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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.
| Autorius: | Mickaël D. Chekroun, Shouhong Wang, Honghu Liu, |
| Serija: | SpringerBriefs in Mathematics |
| Leidėjas: | Springer Nature Switzerland |
| Išleidimo metai: | 2015 |
| Knygos puslapių skaičius: | 144 |
| ISBN-10: | 3319124951 |
| ISBN-13: | 9783319124957 |
| Formatas: | 235 x 155 x 9 mm. Knyga minkštu viršeliu |
| Kalba: | Anglų |
Parašykite atsiliepimą apie „Approximation of Stochastic Invariant Manifolds: Stochastic Manifolds for Nonlinear SPDEs I“
