Topological dimensions of random attractors for a stochastic reaction-diffusion equation with delay
The aim of this paper is to obtain an estimation of Hausdorff as well as fractal dimensions of random attractors for a stochastic reaction-diffusion equation with delay. The stochastic equation is firstly transformed into a delayed random partial differential equation by means of a random conjugatio...
| Autores: | , |
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| Formato: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2024 |
| País: | España |
| Recursos: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/164395 |
| Acesso em linha: | https://hdl.handle.net/11441/164395 https://doi.org/10.14232/ejqtde.2024.1.56 |
| Access Level: | acceso abierto |
| Palavra-chave: | Hausdorff dimension Fractal dimension Random dynamical system Random attractors Delay Stochastic reaction-diffusion equations |
| Resumo: | The aim of this paper is to obtain an estimation of Hausdorff as well as fractal dimensions of random attractors for a stochastic reaction-diffusion equation with delay. The stochastic equation is firstly transformed into a delayed random partial differential equation by means of a random conjugation, which is then recast into an auxiliary Hilbert space. For the obtained equation, it is firstly proved that it generates a random dynamical system (RDS) in the auxiliary Hilbert space. Then it is shown that the equation possesses random attractors by a uniform estimate of the solution and the asymptotic compactness of the generated RDS. After establishing the variational equation in the auxiliary Hilbert space and the almost surely differentiable properties of the RDS, upper estimates of both Hausdorff and fractal dimensions of the random attractors are obtained. |
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