Invariant manifolds for random and stochastic partial differential equations

Details Invariant manifolds for random and stochastic partial differential equations Invariant manifolds for random and stochastic partial differential equations

2009-01-04

arxiv.org/abs/0901.0382v1

Mathematics

Dynamical Systems

Adv. Nonlinear Studies, in press, 2009

Scientific paper

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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