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

Farid Ammar Khodja; Assia Benabdallah; Cédric Dupaix; Ilya Kostin

ESAIM: Control, Optimisation and Calculus of Variations (2010)

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

Abstract

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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.

How to cite

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Khodja, 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 (2010): 426-448. <http://eudml.org/doc/90771>.

@article{Khodja2010,
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. },
author = {Khodja, Farid Ammar, Benabdallah, Assia, Dupaix, Cédric, Kostin, Ilya},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Control; parabolic systems.; parabolic systems},
language = {eng},
month = {3},
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/90771},
volume = {11},
year = {2010},
}

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
DA - 2010/3//
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.; parabolic systems
UR - http://eudml.org/doc/90771
ER -

References

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  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 Linéaire17 (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).  
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  13. J. Zabczyk, Mathematical Control Theory: An Introduction. Birkhäuser (1992).  Zbl1071.93500

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