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arXiv · 0901.0382

Invariant manifolds for random and stochastic partial differential equations

Tomas Caraballo·Jinqiao Duan·Kening Lu·Bjorn Schmalfuss
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Abstract

Random invariant manifolds are geometric objects useful for understanding complex dynamics under stochastic influences. Under a nonuniform hyperbolicity or a nonuniform exponential dichotomy condition, the existence of random pseudo-stable and pseudo-unstable manifolds for a class of \emph{random} partial differential equations and \emph{stochastic} partial differential equations is shown. Unlike the invariant manifold theory for stochastic \emph{ordinary} differential equations, random norms are not used. The result is then applied to a nonlinear stochastic partial differential equation with linear multiplicative noise.

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Tomas Caraballo, Jinqiao Duan, Kening Lu, Bjorn Schmalfuss. 2009-01-04. Invariant manifolds for random and stochastic partial differential equations. https://arxiv.org/abs/0901.0382

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