一类具有乘性噪声的时滞随机演化方程的随机中心流形的存在性与光滑性

The Existence and Smoothness of Random Center Manifolds for a Class of Delay Stochastic Evolutionary Equations with Multiplicative Noise

研究一类具有乘性噪声的时滞随机演化方程的随机中心流形的存在性与光滑性.由于时滞的影响,首先对带时滞的非线性项进行转化并处理由时滞影响产生的系数,从而得到中心流形的存在性,然后利用Lyapunov-Perron方法证明方程的中心流形的光滑性.

We study the existence and smoothness of random center manifolds for a class of delay stochastic evolutionary equations with multiplicative noise.Due to the effect of delay,we first transform the nonlinear terms with delay and deal with the coefficients generated by the effect of delay,thus the existence of center manifolds is obtained.Then,we use the Lyapunov-Perron method to investigate the smoothness of center manifolds for the equations with delay.