Approximation of Stochastic Invariant Manifolds
| Autor: | Mickaël D. Chekroun, Honghu Liu, Shouhong Wang |
|---|---|
| EAN: | 9783319124964 |
| eBook Format: | |
| Sprache: | Englisch |
| Produktart: | eBook |
| Veröffentlichungsdatum: | 20.12.2014 |
| Untertitel: | Stochastic Manifolds for Nonlinear SPDEs I |
| Kategorie: | |
| Schlagworte: | 35B42 37D10 37L10 37L25 37L55. 37L65 Leading-Order Taylor Approximations Lyapunov-Perron Integrals Stochastic Invariant Manifolds Stochastic Partial Differential Equations Weak Non-Resonance Conditions |
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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.
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