Averaging principle for dissipative dynamical systems with rapidly oscillating right-hand sides

Abstract

We consider two-dimensional Navier-Stokes equations and a?damped non-linear hyperbolic equation. We suppose that the?right-hand sides of these equations have the?form , . We suppose also that has an?average. The?main result of the?paper is proof of a?global averaging theorem on the?convergence of attractors of non-autonomous equations to the?attractor of the?average autonomous equation as .