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| Approximate Solution of the Kuramoto-Shivashinsky Equation on an Unbounded Domain |
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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 |
| Page view： 1700
Net amount： 1566 |
Authors： |
Wael W. MOHAMMED; |
Foundation： |
This work was supported by the Deanship of Scientific
Research, University of Hail, KSA (No.0150258). |
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| 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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