Article citationsMore >>

Schmalfuss B., Backword cocycle and attractors of stochastic differential equations in: V. Reitmann, T. Riedrich, N. Koksch(Eds.), International Seminar on Applied Mathematics-Nonlinear Dynamics: Attractor Approximation and Global Behavior, Technische Universität, Dresden, 1992, pp. 185-192.

has been cited by the following article:

Article

Random Exponential Attractor and Equilibrium for a Stochastic Reaction-diffusion Equation with Multiplicative Noise

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 Publishing

Cite 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.com

Abstract

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