UNIFORM STABILIZATION OF A NONLINEARCOUPLED SYSTEM OF KORTEWEG-DE VRIESEQUATIONS AS A SINGULAR LIMIT OF THEKURAMOTO-SIVASHINSKY SYSTEM

C.P. MASSAROLO; A.F. PAZOTO

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UNIFORM STABILIZATION OF A NONLINEARCOUPLED SYSTEM OF KORTEWEG-DE VRIESEQUATIONS AS A SINGULAR LIMIT OF THEKURAMOTO-SIVASHINSKY SYSTEM

机译：KURTEWEG-DE序列的非线性耦合系统的一致稳定，作为KURAMOTO-SIVASHINSKY系统的奇异极限

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We consider a coupled system of Kuramoto-Sivashinskyequations depending on a suitable parameter v > 0 and study its asymp-totic behavior for t large, as v →0. Introducing appropriate boundaryconditions we show that the energy of the solutions decays exponentiallyuniformly with respect to the parameter v. In the limit, as v→0, we ob-tain a coupled system of Korteweg-de Vries equations known to describestrong interactions of two long internal gravity waves in a stratified fluidfor which the energy tends to zero exponentially as well. The decay failswhen the length of the space interval L lies in a set of critical lengths.

机译：我们考虑取决于合适的参数v> 0的Kuramoto-Sivashinsky方程的耦合系统，并研究当t→0时t大的渐近行为。引入适当的边界条件，我们证明了解的能量相对于参数v呈指数均匀衰减。在极限条件下，当v→0时，我们获得了一个Korteweg-de Vries方程的耦合系统，该方程描述了两个长内在相互作用的强相互作用。重力波在分层流体中，能量也趋于指数性地趋于零。当间隔L的长度位于一组临界长度中时，衰减将失败。

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《Differential and integral equations》 |2009年第2期|共16页
作者
C.P. MASSAROLO; A.F. PAZOTO;
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正文语种 eng
中图分类微分方程、积分方程;
关键词
coupled; development; depending;

机译：耦合;发展;依赖;

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1. UNIFORM STABILIZATION OF A NONLINEARCOUPLED SYSTEM OF KORTEWEG-DE VRIESEQUATIONS AS A SINGULAR LIMIT OF THEKURAMOTO-SIVASHINSKY SYSTEM [J] . C.P. MASSAROLO, A.F. PAZOTO Differential and integral equations . 2009,第1a2期

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UNIFORM STABILIZATION OF A NONLINEARCOUPLED SYSTEM OF KORTEWEG-DE VRIESEQUATIONS AS A SINGULAR LIMIT OF THEKURAMOTO-SIVASHINSKY SYSTEM

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