具有加性噪声的Boussinesq方程的随机吸引子

Random Attroctor for a Type of Boussinesq Equation with Additive White Noise

研究带有加性噪声项的Boussinesq型方程初边值问题的解的长时间动力学行为,首先通过一系列变换,把具有加性噪声项的随机微分方程转化为不具有噪声项的微分方程,由确定性理论得到该方程决定一个随机动力系统,然后利用周盛凡和范小明的方法[1-2]对一类算子进行估计,证明半群存在有界吸收集,且半群是一致渐近紧的,从而得到该半群存在全局吸引子.

The long-time behavior for a type of Boussinesq equation was explored in this paper with additive white noise.Fristly,the stochastic differential equation with additive noise term was transformed into a differential equation without noise by some column transformations.A stochastic dynamical system was obtained from the deterministic theory.Then,we estimated a type of operator which was useful to obtain the existence of absorbing sets and asymptotical compactness for the semigroup on the basis of Zhou and Fan’s method1-2.Thus,we can get this semigroup the exist global attractors.