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Null controllability and stabilization of the linear Kuramoto-Sivashinsky equation

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

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