具有白噪声的高阶光束方程的随机吸引子族

Guoguang Lin, Jie Liu
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引用次数: 0

摘要

本文研究了一类含白噪声的阻尼高阶梁方程随机动力系统。首先,利用Ornstein-Uhlenbeck过程将方程转化为以随机变量为参数的无噪声随机方程。其次,通过估计方程的解,得到有界随机吸收集。最后,利用同构映射法和紧嵌入定理得到系统。它是渐进紧的,然后我们可以证明随机吸引子的存在性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A Random Attractor Family of the High Order Beam Equations with White Noise
In this paper, we studied a class of damped high order Beam equation stochas-tic dynamical systems with white noise. First, the Ornstein-Uhlenbeck process is used to transform the equation into a noiseless random equation with random variables as parameters. Secondly, by estimating the solution of the equation, we can obtain the bounded random absorption set. Finally, the isomorphism mapping method and compact embedding theorem are used to obtain the system. It is progressively compact, then we can prove the existence of ran-dom attractors.
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