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January  2020, 19(1): 293-310. doi: 10.3934/cpaa.2020016

## Averaging principles for the Swift-Hohenberg equation

 School of Mathematics and Statistics, and Center for Mathematics and Interdisciplinary Sciences, Northeast Normal University, Changchun 130024, China

* Corresponding author

Received  December 2018 Revised  April 2019 Published  July 2019

Fund Project: This work is supported by NSFC Grant (11601073)

This work studies the effects of rapid oscillations (with respect to time) of the forcing term on the long-time behaviour of the solutions of the Swift-Hohenberg equation. More precisely, we establish three kinds of averaging principles for the Swift-Hohenberg equation, they are averaging principle in a time-periodic problem, averaging principle on a finite time interval and averaging principle on the entire axis.

Citation: Peng Gao. Averaging principles for the Swift-Hohenberg equation. Communications on Pure & Applied Analysis, 2020, 19 (1) : 293-310. doi: 10.3934/cpaa.2020016
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