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arXiv · 1712.09807

Control theory for the Burgers equation: Agrachev-Sarychev approach

Armen Shirikyan
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Abstract

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.

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Armen Shirikyan. 2017-12-28. Control theory for the Burgers equation: Agrachev-Sarychev approach. https://arxiv.org/abs/1712.09807

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