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Approximation of Stochastic Invariant Manifolds = Stochastic Manifolds for Nonlinear SPDEs I /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Approximation of Stochastic Invariant Manifolds/ by Mickaël D. Chekroun, Honghu Liu, Shouhong Wang.
Reminder of title:	Stochastic Manifolds for Nonlinear SPDEs I /
Author:	Chekroun, Mickaël D.
other author:	Liu, Honghu.
Description:	XV, 127 p. 1 illus. in color.online resource. :
Contained By:	Springer Nature eBook
Subject:	Dynamics. -
Online resource:	https://doi.org/10.1007/978-3-319-12496-4
ISBN:	9783319124964

Approximation of Stochastic Invariant Manifolds = Stochastic Manifolds for Nonlinear SPDEs I /
Chekroun, Mickaël D.

Approximation of Stochastic Invariant ManifoldsStochastic Manifolds for Nonlinear SPDEs I /[electronic resource] :by Mickaël D. Chekroun, Honghu Liu, Shouhong Wang. - 1st ed. 2015. - XV, 127 p. 1 illus. in color.online resource. - SpringerBriefs in Mathematics,2191-8198. - SpringerBriefs in Mathematics,.

General Introduction -- Stochastic Invariant Manifolds: Background and Main Contributions -- Preliminaries -- Stochastic Evolution Equations -- Random Dynamical Systems -- Cohomologous Cocycles and Random Evolution Equations -- Linearized Stochastic Flow and Related Estimates -- Existence and Attraction Properties of Global Stochastic Invariant Manifolds -- Existence and Smoothness of Global Stochastic Invariant Manifolds -- Asymptotic Completeness of Stochastic Invariant Manifolds -- Local Stochastic Invariant Manifolds: Preparation to Critical Manifolds -- Local Stochastic Critical Manifolds: Existence and Approximation Formulas -- Standing Hypotheses -- Existence of Local Stochastic Critical Manifolds -- Approximation of Local Stochastic Critical Manifolds -- Proofs of Theorem 6.1 and Corollary 6.1 -- Approximation of Stochastic Hyperbolic Invariant Manifolds -- A Classical and Mild Solutions of the Transformed RPDE -- B Proof of Theorem 4.1 -- References.

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.

ISBN: 9783319124964

Standard No.: 10.1007/978-3-319-12496-4doiSubjects--Topical Terms:

592238
Dynamics.

LC Class. No.: QA313

Dewey Class. No.: 515.39

Approximation of Stochastic Invariant Manifolds = Stochastic Manifolds for Nonlinear SPDEs I /
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