Armen Shirikyan
Published 2017-12-28Version 1
This paper is devoted to a description of a general approach introduced by Agrachev and Sarychev in 2005 for studying some control problems for Navier-Stokes equations. The example of a 1D Burgers equation is used to illustrate the main ideas. We begin with a short discussion of the Cauchy problem and establish a continuity property for the resolving operator. We next turn to the property of approximate controllability and prove that it can be achieved by a two-dimensional external force. Finally, we investigate a stronger property, when the approximate controllability and the exact controllability of finite-dimensional functionals are proved simultaneously.
Comments: This paper is an extended version of the lectures on the control theory delivered at the University of Iasi (Romania) in 2010. It will be published in Pure and Applied Functional Analysis (2018, volume 3, number 2). A short version was published earlier in the proceedings of the conference Journ\'ees EDP (Evian, 4-8 June 2007)
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