In this paper we prove a unique continuation result for a cascade system of parabolic equations, in which the solution of the first equation is (partially) used as a forcing term for the second equation. As a consequence we prove the existence of ε-insensitizing controls for some parabolic equations when the control region and the observability region do not intersect.
Mots clés : unique continuation, approximate controllability, cascade systems of parabolic equations
@article{COCV_2010__16_2_247_0, author = {Kavian, Otared and de Teresa, Luz}, title = {Unique continuation principle for systems of parabolic equations}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {247--274}, publisher = {EDP-Sciences}, volume = {16}, number = {2}, year = {2010}, doi = {10.1051/cocv/2008077}, mrnumber = {2654193}, zbl = {1195.35080}, language = {en}, url = {http://www.numdam.org/articles/10.1051/cocv/2008077/} }
TY - JOUR AU - Kavian, Otared AU - de Teresa, Luz TI - Unique continuation principle for systems of parabolic equations JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2010 SP - 247 EP - 274 VL - 16 IS - 2 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2008077/ DO - 10.1051/cocv/2008077 LA - en ID - COCV_2010__16_2_247_0 ER -
%0 Journal Article %A Kavian, Otared %A de Teresa, Luz %T Unique continuation principle for systems of parabolic equations %J ESAIM: Control, Optimisation and Calculus of Variations %D 2010 %P 247-274 %V 16 %N 2 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv/2008077/ %R 10.1051/cocv/2008077 %G en %F COCV_2010__16_2_247_0
Kavian, Otared; de Teresa, Luz. Unique continuation principle for systems of parabolic equations. ESAIM: Control, Optimisation and Calculus of Variations, Tome 16 (2010) no. 2, pp. 247-274. doi : 10.1051/cocv/2008077. http://www.numdam.org/articles/10.1051/cocv/2008077/
[1] Controls insensitizing the norm of the solution of a semilinear heat equation. J. Math. Anal. Appl. 195 (1995) 658-683. | Zbl
and ,[2] Maximal regularity and kernel bounds: observations on a theorem by Hieber and Prüss. Adv. Differ. Equ. 5 (2000) 343-368. | Zbl
and ,[3] Controls insensitizing the semilinear heat equation. Comm. P.D.E. 25 (2000) 39-72. | Zbl
,[4] Approximate controllability of the semilinear heat equation. Proc. Roy. Soc. Edinburgh Sect. A 125 (1995) 31-61. | Zbl
, and ,[5] Boundary controllability results on a cascade system of 1-d heat equations. (In preparation).
, and ,[6] Controllability of systems of Stokes equations with one control force: existence of insensitizing controls. Ann. Inst. H. Poincaré Anal. Non Linéaire 24 (2007) 1029-1054. | Numdam
,[7] Remarques préliminaires sur le contrôle des systèmes à données incomplètes, in Proceedings of the “XI Congreso de Ecuaciones Diferenciales y Aplicaciones (CEDYA)", Málaga (Spain) (1989) 43-54. | Zbl
,[8] Semigroups of linear operators and applications to partial differential equations, Applied Mathematical Sciences 44. Springer-Verlag (1983). | Zbl
,[9] Unique continuation for some evolution equations. J. Differ. Equ. 66 (1987) 118-139. | Zbl
and ,[10] Functional Analysis, Die Grundlehren der Mathematischen Wissenschaften 123. Springer-Verlag, New York, (1974). | Zbl
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