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Invariant manifolds for stochastic partial differential equations. (English) Zbl 1052.60048
Stochastic partial differential equations with multiplicative noises are considered and the existence of invariant manifold is studied. Firstly, random graph transforms are introduced and a fixed point theorem for nonautonomous systems is given. Generalized fixed points of this transform give the desired manifold.

60H15 Stochastic partial differential equations (aspects of stochastic analysis)
37H10 Generation, random and stochastic difference and differential equations
37L55 Infinite-dimensional random dynamical systems; stochastic equations
37D10 Invariant manifold theory for dynamical systems
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