Approximation of Smooth Stable Invariant Manifolds for Stochastic Partial Differential Equations

Abstract

Invariant manifolds are complicate random sets useful for describing and understanding the qualitative behavior of nonlinear dynamical systems. The purpose of the present paper is try to approximate smooth stable invariant manifolds for a type of stochastic partial differential equations with multiplicative white noise near the fixed point. Two examples are given to illustrate our results. AMS Subject Classifications: 35B40, 35B41, 35Q30, 76D03, 76D05 Chinese Library Classifications: O175.27