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.
Classification : 93B05, 93C20, 93C25, 35K90
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}, zbl = {1125.93005}, mrnumber = {2148852}, 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 DA - 2005/// SP - 426 EP - 448 VL - 11 IS - 3 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv:2005013/ UR - https://zbmath.org/?q=an%3A1125.93005 UR - https://www.ams.org/mathscinet-getitem?mr=2148852 UR - https://doi.org/10.1051/cocv:2005013 DO - 10.1051/cocv:2005013 LA - en ID - COCV_2005__11_3_426_0 ER -
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 1052.35080
, , and ,[2] Controllability of some reaction-diffusion models by one control force. To appear. | Zbl 1157.93004
, and ,[3] Local exact controllability of a reaction-diffusion system. Diff. Integral Equ. 14 (2001) 577-587. | Zbl 1013.93028
and ,[4] Exact controllability of the superlinear heat equation. Appl. Math. Optim. 42 (2000) 73-89. | Zbl 0964.93046
,[5] Local controllability of the phase field system. Nonlinear Analysis 50 (2002) 363-372. | Zbl 1006.35013
,[6] Contrôle exact de l'équation de la chaleur. Comm. Partial Diff. Equ. 20 (1995) 335-356. | Zbl 0819.35071
and ,[7] Controllability of Evolution Equations. Seoul National University, Korea. Lect. Notes Ser. 34 (1996). | MR 1406566 | Zbl 0862.49004
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 78502 | Numdam | Zbl 0970.93023
and ,[9] Linear and Quasilinear Equations of Parabolic Type. Translations of Mathematical Monographs, AMS 23 (1968). | Zbl 0174.15403
, and ,[10] Semigroups of linear operators and applications to partial differential equations. Springer-Verlag New York (1983). | MR 710486 | Zbl 0516.47023
,[11] How fast are violent controls? Math. Control Signals Syst. 1 (1988) 89-95. | Zbl 0663.49018
,[12] How fast are violent controls, II? Math Control Signals Syst. 9 (1997) 327-340. | Zbl 0906.93007
and ,[13] Mathematical Control Theory: An Introduction. Birkhäuser (1992). | MR 1193920 | Zbl 1071.93500
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