Affiliations: [a] Hunan Province Cooperative Innovation Center for the Construction and Development of Dongting Lake Ecological Economic Zone, College of Mathematics and Physics Science, Hunan University of Arts and Science, Changde, 415000, P.R. China. E-mail: zhukx12@163.com | [b] School of Mathematics and Statistics, Changsha University of Science and Technology, Changsha, 410114, P.R. China. E-mail: xieyq@csust.edu.cn | [c] College of Science, China University of Petroleum (East China), Qingdao, 266580, P.R. China. E-mail: zhoufeng13@upc.edu.cn | [d] School of Science, Yanshan University, Qinhuangdao, 066004, P.R. China. E-mail: lix13@lzu.edu.cn
Abstract: In this paper, we consider a non-autonomous reaction-diffusion equation with hereditary effects and the nonlinearity f satisfying the polynomial growth of arbitrary p−1 (p⩾2) order. We employ the asymptotic a priori estimate method (see (J. Differential Equations 223 (2006) 367–399)) to our problem and establish an existence criterion for the (CL2(Ω),CLp(Ω))-uniform (w.r.t σ∈Σ) attractors (see Theorem 2.18). Then, we obtain the (CL2(Ω),CLp(Ω)) and (CL2(Ω),CH01(Ω))-uniform (w.r.t σ∈Σ) attractors by applying the existence criterion and the uniform (w.r.t σ∈Σ) Condition (C) respectively.
