TITLE:
Random Attractors of Stochastic Non-Autonomous Nonclassical Diffusion Equations with Linear Memory on a Bounded Domain
AUTHORS:
Ahmed Eshag Mohamed, Qiaozhen Ma, Mohamed Y. A. Bakhet
KEYWORDS:
Stochastic Nonclassical Diffusion Equation, Random Attractors, Asymptotic Compactness, Linear Memory
JOURNAL NAME:
Applied Mathematics,
Vol.9 No.11,
November
30,
2018
ABSTRACT:
In this article, we discuss the long-time dynamical behavior of the stochastic non-autonomous nonclassical diffusion equations with linear memory and additive white noise in the weak topological space . By decomposition method of the solution, we give the necessary condition of asymptotic compactness of the solutions, and then prove the existence of random attractor, while the time-dependent forcing term only satisfies an integral condition.