Existence and characterization of attractors for a nonlocal reaction-diffusion equation having an energy functional
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866910034153177088 |
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| author | Caballero, Rubén Marín-Rubio, Pedro Valero, José |
| author_facet | Caballero, Rubén Marín-Rubio, Pedro Valero, José |
| contents | In this paper we study a nonlocal reaction-diffusion equation in which the diffusion depends on the gradient of the solution. We prove first the existence and uniqueness of regular and strong solutions. Second, we obtain the existence of global attractors in both situations under rather weak assumptions by the defining a multivalued semiflow (which is a semigroup in the particular situation when uniqueness of the Cauchy problem is satisfied). Third, we characterize the attractor either as the unstable manifold of the set of stationary points or as the stable one when we consider solutions only in the set of bounded complete trajectories. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_23162 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Existence and characterization of attractors for a nonlocal reaction-diffusion equation having an energy functional Caballero, Rubén Marín-Rubio, Pedro Valero, José Dynamical Systems 35B40, 35B41, 35B51, 35K55, 35K57 In this paper we study a nonlocal reaction-diffusion equation in which the diffusion depends on the gradient of the solution. We prove first the existence and uniqueness of regular and strong solutions. Second, we obtain the existence of global attractors in both situations under rather weak assumptions by the defining a multivalued semiflow (which is a semigroup in the particular situation when uniqueness of the Cauchy problem is satisfied). Third, we characterize the attractor either as the unstable manifold of the set of stationary points or as the stable one when we consider solutions only in the set of bounded complete trajectories. |
| title | Existence and characterization of attractors for a nonlocal reaction-diffusion equation having an energy functional |
| topic | Dynamical Systems 35B40, 35B41, 35B51, 35K55, 35K57 |
| url | https://arxiv.org/abs/2602.23162 |