Mickaël D. Chekroun, Honghu Liu, Shouhong Wang

Approximation of Stochastic Invariant Manifolds

Stochastic Manifolds for Nonlinear SPDEs I

• Broschiertes Buch

Produktbeschreibung

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.

Produktdetails

• SpringerBriefs in Mathematics
• Verlag: Springer / Springer International Publishing / Springer, Berlin
• Artikelnr. des Verlages: 86381474, 978-3-319-12495-7
• 2015
• Seitenzahl: 144
• Erscheinungstermin: 13. Januar 2015
• Englisch
• Abmessung: 235mm x 155mm x 9mm
• Gewicht: 239g
• ISBN-13: 9783319124957
• ISBN-10: 3319124951
• Artikelnr.: 41483794

Inhaltsangabe

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.

Rezensionen

"The book under review is the first in a two-volume series and deals with approximation of stochastic manifolds that are invariant for dynamics of a parabolic Stratonovich SPDE driven by a one-dimensional Wiener process. ... The book is aimed at readers interested in stochastic partial differential equations and random dynamical systems." (Martin Ondreját, zbMATH 1319.60002, 2015)