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This paper tries to summarize recent results on the controllability ofsystems of (several) parabolic equations. The emphasis is placed on theextension of the Kalman rank condition (for finite dimensional systems ofdifferential equations) to parabolic systems. This question is itself tiedwith the proof of global Carleman estimates for systems and leads to a widefield of open problems.
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Ammar-Khodja et al. (2011) studied this question.
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