# Unique continuation principle for systems of parabolic equations

ESAIM: Control, Optimisation and Calculus of Variations (2010)

- Volume: 16, Issue: 2, page 247-274
- ISSN: 1292-8119

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topKavian, Otared, and de Teresa, Luz. "Unique continuation principle for systems of parabolic equations." ESAIM: Control, Optimisation and Calculus of Variations 16.2 (2010): 247-274. <http://eudml.org/doc/250733>.

@article{Kavian2010,

abstract = {
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.
},

author = {Kavian, Otared, de Teresa, Luz},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Unique continuation; approximate controllability; cascade systems of parabolic equations},

language = {eng},

month = {4},

number = {2},

pages = {247-274},

publisher = {EDP Sciences},

title = {Unique continuation principle for systems of parabolic equations},

url = {http://eudml.org/doc/250733},

volume = {16},

year = {2010},

}

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

DA - 2010/4//

PB - EDP Sciences

VL - 16

IS - 2

SP - 247

EP - 274

AB -
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.

LA - eng

KW - Unique continuation; approximate controllability; cascade systems of parabolic equations

UR - http://eudml.org/doc/250733

ER -

## References

top- 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.
- 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.
- L. de Teresa, Controls insensitizing the semilinear heat equation. Comm. P.D.E.25 (2000) 39–72.
- C. Fabre, J.P. Puel and E. Zuazua, Approximate controllability of the semilinear heat equation. Proc. Roy. Soc. Edinburgh Sect. A125 (1995) 31–61.
- E. Fernández-Cara, M. González-Burgos and L. de Teresa, Boundary controllability results on a cascade system of 1-d heat equations. (In preparation).
- S. Guerrero, Controllability of systems of Stokes equations with one control force: existence of insensitizing controls. Ann. Inst. H. Poincaré Anal. Non Linéaire24 (2007) 1029–1054.
- 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.
- A. Pazy, Semigroups of linear operators and applications to partial differential equations, Applied Mathematical Sciences44. Springer-Verlag (1983).
- J.C. Saut and B. Scheurer, Unique continuation for some evolution equations. J. Differ. Equ.66 (1987) 118–139.
- K. Yosida, Functional Analysis, Die Grundlehren der Mathematischen Wissenschaften123. Springer-Verlag, New York, (1974).

## Citations in EuDML Documents

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- Otared Kavian, Oumar Traoré, Approximate controllability by birth control for a nonlinear population dynamics model
- Fatiha Alabau-Boussouira, Matthieu Léautaud, Indirect stabilization of locally coupled wave-type systems
- Fatiha Alabau-Boussouira, Matthieu Léautaud, Indirect stabilization of locally coupled wave-type systems
- Sergei Avdonin, Abdon Choque Rivero, Luz de Teresa, Exact boundary controllability of coupled hyperbolic equations

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