Approximate Solution of the Kuramoto-Shivashinsky Equation on an Unbounded Domain

Citation:

Wael W. MOHAMMED.Approximate Solution of the Kuramoto-Shivashinsky Equation on an Unbounded Domain[J].Chinese Annals of Mathematics B,2018,39(1):145~162
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Authors:

Wael W. MOHAMMED;

Foundation:

This work was supported by the Deanship of Scientific Research, University of Hail, KSA (No.0150258).
Abstract: The main goal of this paper is to approximate the Kuramoto-Shivashinsky (K-S for short) equation on an unbounded domain near a change of bifurcation, where a band of dominant pattern is changing stability. This leads to a slow modulation of the dominant pattern. Here we consider PDEs with quadratic nonlinearities and derive rigorously the modulation equation, which is called the Ginzburg-Landau (G-L for short) equation, for the amplitudes of the dominating modes.

Keywords:

Multi-scale analysis, Modulation equation, Kuramoto-Shivashinsky equation,Ginzburg-Landau equation

Classification:

35B20, 35B45, 35B35
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