无界域上带有线性记忆的随机梁方程的吸引子  

The Random Attractors for Beam Equation with Linear Memory on Unbounded Domains

作　　者：刘丹 姜金平[1] 曹宇宇 LIU Dan;JIANG Jinping;CAO Yuyu(School of Mathematics and Computer Science,Yan’an University,Yan’an 716000,China)

机构地区：[1]延安大学数学与计算机科学学院,陕西延安716000

出　　处：《贵州大学学报(自然科学版)》2025年第2期40-47,共8页Journal of Guizhou University:Natural Sciences

基　　金：陕西省自然科学基础研究计划项目(2018JM1042);陕西数理基础科学研究项目(23JSY050)。

摘　　要：考虑带有线性记忆和加法噪声的随机梁方程在无界区域上的长时间行为。首先,给出连续随机动力系统的相关概念;其次,利用Ornstein-Uhlenbeck过程将加法噪声扰动下的梁方程转化为含随机参数而无噪声的确定性动力系统,并且证明方程所生成的随机动力系统与确定性动力系统等价;再次,通过对方程解的渐近先验估计及算子分解克服Sobolev嵌入在无界区域上缺乏紧性带来的困难,得到对应系统的一致有界吸收集和一致渐近紧性,最终得出原系统随机吸引子的存在性。In this study,we discussed the long time behavior of the beam equation with linear memory and additive noise on unbounded domains.First,we introduced the concepts of continuous stochastic dynamical systems.Second,we transferred the beam equation with additive white noise into a deterministic dynamical system with random coefficients and without noise by the Ornstein-Uhlenbeck process,and proved that the stochastic dynamical system determined by the equation is equivalent to the deterministic dynamical system.Third,to overcome the difficulty that Sobolev embeddings on unbounded domains are not compact,we established the uniform asymptotic compactness of the random dynamical system,using the asymptotic priori estimates and the method of operator decomposition.Finally,the existence of the random attractor of the original system was obtained.

关 键 词：梁方程 随机吸引子 渐近先验估计 算子分解 

分 类 号：O175.27[理学—数学]