Approximation of Stochastic Invariant Manifolds : Stochastic Manifolds for Nonlinear SPDEs I / by Mickal͡ D. Chekroun, Honghu Liu, Shouhong Wang
| データ種別 | 電子書籍 |
|---|---|
| 出版者 | Cham : Springer International Publishing : Imprint: Springer |
| 出版年 | 2015 |
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| 書誌ID | OB01016514 |
|---|---|
| 本文言語 | 英語 |
| 一般注記 | 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. License restrictions may limit access Summary: 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 |
| 著者標目 | *Chekroun, Mickal͡ D Liu, Honghu Wang, Shouhong SpringerLink (Online service) |
| 統一書名標目 | SpringerBriefs in Mathematics, |
| 件 名 | LCSH:Mathematics LCSH:Differentiable dynamical systems LCSH:Differential Equations LCSH:Differential equations, partial LCSH:Distribution (Probability theory) FREE:Mathematics FREE:Dynamical Systems and Ergodic Theory FREE:Partial Differential Equations FREE:Probability Theory and Stochastic Processes FREE:Ordinary Differential Equations |
| 分 類 | LCC:QA313 DC23:515.39 DC23:515.48 |
| 巻冊次 | ISBN:9783319124964 RefWorks出力（各巻） print ; ISBN:9783319124957 RefWorks出力（各巻） |
| 資料種別 | 機械可読データファイル |
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