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Journal of Evolution Equations

, Volume 9, Issue 2, pp 267–291 | Cite as

A Kalman rank condition for the localized distributed controllability of a class of linear parabolic systems

  • Farid Ammar-Khodja
  • Assia Benabdallah
  • Cédric Dupaix
  • Manuel González-Burgos
Article

Abstract

We present a generalization of the Kalman rank condition to the case of n × n linear parabolic systems with constant coefficients and diagonalizable diffusion matrix. To reach the result, we are led to prove a global Carleman estimate for the solutions of a scalar 2n-order parabolic equation and deduce from it an observability inequality for our adjoint system.

Keywords

Kalman Condition Control Observability Carleman estimates Reaction diffusion systems 

Mathematical Subject Classification (2000).

3B07 35K05 35K55 35R30 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2009

Authors and Affiliations

  • Farid Ammar-Khodja
    • 1
  • Assia Benabdallah
    • 2
  • Cédric Dupaix
    • 3
  • Manuel González-Burgos
    • 4
  1. 1.Laboratoire de Mathématiques UMR 6623Université de Franche-ComtéBesançon cedexFrance
  2. 2.CMI-LATP, UMR 6632Université de Provence, Technopôle Château-GombertMarseille cedex 13France
  3. 3.Laboratoire de Mathématiques UMR 6623Université de Franche-ComtéBesançon cedexFrance
  4. 4.Dpto, E.D.A.NUniversidad de Sevilla, Aptdo. 1160SevillaSpain

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