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Research Article Open access CC BY 4.0

Dynamics for the Stochastic Reaction-diffusion Equation with Distribution Derivatives and Multiplicative Noise on ℝn

Fadlallah Mustafa Mosa, Qiaozhen Ma, Xiaobin Yao

Asian Research Journal of Mathematics · pp. 1–15 · Published 22 Jan 2019

10.9734/ARJOM/2019/46304

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.

Random attractors Stochastic Reaction-Di usion Equation distribution derivatives asymptotic compactness.

Cited by 1

Existence and Upper Semi-Continuity of Random Attractors for Nonclassical Diffusion Equation with Multiplicative Noise on R<sup>n</sup>

Fadlallah Mustafa Mosa, Abdelmajid Ali Dafallah, Qiaozhen Ma · Journal of Applied Mathematics and Physics · 2022

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