拉回
紧凑空间
噪音的颜色
索波列夫空间
独特性
数学
吸引子
随机游动
数学分析
噪音(视频)
拉回吸引子
扩散
嵌入
非线性系统
物理
白噪声
量子力学
统计
图像(数学)
人工智能
计算机科学
作者
Renhai Wang,Yangrong Li,Bixiang Wang
出处
期刊:Discrete and Continuous Dynamical Systems
[American Institute of Mathematical Sciences]
日期:2019-01-01
卷期号:39 (7): 4091-4126
被引量:76
摘要
The random dynamics in $ H^s(\mathbb{R}^n) $ with $ s\in (0,1) $ is investigated for the fractional nonclassical diffusion equations driven by colored noise. Both existence and uniqueness of pullback random attractors are established for the equations with a wide class of nonlinear diffusion terms. In the case of additive noise, the upper semi-continuity of these attractors is proved as the correlation time of the colored noise approaches zero. The methods of uniform tail-estimate and spectral decomposition are employed to obtain the pullback asymptotic compactness of the solutions in order to overcome the non-compactness of the Sobolev embedding on an unbounded domain.
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