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Duan, J.Q., Lu, K.N. and Schmalfuss, B. (2003) Invariant Manifolds for Stochastic Partial Differential Equations. Annals of Probability, 31, 2109-2135.
https://doi.org/10.1214/aop/1068646380

has been cited by the following article:

• TITLE: Existence and Upper Semi-Continuity of Random Attractors for Nonclassical Diffusion Equation with Multiplicative Noise on Rn

  AUTHORS: Fadlallah Mustafa Mosa, Abdelmajid Ali Dafallah, Qiaozhen Ma, Eshag Mohamed Ahmed, Mohamed Y. A. Bakhet

  KEYWORDS: Random Attractors, Nonclassical Diffusion Equations, Asymptotic Compactness, Upper Semi-Continuity

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.10 No.12, December 30, 2022

  ABSTRACT: This paper is concerned with the existence and upper semi-continuity of random attractors for the nonclassical diffusion equation with arbitrary polynomial growth nonlinearity and multiplicative noise in H1(Rn). First, we study the existence and uniqueness of solutions by a noise arising in a continuous random dynamical system and the asymptotic compactness is established by using uniform tail estimate technique, and then the existence of random attractors for the nonclassical diffusion equation with arbitrary polynomial growth nonlinearity. As a motivation of our results, we prove an existence and upper semi-continuity of random attractors with respect to the nonlinearity that enters the system together with the noise.