中文摘要：

通过Karhunen-Loeve展式将随机Kuramoto-Sinvashinsky方程转化为确定型方程,分别利用差分和有限元对时间和空间进行离散,证明了解的存在唯一性和逼近性.

英文摘要：

In this paper, the existence, uniqueness and approximation of the solutions to the stochastic Kuramoto -Sinvashinsky equation are proved, by being transformed into a deterministic equation through the KarhunenLoeve expansion, and dispersing time and space with difference and definite elements respectively.