Unique continuation principle for systems of parabolic equations

Otared Kavian; Luz de Teresa

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

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

Abstract

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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.

How to cite

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Kavian, 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

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  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.  Zbl0852.35070
  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.  Zbl1001.34046
  3. L. de Teresa, Controls insensitizing the semilinear heat equation. Comm. P.D.E.25 (2000) 39–72.  Zbl0942.35028
  4. C. Fabre, J.P. Puel and E. Zuazua, Approximate controllability of the semilinear heat equation. Proc. Roy. Soc. Edinburgh Sect. A125 (1995) 31–61.  Zbl0818.93032
  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).  Zbl1146.93009
  6. 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.  Zbl1248.93025
  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.  
  8. A. Pazy, Semigroups of linear operators and applications to partial differential equations, Applied Mathematical Sciences44. Springer-Verlag (1983).  Zbl0516.47023
  9. J.C. Saut and B. Scheurer, Unique continuation for some evolution equations. J. Differ. Equ.66 (1987) 118–139.  Zbl0631.35044
  10. K. Yosida, Functional Analysis, Die Grundlehren der Mathematischen Wissenschaften123. Springer-Verlag, New York, (1974).  

Citations in EuDML Documents

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

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