Invariant manifolds for stochastic partial differential equations

• 成果类型: Article
• 署名作者: Duan, JQ; Lu, KN; Schmalfuss, B
• 署名单位: Illinois Institute of Technology; Chinese Academy of Sciences; University of Science & Technology of China, CAS; Brigham Young University; Michigan State University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 2003
• 页码: 2109-2135
• 关键词: theorem

摘要

Invariant manifolds provide the geometric structures for describing and understanding dynamics of nonlinear systems. The theory of invariant manifolds for both finite- and infinite-dimensional autonomous deterministic systems and for stochastic ordinary differential equations is relatively mature. In this paper, we present a unified theory of invariant manifolds for infinite-dimensional random dynamical systems generated by stochastic partial differential equations. We first introduce a random graph transform and a fixed point theorem for nonautonomous systems. Then we show the existence of generalized fixed points which give the desired invariant manifolds.