Dynamics for the Stochastic Reaction-diffusion Equation with Distribution Derivatives and Multiplicative Noise on ℝn
Fadlallah Mustafa Mosa
College of Mathematics and Statistics, Northwest Normal University, Lanzhou, Gansu 730070, China and Department of Mathematics and Physics, Faculty of Education, University of Kassala, Kassala, Sudan.
Qiaozhen Ma *
College of Mathematics and Statistics, Northwest Normal University, Lanzhou, Gansu 730070, China.
Xiaobin Yao
College of Mathematics and Statistics, Northwest Normal University, Lanzhou, Gansu 730070, China.
*Author to whom correspondence should be addressed.
Abstract
Recently the existence of random attractors for a stochastic reaction-diffusion equation without distribution derivatives has been studied by many authors, the existence of global attractors was established for the deterministic reaction-diffusion equation with distribution derivatives has been studied by Sun et al. in [1, 2]. In this paper, we prove the existence of random attractors for a stochastic reaction-diffusion equation with distribution derivatives and multiplicative noise defined on unbounded domains. In order to obtain the asymptotic compactness of the random dynamical system, we make use of a priori estimates for far-field values of solutions as well as the cut-off technique.
Keywords: Random attractors, Stochastic Reaction-Di usion Equation, distribution derivatives, asymptotic compactness.