Dynamics of a 3D Benjamin-Bona-Mahony equations with sublinear operator

摘要

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.