# Null-controllability of some systems of parabolic type by one control force

Farid Ammar Khodja; Assia Benabdallah; Cédric Dupaix; Ilya Kostin^{[1]}

- [1] Université de Saint-Etienne, Équipe d’Analyse Numérique, 23 rue Paul MICHELON, 42023 Saint-Etienne Cedex 02, France;

ESAIM: Control, Optimisation and Calculus of Variations (2005)

- Volume: 11, Issue: 3, page 426-448
- ISSN: 1292-8119

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topKhodja, Farid Ammar, et al. "Null-controllability of some systems of parabolic type by one control force." ESAIM: Control, Optimisation and Calculus of Variations 11.3 (2005): 426-448. <http://eudml.org/doc/244933>.

@article{Khodja2005,

abstract = {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.},

affiliation = {Université de Saint-Etienne, Équipe d’Analyse Numérique, 23 rue Paul MICHELON, 42023 Saint-Etienne Cedex 02, France;},

author = {Khodja, Farid Ammar, Benabdallah, Assia, Dupaix, Cédric, Kostin, Ilya},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {control; parabolic systems; Control},

language = {eng},

number = {3},

pages = {426-448},

publisher = {EDP-Sciences},

title = {Null-controllability of some systems of parabolic type by one control force},

url = {http://eudml.org/doc/244933},

volume = {11},

year = {2005},

}

TY - JOUR

AU - Khodja, Farid Ammar

AU - Benabdallah, Assia

AU - Dupaix, Cédric

AU - Kostin, Ilya

TI - Null-controllability of some systems of parabolic type by one control force

JO - ESAIM: Control, Optimisation and Calculus of Variations

PY - 2005

PB - EDP-Sciences

VL - 11

IS - 3

SP - 426

EP - 448

AB - 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.

LA - eng

KW - control; parabolic systems; Control

UR - http://eudml.org/doc/244933

ER -

## References

top- [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. Zbl1052.35080
- [2] F. Ammar-Khodja, A. Benabdallah and C. Dupaix, Controllability of some reaction-diffusion models by one control force. To appear. Zbl1157.93004
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- [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. Zbl0970.93023
- [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). Zbl0174.15403
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- [11] T.I. Seidman, How fast are violent controls? Math. Control Signals Syst. 1 (1988) 89–95. Zbl0663.49018
- [12] T.I. Seidman and J. Yong, How fast are violent controls, II? Math Control Signals Syst. 9 (1997) 327–340. Zbl0906.93007
- [13] J. Zabczyk, Mathematical Control Theory: An Introduction. Birkhäuser (1992). Zbl1071.93500MR1193920

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