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2010, Volume 9, Issue 1: 91-102. Doi: 10.3934/cpaa.2010.9.91

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Null controllability and stabilization of the linear Kuramoto-Sivashinsky equation

Eduardo Cerpa^1,

1.
Department of Mechanical and Aero. Engineering, University of California at San Diego, 9500 Gilman Drive, La Jolla, CA 92093

Received: January 2009

Revised: June 2009

Published: January 2010

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Abstract

In this article, we study the boundary controllability of the linear Kuramoto-Sivashinsky equation on a bounded interval. The control acts on the first spatial derivative at the left endpoint. First, we prove that this control system is null controllable. It is done using a spectral analysis and the method of moments. Then, we introduce a boundary feedback law stabilizing to zero the solution of the closed-loop system.

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Mathematics Subject Classification: Primary: 93B05, 93D15; Secondary: 93B60.

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