带时滞随机动力系统不变流形的光滑性

Recently, invariant manifold for random dynamical systems is a important problems. However, few papers have been published on random dynamical systems with delays. This project study invariant manifolds for delay parabolic equations with additive noise or multiply noise. By modified Hadamard’s methods or Lyapunov-Perron’s methods, we shall obtain existence, smoothness of unstable manifolds and stable manifolds. Moreover, we shall study the effect of noise and delay on invariant manifolds.

随机动力系统不变流形是近年来研究的热点, 对于带有时滞的随机动力系统不变流形的成果较少. 此项目主要研究具有可加噪声和乘积噪声的带时滞随机抛物型方程，利用修改后的Hadamard图变换方法或Lyapunov-Perron解析方法研究不变流形的存在性， 唯一性以及N阶光滑性, 包括不稳定流形和稳定流形，最后还将讨论噪声因素以及时滞因素对此随机系统这两类不变流形的影响.