no. 2
Unique continuation principle for systems of parabolic equations
ESAIM: Control, Optimisation and Calculus of Variations, Tome 16 (2010) no. 2, pp. 247-274

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.

DOI : 10.1051/cocv/2008077
Classification : 35B37, 35B60, 93C20
Keywords: 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},
     year = {2010},
     publisher = {EDP Sciences},
     volume = {16},
     number = {2},
     doi = {10.1051/cocv/2008077},
     mrnumber = {2654193},
     zbl = {1195.35080},
     language = {en},
     url = {https://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  - https://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 https://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

[1] O. Bodart and C. Fabre, Controls insensitizing the norm of the solution of a semilinear heat equation. J. Math. Anal. Appl. 195 (1995) 658-683. | Zbl

[2] T. Coulhon and X.T. Duong, Maximal regularity and kernel bounds: observations on a theorem by Hieber and Prüss. Adv. Differ. Equ. 5 (2000) 343-368. | Zbl

[3] L. De Teresa, Controls insensitizing the semilinear heat equation. Comm. P.D.E. 25 (2000) 39-72. | Zbl

[4] C. Fabre, J.P. Puel and E. Zuazua, Approximate controllability of the semilinear heat equation. Proc. Roy. Soc. Edinburgh Sect. A 125 (1995) 31-61. | Zbl

[5] E. Fernández-Cara, M. González-Burgos and L. De Teresa, Boundary controllability results on a cascade system of 1-d heat equations. (In preparation).

[6] S. Guerrero, 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] J.L. Lions, 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] A. Pazy, Semigroups of linear operators and applications to partial differential equations, Applied Mathematical Sciences 44. Springer-Verlag (1983). | Zbl

[9] J.C. Saut and B. Scheurer, Unique continuation for some evolution equations. J. Differ. Equ. 66 (1987) 118-139. | Zbl

[10] K. Yosida, Functional Analysis, Die Grundlehren der Mathematischen Wissenschaften 123. Springer-Verlag, New York, (1974). | Zbl

Cité par Sources :