Open Access
February, 2018 Dynamics of a Stochastic Fractional Reaction-Diffusion Equation
Linfang Liu, Xianlong Fu
Taiwanese J. Math. 22(1): 95-124 (February, 2018). DOI: 10.11650/tjm/8161


In this paper, we study the dynamics of a stochastic fractional reaction-diffusion equation with multiplicative noise in three spatial dimension. By proving the well-posedness and conducting a priori estimates for the solutions of the considered equation we obtain simultaneously the existence and the regularity of random attractors of the random dynamical systems for the equation. The main approach here is to establish an abstract result on existence of bi-spatial random attractors for random dynamical systems. Moreover, we also give estimate of the Hausdorff dimension in $L^{2}$ space for the obtained random attractor.


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Linfang Liu. Xianlong Fu. "Dynamics of a Stochastic Fractional Reaction-Diffusion Equation." Taiwanese J. Math. 22 (1) 95 - 124, February, 2018.


Received: 18 March 2017; Revised: 19 June 2017; Accepted: 21 June 2017; Published: February, 2018
First available in Project Euclid: 8 September 2017

zbMATH: 06965362
MathSciNet: MR3749357
Digital Object Identifier: 10.11650/tjm/8161

Primary: 35B40 , 35R11 , 35R60 , 37L55 , 60H15

Keywords: bi-spatial random attractor , Hausdorff dimension , regularity , stochastic fractional reaction-diffusion equation , well-posedness

Rights: Copyright © 2018 The Mathematical Society of the Republic of China

Vol.22 • No. 1 • February, 2018
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