Boundary Controllability of a Stationary Stokes System with Linear Convection Observed on an Interior Curve

A. Osses and J. P. Puel
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A. Osses: Universidad de Chile
J. P. Puel: Université de Versailles Saint-Quentin

Journal of Optimization Theory and Applications, 1998, vol. 99, issue 1, No 11, 234 pages

Abstract: Abstract We study the approximate controllability of a stationary Stokes system with linearized convection in a bounded domain of ℝN. The control acts on a part of the boundary and the velocity field is observed on an interior curve (N=2) or surface (N=3). We establish the L 2-approximate controllability under certain compatibility conditions and suitable geometrical assumptions on the curve or surface. We build controls of minimal L 2-norm by duality. To compute the control, we propose a numerical method, based on duality techniques, consisting in the minimization of a nonquadratic functional coupled to a Stokes system. It is tested in several situations leading to interesting numerical results.

Keywords: Stokes systems; inverse problems; approximate controllability; duality; computational methods (search for similar items in EconPapers)
Date: 1998
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DOI: 10.1023/A:1021760429614

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