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.
Mots clés : control, parabolic systems
@article{COCV_2005__11_3_426_0, 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}, publisher = {EDP-Sciences}, volume = {11}, number = {3}, year = {2005}, doi = {10.1051/cocv:2005013}, mrnumber = {2148852}, zbl = {1125.93005}, language = {en}, url = {http://www.numdam.org/articles/10.1051/cocv:2005013/} }
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 SP - 426 EP - 448 VL - 11 IS - 3 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv:2005013/ DO - 10.1051/cocv:2005013 LA - en ID - COCV_2005__11_3_426_0 ER -
%0 Journal Article %A Khodja, Farid Ammar %A Benabdallah, Assia %A Dupaix, Cédric %A Kostin, Ilya %T Null-controllability of some systems of parabolic type by one control force %J ESAIM: Control, Optimisation and Calculus of Variations %D 2005 %P 426-448 %V 11 %N 3 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv:2005013/ %R 10.1051/cocv:2005013 %G en %F COCV_2005__11_3_426_0
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] Controllability to the trajectories of phase-field models by one control force. SIAM J. Control. Opt. 42 (2003) 1661-1680. | Zbl
, , and ,[2] Controllability of some reaction-diffusion models by one control force. To appear. | Zbl
, and ,[3] Local exact controllability of a reaction-diffusion system. Diff. Integral Equ. 14 (2001) 577-587. | Zbl
and ,[4] Exact controllability of the superlinear heat equation. Appl. Math. Optim. 42 (2000) 73-89. | Zbl
,[5] Local controllability of the phase field system. Nonlinear Analysis 50 (2002) 363-372. | Zbl
,[6] Contrôle exact de l'équation de la chaleur. Comm. Partial Diff. Equ. 20 (1995) 335-356. | Zbl
and ,[7] Controllability of Evolution Equations. Seoul National University, Korea. Lect. Notes Ser. 34 (1996). | MR | Zbl
and ,[8] Null and approximate controllability for weakly blowing up semilinear heat equations. Ann. Inst. H. Poincaré, Anal. Non Linéaire 17 (2000) 583-616. | EuDML | Numdam | Zbl
and ,[9] Linear and Quasilinear Equations of Parabolic Type. Translations of Mathematical Monographs, AMS 23 (1968). | Zbl
, and ,[10] Semigroups of linear operators and applications to partial differential equations. Springer-Verlag New York (1983). | MR | Zbl
,[11] How fast are violent controls? Math. Control Signals Syst. 1 (1988) 89-95. | Zbl
,[12] How fast are violent controls, II? Math Control Signals Syst. 9 (1997) 327-340. | Zbl
and ,[13] Mathematical Control Theory: An Introduction. Birkhäuser (1992). | MR | Zbl
,Cité par Sources :