Evolution Equations and Control Theory (EECT)

Null controllability with constraints on the state for the 1-D Kuramoto-Sivashinsky equation

Pages: 281 - 296, Volume 4, Issue 3, September 2015      doi:10.3934/eect.2015.4.281

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Peng Gao - School of Mathematics and Statistics and Center for Mathematics and Interdisciplinary Sciences, Northeast Normal University, Changchun 130024, China (email)

Abstract: This paper is addressed to study the null controllability with constraints on the state for the Kuramoto-Sivashinsky equation. We first consider the linearized problem. Then, by Kakutani fixed point theorem, we show that the same result holds for the Kuramoto-Sivashinsky equation.

Keywords:  Null controllability, 1-D Kuramoto-Sivashinsky equation, constraints on the state.
Mathematics Subject Classification:  Primary: 35K35, 35K55; Secondary: 93B05.

Received: March 2015;      Revised: June 2015;      Available Online: September 2015.