SpringerBriefs in Mathematics: Stochastic Manifolds for Nonlinear SPDEs I

Chekroun, Mickaël D.; Liu, Honghu; Wang, Shouhong

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.

Details

Published by: Springer

Publication Date: 2015-01-13

Format: Paperback

ISBN-13: 9783319124957

DOI: 10.1007/978-3-319-12496-4

Dimensions: 235cm x155cm

Pages: 127