# American Institute of Mathematical Sciences

January  2010, 9(1): 91-102. doi: 10.3934/cpaa.2010.9.91

## Null controllability and stabilization of the linear Kuramoto-Sivashinsky equation

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

Received  January 2009 Revised  June 2009 Published  October 2009

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.
Citation: Eduardo Cerpa. Null controllability and stabilization of the linear Kuramoto-Sivashinsky equation. Communications on Pure & Applied Analysis, 2010, 9 (1) : 91-102. doi: 10.3934/cpaa.2010.9.91
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