1School of Science, Hubei University of Technology, Wuhan, China
International Journal of Partial Differential Equations and Applications.
2016,
Vol. 4 No. 2, 25-31
DOI: 10.12691/ijpdea-4-2-2
Copyright © 2016 Science and Education PublishingCite this paper: Gang Wang. Random Exponential Attractor and Equilibrium for a Stochastic Reaction-diffusion Equation with Multiplicative Noise.
International Journal of Partial Differential Equations and Applications. 2016; 4(2):25-31. doi: 10.12691/ijpdea-4-2-2.
Correspondence to: Gang Wang, School of Science, Hubei University of Technology, Wuhan, China. Email:
wgfeiyu@sina.comAbstract
In this paper, we present a result on existence of exponential attractors for abstract random dynamical systems, and then give a criterion for exponentially attractive property of random attractors. As an application, we first prove that the random dynamical system generated by a stochastic reaction-diffusion equation possesses a random exponential attractor. Then we show that the unique random equilibrium when the nonlinearity satisfies some restrictive condition is exactly an exponential attractor.
Keywords