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Smooth stable and unstable manifolds for stochastic evolutionary equations. (English) Zbl 1065.60077
The paper gives conditions for existence and smoothness of stable and unstable manifolds for a class of abstract stochastic partial differential equations of the form \(du=\bigl(Au+F(u)\bigr)\,dt+u\circ dW_t\), where \(A\) is a generator of a strongly continuous semigroup on a separable Hilbert space \(H\), \(F:H\to H\) is globally Lipschitz with \(F(0)=0\), and \(W\) is a one-dimensional Wiener process.

MSC:
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
37L55 Infinite-dimensional random dynamical systems; stochastic equations
37D10 Invariant manifold theory for dynamical systems
37L25 Inertial manifolds and other invariant attracting sets of infinite-dimensional dissipative dynamical systems
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