no. 6
Controllability of systems of Stokes equations with one control force : existence of insensitizing controls
Guerrero, Sergio1
1 Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, boîte courrier 187, 75035 Cedex 05, Paris, France;
Annales de l'I.H.P. Analyse non linéaire, Tome 24 (2007) no. 6, pp. 1029-1054.
DOI : 10.1016/j.anihpc.2006.11.001
Guerrero, Sergio 1

1 Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, boîte courrier 187, 75035 Cedex 05, Paris, France; 
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Guerrero, Sergio. Controllability of systems of Stokes equations with one control force : existence of insensitizing controls. Annales de l'I.H.P. Analyse non linéaire, Tome 24 (2007) no. 6, pp. 1029-1054. doi : 10.1016/j.anihpc.2006.11.001. http://archive.numdam.org/articles/10.1016/j.anihpc.2006.11.001/

[1] Bodart O., Fabre C., Controls insensitizing the norm of the solution of a semilinear heat equation, J. Math. Anal. Appl. 195 (3) (1995) 658-683. | MR | Zbl

[2] Bodart O., González-Burgos M., Pérez-García R., Existence of insensitizing controls for a semilinear heat equation with a superlinear nonlinearity, Comm. Partial Differential Equations 29 (7-8) (2004) 1017-1050. | Zbl

[3] De Teresa L., Insensitizing controls for a semilinear heat equation, Comm. Partial Differential Equations 25 (1-2) (2000) 39-72. | Zbl

[4] L. De Teresa, O. Kavian, Unique continuation principle for systems of parabolic equations, in preparation.

[5] Fernández-Cara E., González-Burgos M., Guerrero S., Puel J.-P., Null controllability of the heat equation with boundary Fourier conditions: The linear case, ESAIM Control Optim. Calc. Var. 12 (3) (2006) 442-465. | EuDML | Numdam | MR | Zbl

[6] Fernández-Cara E., Guerrero S., Imanuvilov O.Yu., Puel J.-P., Local exact controllability of the Navier-Stokes system, J. Math. Pures Appl. (9) 83 (12) (2004) 1501-1542. | Zbl

[7] E. Fernández-Cara, S. Guerrero, Local exact controllability of micropolar fluids, J. Math. Fluid Mech., doi:10.1007/s00021-005-0207-1. | MR | Zbl

[8] E. Fernández-Cara, S. Guerrero, Global Carleman estimates for solutions of parabolic systems defined by transposition and some applications to controllability, AMRX Appl. Math. Res. Express 2006, Art. ID 75090, 31 pp. | MR | Zbl

[9] Fursikov A.V., Imanuvilov O.Yu., Controllability of Evolution Equations, Lecture Notes, vol. 34, Seoul National University, Korea, 1996. | MR | Zbl

[10] S. Guerrero, Null controllability of some systems of two parabolic equations with one control force, SIAM J. Control Optim., in press. | MR

[11] Imanuvilov O.Yu., Remarks on exact controllability for the Navier-Stokes equations, ESAIM Control Optim. Calc. Var. 6 (2001) 39-72. | Numdam | Zbl

[12] Imanuvilov O.Yu., Yamamoto M., Carleman inequalities for parabolic equations in Sobolev spaces of negative order and exact controllability for semilinear parabolic equations, Publ. Res. Inst. Math. Sci. 39 (2) (2003) 227-274. | MR | Zbl

[13] Ladyzenskaya O.A., The Mathematical Theory of Viscous Incompressible Flow, Translated from the Russian by Richard A. Silverman, Revised, English edition, Gordon and Breach Science Publishers, New York-London, 1963. | Zbl

[14] Lions J.-L., Quelques notions dans l'analyse et le contrôle de systèmes à données incomplètes, in: Málaga, 1989, Proceedings of the XIth Congress on Differential Equations and Applications/First Congress on Applied Mathematics, Univ. Málaga, Málaga, 1990, pp. 43-54. | MR | Zbl

[15] Lions J.-L., Sentinelles pour les systèmes distribués à données incomplètes, Recherches en Mathématiques Appliquées, vol. 21, Masson, Paris, 1992. | MR | Zbl

[16] R. Pérez-García, Algunos resultados de control para algunos problemas parabólicos acoplados no lineales: controlabilidad y controles insensibilizantes, PhD Thesis, Sevilla, 2004.

[17] Temam R., Navier-Stokes Equations. Theory and Numerical Analysis, Studies in Mathematics and its Applications, vol. 2, North Holland Publishing Co., Amsterdam, 1977. | Zbl

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