Approximation of Stochastic Invariant Manifolds : Stochastic Manifolds for Nonlinear SPDEs I / / by Mickaël D. Chekroun, Honghu Liu, Shouhong Wang

• Record Nr.: UNINA9910299760903321
• Autore: Chekroun Mickaël D.
• Pubbl/distr/stampa: Cham : , : Springer International Publishing : , : Imprint : Springer, , 2015
• ISBN: 3-319-12496-X
• Edizione: [1st ed. 2015.]
• Descrizione fisica: 1 online resource (136 p.)
• Collana: SpringerBriefs in Mathematics, , 2191-8201
• Disciplina: 510; 515.352; 515.353; 515.39
• Soggetti: Dynamical systems; Differential equations; Probabilities; Dynamical Systems; Differential Equations; Probability Theory
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: 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.
• Sommario/riassunto: 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.