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

A. A. Ilyin

Sbornik. Mathematics, Tome 187 (1996) no. 5, pp. 635-677

Résumé

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 $\omega \to \infty$.

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