Approximation of Stochastic Invariant Manifolds: Stochastic Manifolds for Nonlinear Spdes I

by Liu Honghu, Honghu Liu, Wang Shouhong, et al.

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.

• Format: Paperback
• Language: English
• ISBN: 3319124951
• ISBN13: 9783319124957
• Release Date: January 2015
• Publisher: Springer
• Length: 127 Pages
• Weight: 0.47 lbs.
• Dimensions: 0.3" x 6.1" x 9.2"