Approximation of Stochastic Invariant Manifolds

Stochastic Manifolds for Nonlinear SPDEs I

Nonfiction, Science & Nature, Mathematics, Differential Equations, Mathematical Analysis
Cover of the book Approximation of Stochastic Invariant Manifolds by Honghu Liu, Mickaël D. Chekroun, Shouhong Wang, Springer International Publishing
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Author: Honghu Liu, Mickaël D. Chekroun, Shouhong Wang ISBN: 9783319124964
Publisher: Springer International Publishing Publication: December 20, 2014
Imprint: Springer Language: English
Author: Honghu Liu, Mickaël D. Chekroun, Shouhong Wang
ISBN: 9783319124964
Publisher: Springer International Publishing
Publication: December 20, 2014
Imprint: Springer
Language: English

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.

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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.

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