Approximation of Stochastic Invariant Manifolds: Stochastic Manifolds for Nonlinear SPDEs I (Repost)
Approximation of Stochastic Invariant Manifolds: Stochastic Manifolds for Nonlinear SPDEs I By Mickaël D. Chekroun, Honghu Liu, Shouhong Wang
2015 | 144 Pages | ISBN: 3319124951 | PDF | 3 MB
2015 | 144 Pages | ISBN: 3319124951 | PDF | 3 MB
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.