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arXiv · 2311.17625

Smooth center-stable/unstable manifolds and foliations of stochastic evolution equations with non-dense domain

Zonghao Li·Caibin Zeng·Jianhua Huang
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Abstract

The current paper is devoted to the asymptotic behavior of a class of stochastic PDE. More precisely, with the help of the theory of integrated semigroups and a crucial estimate of the random Stieltjes convolution, we study the existence and smoothness of center-unstable invariant manifolds and center-stable foliations for a class of stochastic PDE with non-dense domain through the Lyapunov-Perron method. Finally, we give two examples about a stochastic age-structured model and a stochastic parabolic equation to illustrate our results.

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Zonghao Li, Caibin Zeng, Jianhua Huang. 2023-11-29. Smooth center-stable/unstable manifolds and foliations of stochastic evolution equations with non-dense domain. https://arxiv.org/abs/2311.17625

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