具乘性白噪声耗散KdV型方程的随机吸引子

Random attractor for dissipative Kd V equation with multiplicative white noise

考虑具乘性噪声的耗散Kd V型方程在一维有界区域上的长时间行为.通过变换将该方程化为不含白噪声的随机Kd V型方程,通过讨论新方程所确定动力系统的吸收性与渐近紧性,从而证明了原方程所确定动力系统随机吸引子的存在性.

This paper considers the long time behavior of the dissipative Kd V equation on one dimension dounded domain D. A process is introduced, which enables us to transform this equation into a stochastic equation without white noise. Then this paper studies the absorbent and asymptotic compactness of the dynamical system generated by the new equation. It proves the existence of random attractor for the dissipative Kd V equation finally.