摘要
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 H<sup>1</sup>(R<sup>n</sup>). 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.
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 H<sup>1</sup>(R<sup>n</sup>). 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.
作者
Fadlallah Mustafa Mosa
Abdelmajid Ali Dafallah
Qiaozhen Ma
Eshag Mohamed Ahmed
Mohamed Y. A. Bakhet
Fadlallah Mustafa Mosa;Abdelmajid Ali Dafallah;Qiaozhen Ma;Eshag Mohamed Ahmed;Mohamed Y. A. Bakhet(Department of Mathematics and Physics, Faculty of Education, University of Kassala, Kassala, Sudan;Department of Mathematics, Faculty of Petroleum and Hydrology Engineering, Alsalam University, Al-Fulah, Sudan;College of Mathematics and Statistics, Northwest Normal University, Lanzhou, China;Faculty of Pure and Applied Sciences, International University of Africa, Khartoum, Sudan;School of Mathematics, University of Juba, Juba, South Sudan)