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

Gang Wang^1,

¹School of Science, Hubei University of Technology, Wuhan, China

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

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:
random dynamical system random exponential attractor random equilibrium stochastic reaction-diffusion equation

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