Affiliations: [a] Department of Mathematics, China University of Mining and Technology, Xuzhou, Jiangsu, 221116, P.R. China | [b] School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, 450001, Henan, P.R. China | [c] Department of Mathematics and Information Science, Henan Normal University, Xinxiang, 453007, Henan, P.R. China | [d] Computer Science and Engineering, Changchun University of Technology, Changchun 130012, P.R. China
Abstract: This paper is concerned with the long time behavior of solutions for a non-autonomous reaction-diffusion equations with anomalous diffusion. Under suitable assumptions on nonlinearity and external force, the global well-posedness has been studied. Then the pullback attractors in L2(Ω) and H0α(Ω) (0<α<1) have been achieved with a restriction on the growth order of nonlinearity as 2⩽p⩽2(n−α)n−2α. The results presented can be seen as the extension for classical theory of infinite dimensional dynamical system to the fractional diffusion equations.
