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Control theory for the Burgers equation: Agrachev-Sarychev approach. (arXiv:1712.09807v1 [math.AP])
来源于:arXiv
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. 查看全文>>