Artículo
Invariant manifolds for stochastic delayed partial differential equations of parabolic type
Autor/es | Hu, Wenjie
Caraballo Garrido, Tomás |
Departamento | Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico |
Fecha de publicación | 2023-06-12 |
Fecha de depósito | 2023-11-06 |
Publicado en |
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Resumen | The aim of this paper is to prove the existence and smoothness of stable and unstable
invariant manifolds for a stochastic delayed partial differential equation of parabolic type.
The stochastic delayed partial differential ... The aim of this paper is to prove the existence and smoothness of stable and unstable invariant manifolds for a stochastic delayed partial differential equation of parabolic type. The stochastic delayed partial differential equation is firstly transformed into a random delayed partial differential equation by a conjugation, which is then recast into a Hilbert space. For the auxiliary equation, the variation of constants formula holds and we show the existence of Lipschitz continuous stable and unstable manifolds by the Lyapunov-Perron method. Subsequently, we prove the smoothness of these invariant manifolds under appropriate spectral gap condition by carefully investigating the smoothness of auxiliary equation, after which, we obtain the invariant manifolds of the original equation by projection and inverse transformation. Eventually, we illustrate the obtained theoretical results by their application to a stochastic single-species population model. |
Cita | Hu, W. y Caraballo Garrido, T. (2023). Invariant manifolds for stochastic delayed partial differential equations of parabolic type. Chaos, Solitons & Fractals, 176 (noviembre), 114189-1. https://doi.org/10.1016/j.chaos.2023.114189. |
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