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Volume 33, Issue 4
Fractal Dimension of Random Attractors for Non-Autonomous Fractional Stochastic Reaction-Diffusion Equations

Ji Shu, Qianqian Bai, Xin Huang & Jian Zhang

DOI: 10.4208/jpde.v33.n4.4

J. Part. Diff. Eq., 33 (2020), pp. 377-394.

Published online: 2020-08

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  • Abstract

This paper deals with non-autonomous fractional stochastic reaction-diffusion equations driven by multiplicative noise with $s ∈ (0,1).$ We first present some  conditions for estimating the boundedness of fractal dimension of a random invariant set. Then we establish the existence and uniqueness of tempered pullback random attractors. Finally, the finiteness of fractal dimension of the random attractors is proved.

  • Keywords

Random dynamical system, random attractor, fractal dimension, fractional reaction-diffusion equation, multiplicative noise.

  • AMS Subject Headings

35B40, 35B41, 60H15

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

shuji@sicnu.edu.cn (Ji Shu)

1370733971@qq.com (Qianqian Bai)

huangxinnv@163.com (Xin Huang)

zhangjiancdv00@sina.com (Jian Zhang)

  • BibTex
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  • TXT
@Article{JPDE-33-377, author = {Shu , JiBai , QianqianHuang , Xin and Zhang , Jian}, title = {Fractal Dimension of Random Attractors for Non-Autonomous Fractional Stochastic Reaction-Diffusion Equations}, journal = {Journal of Partial Differential Equations}, year = {2020}, volume = {33}, number = {4}, pages = {377--394}, abstract = {

This paper deals with non-autonomous fractional stochastic reaction-diffusion equations driven by multiplicative noise with $s ∈ (0,1).$ We first present some  conditions for estimating the boundedness of fractal dimension of a random invariant set. Then we establish the existence and uniqueness of tempered pullback random attractors. Finally, the finiteness of fractal dimension of the random attractors is proved.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v33.n4.4}, url = {http://global-sci.org/intro/article_detail/jpde/17864.html} }
TY - JOUR T1 - Fractal Dimension of Random Attractors for Non-Autonomous Fractional Stochastic Reaction-Diffusion Equations AU - Shu , Ji AU - Bai , Qianqian AU - Huang , Xin AU - Zhang , Jian JO - Journal of Partial Differential Equations VL - 4 SP - 377 EP - 394 PY - 2020 DA - 2020/08 SN - 33 DO - http://doi.org/10.4208/jpde.v33.n4.4 UR - https://global-sci.org/intro/article_detail/jpde/17864.html KW - Random dynamical system, random attractor, fractal dimension, fractional reaction-diffusion equation, multiplicative noise. AB -

This paper deals with non-autonomous fractional stochastic reaction-diffusion equations driven by multiplicative noise with $s ∈ (0,1).$ We first present some  conditions for estimating the boundedness of fractal dimension of a random invariant set. Then we establish the existence and uniqueness of tempered pullback random attractors. Finally, the finiteness of fractal dimension of the random attractors is proved.

Shu , JiBai , QianqianHuang , Xin and Zhang , Jian. (2020). Fractal Dimension of Random Attractors for Non-Autonomous Fractional Stochastic Reaction-Diffusion Equations. Journal of Partial Differential Equations. 33 (4). 377-394. doi:10.4208/jpde.v33.n4.4
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