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

Author

Listed:
  • A. Osses

    (Universidad de Chile)

  • J. P. Puel

    (Université de Versailles Saint-Quentin)

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.

Suggested Citation

  • A. Osses & J. P. Puel, 1998. "Boundary Controllability of a Stationary Stokes System with Linear Convection Observed on an Interior Curve," Journal of Optimization Theory and Applications, Springer, vol. 99(1), pages 201-234, October.
    • Handle: RePEc:spr:joptap:v:99:y:1998:i:1:d:10.1023_a:1021760429614
    DOI: 10.1023/A:1021760429614
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