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.

中文翻译：

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具有亚线性算子的3D Benjamin–Bona–Mahony方程的动力学

本文关注带界域上具有次线性算子的三维Benjamin-Bona-Mahony方程的回火动力学，该方程描述了浅水带摩擦的长波模型的长时间行为。借助于新的延迟Gronwall不等式，并使用JM Ball的能量方程方法（Disc。Cont。Dyn。Syst。10（2004）31-52）来实现求解过程的渐近紧致性，最小的回拉吸引子族具有获得了足够的条件下的单个轨迹。