Identyfikatory
Warianty tytułu
Języki publikacji
Abstrakty
An optimal control problem with quadratic cost functional for the steady-state Navier-Stokes equations with no-slip boundary condition is considered. Lipschitz stability of locally optimal controls with respect to certain perturbations of both the cost functional and the equation is proved provided a second-order sufficient optimality condition holds. For a sufficiently small Reynolds number, even global Lipschitz stability of the unique optimal control is shown.
Czasopismo
Rocznik
Tom
Strony
683--705
Opis fizyczny
Bibliogr. 31 poz.
Twórcy
autor
- Mathematical Institute, Charles University, Sokolovsk´a 83 CZ-186 75 Praha 8, Czech Republic
autor
- Institut fur Mathematik, Technische Universitat Berlin D-10623 Berlin, Germany
Bibliografia
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- Bonnans, J. F. and Shapiro, A. (2000) Perturbation Analysis of Optimization Problems. Springer, New York.
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- Casas, E. (1995) Optimality conditions for some control problems of turbulent flow. In: M. D. Gunzburger, ed., Flow Control. IMA Vol. Math. Appl. 68, Springer, New York, 127–147.
- Casas, E. and Troltzsch, F. (2002) Second order necessary and sufficient optimality conditions for optimization problems and applications to control theory, to appear in SIAM J. Optimization.
- Chebotarev, A. Yu. (1993) Principle of maximum in the problem of boundary control of flow of viscous fluid (in Russian). Sib. Mat. J. 34, 189–197.
- Constantin, P. and Foias, P. (1989) Navier-Stokes equations. The University of Chicago Press.
- Desai, M. C. and Ito, K. (1994) Optimal control of Navier-Stokes equations. SIAM J. Control Optim. 32, 1428–1446.
- Dontchev, A. L. and Malanowski, K. (1999) A characterization of Lipschitzian stability in optimal control. In: A. Ioffe, S. Reich and I. Shafrir, eds., Calculus of Variations and Optimal Control. Chapman and Hall, Boca Raton, 62–76.
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- Gunzburger, M.D. (1995) A prehistory of flow control and optimization. In: M. D. Gunzburger, ed., Flow Control. IMA Vol. Math. Appl. 68, Springer, New York, 185–195.
- Gunzburger, M. D. and Hou, L. and Svobodny, T. P. (1991) Analysis and finite element approximation of optimal control problems for stationary Navier-Stokes equations with distributed and Neumann controls. Math. Comp. 57, 123–151.
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- Gunzburger, M. D. and Manservisi, S. (1999) The velocity tracking problem for Navier-Stokes flow with bounded distributed controls. SIAM J. Control Optim. 37, 1913-1945.
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- Malanowski, K. and Troltzsch, F. (1999) Lipschitz stability of solutions to parametric optimal control for parabolic equations. Journal of Analysis and its Applications (ZAA) 18, 469–489.
- Malanowski, K. and Troltzsch, F. (2000) Lipschitz stability of solutions to parametric optimal control for elliptic equations. Control and Cybernetics 29, 237–256.
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- Roubıcek, T. (2002) Optimization of steady-state flow of incompressible fluids. Proc. IFIP Conf. Analysis and Optimization of Differential Systems, Kluwer Publ., submitted.
- Sritharan, S. S. (1992) An optimal control problem in exterior hydrodynamics. Proc. Royal Soc. Edinburgh 121A , 5–32.
- Sritharan, S. S. (2000) Deterministic and stochastic control of NavierStokes equation with linear, monotone and hyperviscosities. Appl. Math. Optimization 41, 255–308.
- Temam, R. (1995) Remarks on the control of turbulent flows. In: M. D. Gunzburger, ed., Flow Control. IMA Vol. Math. Appl. 68, Springer, New York, 357–381.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT5-0007-0029