Invariant manifolds for stochastic partial differential equations.

DOI10.1214/aop/1068646380zbMath1052.60048arXivmath/0409485OpenAlexW1963932485MaRDI QIDQ1433894

Kening Lu, Björn Schmalfuss, Jin-qiao Duan

Publication date: 1 July 2004

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0409485

zbMATH Keywords

invariant manifoldscocyclesstochastic partial differential equationgeneralized fixed pointnonautonomous dynamical systems

Mathematics Subject Classification ID

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

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Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Geometric theory of semilinear parabolic equations
• Characteristic exponents and invariant manifolds in Hilbert space
• Smooth invariant foliations in infinite dimensional spaces
• Convex analysis and measurable multifunctions
• A random fixed point theorem and the random graph transformation
• The random attractor of the stochastic Lorenz system
• Center manifolds for infinite dimensional nonautonomous differential equations
• Invariant manifolds for stochastic partial differential equations.
• The stable manifold theorem for stochastic differential equations
• Pullback attracting inertial manifolds for nonautonomous dynamical systems
• Existence and persistence of invariant manifolds for semiflows in Banach space
• Construction of stochastic inertial manifolds using backward integration
• A stochastic pitchfork bifurcation in a reaction-diffusion equation
• Inertial manifolds and stationary measures for stochastically perturbed dissipative dynamical systems
• Stochastic inertial manifold
• Stochastic Equations in Infinite Dimensions

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