Geodesic
Averaging principle for dissipative dynamical systems with rapidly oscillating right-hand sides
Sbornik. Mathematics, Tome 187 (1996) no. 5, pp. 635-677

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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 $f(\omega t)$, $\omega \gg 1$. We suppose also that $f$ 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 $\omega \to \infty$. 
@article{SM_1996_187_5_a1,
     author = {A. A. Ilyin},
     title = {Averaging principle for dissipative dynamical systems with rapidly oscillating right-hand sides},
     journal = {Sbornik. Mathematics},
     pages = {635--677},
     publisher = {mathdoc},
     volume = {187},
     number = {5},
     year = {1996},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1996_187_5_a1/}
}
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A. A. Ilyin. Averaging principle for dissipative dynamical systems with rapidly oscillating right-hand sides. Sbornik. Mathematics, Tome 187 (1996) no. 5, pp. 635-677. http://geodesic.mathdoc.fr/item/SM_1996_187_5_a1/