Finite Fractal Dimension of uniform attractors for non-autonomous dynamical systems with infinite dimensional symbol space
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866913375049482240 |
|---|---|
| author | Moura, Rafael de Oliveira de Carvalho, Alexandre Nolasco Langa, José A. |
| author_facet | Moura, Rafael de Oliveira de Carvalho, Alexandre Nolasco Langa, José A. |
| contents | The aim of this paper is to find an upper bound for the box-counting dimension of uniform attractors for non-autonomous dynamical systems. Contrary to the results in literature, we do not ask the symbol space to have finite box-counting dimension. Instead, we ask a condition on the semi-continuity of pullback attractors of the system as time goes to infinity. This semi-continuity can be achieved if we suppose the existence of finite-dimensional exponential uniform attractors for the limit symbols. After showing these new results, we apply them to study the box-counting dimension of the uniform attractor for a reaction-diffusion equation, and we find a specific forcing term such that the symbol space has infinite box-counting dimension but the uniform attractor has finite box-counting dimension anyway. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_17367 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Finite Fractal Dimension of uniform attractors for non-autonomous dynamical systems with infinite dimensional symbol space Moura, Rafael de Oliveira de Carvalho, Alexandre Nolasco Langa, José A. Dynamical Systems Analysis of PDEs 35Q30, 35B41, 35K58, 76D05 The aim of this paper is to find an upper bound for the box-counting dimension of uniform attractors for non-autonomous dynamical systems. Contrary to the results in literature, we do not ask the symbol space to have finite box-counting dimension. Instead, we ask a condition on the semi-continuity of pullback attractors of the system as time goes to infinity. This semi-continuity can be achieved if we suppose the existence of finite-dimensional exponential uniform attractors for the limit symbols. After showing these new results, we apply them to study the box-counting dimension of the uniform attractor for a reaction-diffusion equation, and we find a specific forcing term such that the symbol space has infinite box-counting dimension but the uniform attractor has finite box-counting dimension anyway. |
| title | Finite Fractal Dimension of uniform attractors for non-autonomous dynamical systems with infinite dimensional symbol space |
| topic | Dynamical Systems Analysis of PDEs 35Q30, 35B41, 35K58, 76D05 |
| url | https://arxiv.org/abs/2405.17367 |