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

• Κύριοι συγγραφείς: Chekroun, Mickaël D. (Συγγραφέας), Liu, Honghu (Συγγραφέας), Wang, Shouhong (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Cham : Springer International Publishing : Imprint: Springer, 2015.
• Σειρά: SpringerBriefs in Mathematics,
• Θέματα: Mathematics.; Dynamics.; Ergodic theory.; Differential equations.; Partial differential equations.; Probabilities.; Dynamical Systems and Ergodic Theory.; Partial Differential Equations.; Probability Theory and Stochastic Processes.; Ordinary Differential Equations.

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...

Πίνακας περιεχομένων:

• 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.