This first volume is concerned with the analytic derivation of explicit formulas for the leading-order Taylor approximations of (local) stochastic invariant manifolds associated with a broad class of nonlinear stochastic partial differential equations. These approximations take the form of Lyapunov-Perron integrals, which are further characterized in Volume II as pullback limits associated with some partially coupled backward-forward systems. This pullback characterization provides a useful interpretation of the corresponding approximating manifolds and leads to a simple framework that unifies some other approximation approaches in the literature. A self-contained survey is also included on the existence and attraction of one-parameter families of stochastic invariant manifolds, from the point of view of the theory of random dynamical systems.
Approximation of Stochastic Invariant Manifolds Ebook
Stochastic Manifolds for Nonlinear SPDEs I
By: Micka?l D. Chekroun; Honghu Liu; Shouhong Wang
Publisher:
Springer
Print ISBN: 9783319124957, 3319124951
eText ISBN: 9783319124964, 331912496X
Copyright year: 2015
Format: PDF
Available from $ 54.99 USD
SKU: 9783319124964
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