| Fractal Dimension of Random Attractors for Non-autonomous Fractional Stochastic Ginzburg–Landau Equations |
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| 基金项目： | Supported by National Natural Science Foundation of China (Grant Nos. 11571245, 11771444, 11871138 and 11871049), funding of V. C. & V. R. Key Lab of Sichuan Province, the Yue Qi Young Scholar Project, China University of Mining and Technology (Beijing) and China Scholarship Council (CSC) |
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| 摘 要： | This paper considers the dynamical behavior of solutions for non-autonomous stochastic fractional Ginzburg–Landau equations driven by additive noise with α∈(0, 1). First, we give some conditions for bounding the fractal dimension of a random invariant set of non-autonomous random dynamical system. Second, we derive uniform estimates of solutions and establish the existence and uniqueness of tempered pullback random attractors for the equation in H. At last, we prove the finiteness of fractal dimension of random attractors.
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| 关 键 词： | NON-AUTONOMOUS STOCHASTIC FRACTIONAL Ginzburg–Landau equation RANDOM dynamical system RANDOM ATTRACTOR additive noise fractal dimension |
Fractal Dimension of Random Attractors for Non-autonomous Fractional Stochastic Ginzburg—Landau Equations |
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| Chun Xiao Guo,Ji Shu,Xiao Hu Wang. Fractal Dimension of Random Attractors for Non-autonomous Fractional Stochastic Ginzburg—Landau Equations[J]. Acta Mathematica Sinica(English Series), 2020, 36(3): 318-336. DOI: 10.1007/s10114-020-8407-4 |
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| Authors: | Chun Xiao Guo Ji Shu Xiao Hu Wang |
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| Affiliation: | 1. Department of Mathematics, China University of Mining and Technology Beijing, Beijing 100083, P. R. China;2. School of Mathematical Science and V. C. & V. R. Key Lab, Sichuan Normal University, Chengdu 610068, P. R. China;3. Department of Mathematics, Sichuan University, Chengdu 610064, P. R. China |
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| Abstract: | This paper considers the dynamical behavior of solutions for non-autonomous stochastic fractional Ginzburg-Landau equations driven by additive noise with & |
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| Keywords: | Non-autonomous stochastic fractional Ginzburg-Landau equation random dynamical system random attractor additive noise fractal dimension |
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