About the structure of attractors for a nonlocal Chafee-Infante problem
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866910034725699584 |
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| author | Caballero, Rubén Carvalho, Alexandre Nolasco Marín-Rubio, Pedro Valero, José |
| author_facet | Caballero, Rubén Carvalho, Alexandre Nolasco Marín-Rubio, Pedro Valero, José |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_23451 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | About the structure of attractors for a nonlocal Chafee-Infante problem Caballero, Rubén Carvalho, Alexandre Nolasco Marín-Rubio, Pedro Valero, José Dynamical Systems 35B40, 35B41, 35B51, 35K55, 35K57 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. |
| title | About the structure of attractors for a nonlocal Chafee-Infante problem |
| topic | Dynamical Systems 35B40, 35B41, 35B51, 35K55, 35K57 |
| url | https://arxiv.org/abs/2602.23451 |