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| 具有乘积噪声的非自治Swift-Hohenberg方程在无界区域上的渐近性（英文） | |
| 引用本文： | 巴 吉 刘亭亭 马巧珍. 具有乘积噪声的非自治Swift-Hohenberg方程在无界区域上的渐近性（英文）[J]. 应用数学, 2019, 32(4): 838-850 |
| 作者姓名： | 巴 吉 刘亭亭 马巧珍 |
| 作者单位： | 1. 西北师范大学数学与统计学院, 甘肃 兰州 730070; 2. 伦贝克科技大学教育学院数学部, 伦贝克 南苏丹 |
| 基金项目： | Supported by the National Natural Science Foundation of China(11561064,11761062) |
| 摘 要： | 本文研究R^2上带有时间依赖外力项与乘性噪声的随机非自治修正Swift-Hohenberg方程的动力行为.为了克服无界域上Sobolev嵌入不紧的困难,我们先定义了问题在L2(R2)上的连续共圈,并且建立了当空间变量足够大时,解尾部的一致估计.通过解的一致估计,我们证明了随机动力系统的拉回渐近紧性,进一步得到了随机吸引子的存在性. |
| 关 键 词： | 随机吸引子 SWIFT-HOHENBERG方程 非自治随机动力系统 连续余圈 |
Asymptotic Dynamics of Non-Autonomous Modified Swift-Hohenberg Equations with Multiplicative Noise on Unbounded Domains |
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| Mohamed Yagoub Abaker,LIU Tingting,MA Qiaozhen. Asymptotic Dynamics of Non-Autonomous Modified Swift-Hohenberg Equations with Multiplicative Noise on Unbounded Domains[J]. Mathematica Applicata, 2019, 32(4): 838-850 | |
| Authors: | Mohamed Yagoub Abaker LIU Tingting MA Qiaozhen |
| Affiliation: | (College of Mathematics and Statistics, Northwest Normal University,Lanzhou 730070, china;Department of Mathematics, College of Education,Rumbek University of Science and Technology, Rumbek, South Sudan) |
| Abstract: | We investigate the dynamical behavior of the stochastic non-autonomous modified Swift-Hohenberg equation with time-dependent forcing term and multiplicative noise on R2. In order to overcome the difficulty that Sobolev embedding are not compact in the unbounded domain, we first define a continuous cocycle associated with the problem in L2(R2), and make some uniform estimates on the tails of solutions for large space variables. With the aid of uniform estimates of solution , we verify the pullback asymptotic compactness of the random dynamical system, and further obtain the existence of random attractors. |
| Keywords: | Random attractor Swift-Hohenberg equation Non-autonomous random dynamical system Continuous cocycle |
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