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 Mat. Sb., 1996, Volume 187, Number 5, Pages 15–58 (Mi msb126)

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

A. A. Ilyin

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 $f(\omega t)$, $\omega \gg 1$. 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 $\omega \to \infty$.

DOI: https://doi.org/10.4213/sm126

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English version:
Sbornik: Mathematics, 1996, 187:5, 635–677

Bibliographic databases:

UDC: 517.9
MSC: 34G20, 35Q30, 35L70

Citation: A. A. Ilyin, “Averaging principle for dissipative dynamical systems with rapidly oscillating right-hand sides”, Mat. Sb., 187:5 (1996), 15–58; Sb. Math., 187:5 (1996), 635–677

Citation in format AMSBIB
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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

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