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Authors: Zhao, Mingxia | Yang, Xin-Guang | Yan, Xingjie | Cui, Xiaona

Article Type: Research Article

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.

Keywords: Benjamin–Bona–Mahony equation, uniformly asymptotic stable, pullback attractors

DOI: 10.3233/ASY-201601

Citation: Asymptotic Analysis, vol. 121, no. 1, pp. 75-100, 2021