Averaging principles for the Swift-Hohenberg equation

Peng Gao

doi:10.3934/cpaa.2020016

Article Contents

2020, Volume 19, Issue 1: 293-310. Doi: 10.3934/cpaa.2020016

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Averaging principles for the Swift-Hohenberg equation

Peng Gao^,

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

^* Corresponding author
^* Corresponding author

Received: November 30, 2018

Revised: March 31, 2019

Published: July 2019

This work is supported by NSFC Grant (11601073)

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Abstract

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.

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Mathematics Subject Classification: Primary: 35B40; Secondary: 58J37, 35K35, 35K55.

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