THE EXISTENCE OF RANDOM $\mathcal{D}$-PULLBACK ATTRACTORS FOR RANDOM DYNAMICAL SYSTEM AND ITS APPLICATIONS

Yongjun Li; Jinying Wei; Tinggang Zhao

doi:10.11948/2156-907X.20190021

2019 Volume 9 Issue 4

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Yongjun Li, Jinying Wei, Tinggang Zhao. THE EXISTENCE OF RANDOM $\mathcal{D}$-PULLBACK ATTRACTORS FOR RANDOM DYNAMICAL SYSTEM AND ITS APPLICATIONS[J]. Journal of Applied Analysis & Computation, 2019, 9(4): 1571-1588. doi: 10.11948/2156-907X.20190021

Citation:

Yongjun Li, Jinying Wei, Tinggang Zhao. THE EXISTENCE OF RANDOM $\mathcal{D}$-PULLBACK ATTRACTORS FOR RANDOM DYNAMICAL SYSTEM AND ITS APPLICATIONS[J]. Journal of Applied Analysis & Computation, 2019, 9(4): 1571-1588. doi: 10.11948/2156-907X.20190021

THE EXISTENCE OF RANDOM $\mathcal{D}$-PULLBACK ATTRACTORS FOR RANDOM DYNAMICAL SYSTEM AND ITS APPLICATIONS

1.
School of Mathematics, Lanzhou City University, No.11, Jiefang Road, 730070, China

Corresponding author: Email address:li_liyong120@163.com(Y. Li)
Fund Project: The authors are supported by National Natural Science Foundation of China (11761044, 11661048) and the key constructive discipline of Lanzhou City University(LZCU-ZDJSXK-201706)

Abstract

Abstract

In this paper, we establish a result on the existence of random $\mathcal{D}$-pullback attractors for norm-to-weak continuous non-autonomous random dynamical system. Then we give a method to prove the existence of random $\mathcal{D}$-pullback attractors. As an application, we prove that the non-autonomous stochastic reaction diffusion equation possesses a random $\mathcal{D}$-pullback attractor in $H_0^1$ with polynomial growth of the nonlinear term.
- Random dynamical system /
- random pullback attractor /
- stochastic reaction diffusion equation
MSC: 35B40, 35B41, 60H15, 60H30, 60H40

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