Invariant Manifolds for Random Parabolic Evolution Equations with almost sectorial operators
Probability
2024-10-28 v1 Dynamical Systems
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.
Keywords
Cite
@article{arxiv.2410.19509,
title = {Invariant Manifolds for Random Parabolic Evolution Equations with almost sectorial operators},
author = {M. Ghani Varzaneh and F. Z. Lahbiri and S. Riedel},
journal= {arXiv preprint arXiv:2410.19509},
year = {2024}
}