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

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 (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

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  1. [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. [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. [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. [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
  10. [10] A. Pazy, Semigroups of linear operators and applications to partial differential equations. Springer-Verlag New York (1983). Zbl0516.47023MR710486
  11. [11] T.I. Seidman, How fast are violent controls? Math. Control Signals Syst. 1 (1988) 89–95. Zbl0663.49018
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  13. [13] J. Zabczyk, Mathematical Control Theory: An Introduction. Birkhäuser (1992). Zbl1071.93500MR1193920

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