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.
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G.-B. Manuel was supported by D.G.E.S. (Spain), grant MTM2006-07932.
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Ammar-Khodja, F., Benabdallah, A., Dupaix, C. et al. A Kalman rank condition for the localized distributed controllability of a class of linear parabolic systems. J. Evol. Equ. 9, 267–291 (2009). https://doi.org/10.1007/s00028-009-0008-8
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DOI: https://doi.org/10.1007/s00028-009-0008-8