Invariant Manifolds for Random Parabolic Evolution Equations with almost sectorial operators

M. Ghani Varzaneh; F. Z. Lahbiri; S. Riedel

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arXiv · 2410.19509

Invariant Manifolds for Random Parabolic Evolution Equations with almost sectorial operators

M. Ghani Varzaneh·F. Z. Lahbiri·S. Riedel

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Abstract

In this paper, we develop a way of analyzing the random dynamics of stochastic evolution equations with a non-dense domain. Such problems cover several types of evolution equations. We are particularly interested in evolution equations with non-homogeneous boundary conditions of white noise type. We prove the existence of stable, unstable, and center manifolds around a stationary trajectory by combining integrated semigroup theory and invariant manifold theory. The results are applied to stochastic parabolic equations with white noise at the boundary.

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M. Ghani Varzaneh, F. Z. Lahbiri, S. Riedel. 2024-10-25. Invariant Manifolds for Random Parabolic Evolution Equations with almost sectorial operators. https://arxiv.org/abs/2410.19509

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