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January/February 2009 Uniform stabilization of a nonlinear coupled system of Korteweg-de Vries equations as a singular limit of the Kuramoto-Sivashinsky system
C.P. Massarolo, A.F. Pazoto
Differential Integral Equations 22(1/2): 53-68 (January/February 2009).

Abstract

We consider a coupled system of Kuramoto-Sivashinsky equations depending on a suitable parameter $\nu > 0$ and study its asymptotic behavior for $t$ large, as $\nu\rightarrow 0$. Introducing appropriate boundary conditions we show that the energy of the solutions decays exponentially uniformly with respect to the parameter $\nu$. In the limit, as $\nu\rightarrow 0$, we obtain a coupled system of Korteweg-de Vries equations known to describe strong interactions of two long internal gravity waves in a stratified fluid for which the energy tends to zero exponentially as well. The decay fails when the length of the space interval $L$ lies in a set of critical lengths.

Citation

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C.P. Massarolo. A.F. Pazoto. "Uniform stabilization of a nonlinear coupled system of Korteweg-de Vries equations as a singular limit of the Kuramoto-Sivashinsky system." Differential Integral Equations 22 (1/2) 53 - 68, January/February 2009.

Information

Published: January/February 2009
First available in Project Euclid: 20 December 2012

zbMATH: 1240.35473
MathSciNet: MR2483012

Subjects:
Primary: 35Q53, 93B05, 93D15

Rights: Copyright © 2009 Khayyam Publishing, Inc.

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Vol.22 • No. 1/2 • January/February 2009
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