Infante problem

Rubén Caballero·Alexandre Nolasco Carvalho·Pedro Marín-Rubio·José Valero
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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 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 dynamically gradient. We prove that the attractor consists of the stationary points and their heteroclinic connections and analyse some of the possible connections.

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Rubén Caballero, Alexandre Nolasco Carvalho, Pedro Marín-Rubio, José Valero. 2026-02-26. About the structure of attractors for a nonlocal Chafee-Infante problem. https://arxiv.org/abs/2602.23451

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