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

Qianqian Bai, Ji Shu, Xin Huang & Jian Zhang

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

Published online: 2020-08

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  • Abstract

This paper dealswith 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

1370733971@qq.com (Qianqian Bai)

shuji@sicnu.edu.cn (Ji Shu)

huangxinnv@163.com (Xin Huang)

zhangjiancdv00@sina.com (Jian Zhang)

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  • RIS
  • TXT
@Article{JPDE-33-377, author = {Bai , Qianqian and Shu , Ji and Huang , 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 dealswith 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 - Bai , Qianqian AU - Shu , Ji 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 KW - random attractor KW - fractal dimension KW - fractional reaction-diffusion equation KW - multiplicative noise. AB -

This paper dealswith 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.

Ji Shu, Qianqian Bai, Xin Huang & Jian Zhang. (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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