Null-controllability of some systems of parabolic type by one control force
ESAIM: Control, Optimisation and Calculus of Variations, Tome 11 (2005) no. 3, pp. 426-448.

We study the null controllability by one control force of some linear systems of parabolic type. We give sufficient conditions for the null controllability property to be true and, in an abstract setting, we prove that it is not always possible to control.

DOI : https://doi.org/10.1051/cocv:2005013
Classification : 93B05,  93C20,  93C25,  35K90
Mots clés : control, parabolic systems
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author = {Khodja, Farid Ammar and Benabdallah, Assia and Dupaix, C\'edric and Kostin, Ilya},
title = {Null-controllability of some systems of parabolic type by one control force},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {426--448},
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Khodja, Farid Ammar; Benabdallah, Assia; Dupaix, Cédric; Kostin, Ilya. Null-controllability of some systems of parabolic type by one control force. ESAIM: Control, Optimisation and Calculus of Variations, Tome 11 (2005) no. 3, pp. 426-448. doi : 10.1051/cocv:2005013. http://www.numdam.org/articles/10.1051/cocv:2005013/

[1] F. Ammar-Khodja, A. Benabdallah, C. Dupaix and I. Kostine, Controllability to the trajectories of phase-field models by one control force. SIAM J. Control. Opt. 42 (2003) 1661-1680. | Zbl 1052.35080

[2] F. Ammar-Khodja, A. Benabdallah and C. Dupaix, Controllability of some reaction-diffusion models by one control force. To appear. | Zbl 1157.93004

[3] S. Anita and V. Barbu, Local exact controllability of a reaction-diffusion system. Diff. Integral Equ. 14 (2001) 577-587. | Zbl 1013.93028

[4] V. Barbu, Exact controllability of the superlinear heat equation. Appl. Math. Optim. 42 (2000) 73-89. | Zbl 0964.93046

[5] V. Barbu, Local controllability of the phase field system. Nonlinear Analysis 50 (2002) 363-372. | Zbl 1006.35013

[6] G. Lebeau and L. Robbiano, Contrôle exact de l'équation de la chaleur. Comm. Partial Diff. Equ. 20 (1995) 335-356. | Zbl 0819.35071

[7] A. Fursikov and O. Yu. Imanuvilov, Controllability of Evolution Equations. Seoul National University, Korea. Lect. Notes Ser. 34 (1996). | MR 1406566 | Zbl 0862.49004

[8] E. Fernández-Cara and E. Zuazua, Null and approximate controllability for weakly blowing up semilinear heat equations. Ann. Inst. H. Poincaré, Anal. Non Linéaire 17 (2000) 583-616. | EuDML 78502 | Numdam | Zbl 0970.93023

[9] O.A. Ladyženskaja, V.A. Solonnikov and N.N. Ural'Ceva, Linear and Quasilinear Equations of Parabolic Type. Translations of Mathematical Monographs, AMS 23 (1968). | Zbl 0174.15403

[10] A. Pazy, Semigroups of linear operators and applications to partial differential equations. Springer-Verlag New York (1983). | MR 710486 | Zbl 0516.47023

[11] T.I. Seidman, How fast are violent controls? Math. Control Signals Syst. 1 (1988) 89-95. | Zbl 0663.49018

[12] T.I. Seidman and J. Yong, How fast are violent controls, II? Math Control Signals Syst. 9 (1997) 327-340. | Zbl 0906.93007

[13] J. Zabczyk, Mathematical Control Theory: An Introduction. Birkhäuser (1992). | MR 1193920 | Zbl 1071.93500

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