Affiliations: [a] School of Mathematics and Statistics, Pingdingshan University, Pingdingshan, 467000, P.R. China. E-mail: [email protected] | [b] Department of Mathematics and Information Science, Henan Normal University, Xinxiang, 453007, P.R. China. E-mails: [email protected], [email protected] | [c] Department of Mathematics, China University of Mining and Technology, Xuzhou, 221008, P.R. China. E-mail: [email protected]
Abstract: This paper is concerned with the tempered pullback dynamics for a three dimensional Benjamin–Bona–Mahony equations with sublinear operator on bounded domain, which describes the long time behavior for long waves model in shallow water with friction. By virtue of a new retarded Gronwall inequality, and using the energy equation method from J.M. Ball (Disc. Cont. Dyn. Syst. 10 (2004) 31–52) to achieve asymptotic compactness for solution process, the minimal family of pullback attractors has been obtained, which reduces a single trajectory under a sufficient condition.
