# Portugaliae Mathematica

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**Volume 74, Issue 2, 2017, pp. 161–168**

**DOI: 10.4171/PM/1998**

Published online: 2017-11-10

Corrigendum and addendum to ‘‘Hierarchic control for a coupled parabolic system’’, Portugaliae Math. 73 (2016), 2: 115–137

Víctor Hernández-Santamaría^{[1]}, Luz de Teresa

^{[2]}and Alexander Poznyak

^{[3]}(1) CINVESTAV del IPN, México DF, Mexico

(2) Universidad Nacional Autónoma de México, México DF, Mexico

(3) CINVESTAV del IPN, México DF, Mexico

In [2] we used three controls for a system of two coupled parabolic equations. We defined three functionals to be minimized and a hierarchy on the controls obtaining from the optimality condition a system of six coupled equations. In order to prove the null controllability, by means of the leader control acting only on the first equation, we give a proof of a Carleman inequality (Proposition 6.4) that in fact is incorrect. In this corrigendum we slightly modify the followers functionals given by (3) page 118 [2] in such a way that for the corresponding hierarchic system a correct Carleman inequality can be proved. This modification allows to introduce a coefficient $a_{12}\not=0$ ($a_{12}$ was zero in [2]).

*Keywords: *Controllabilty, Stackelberg–Nash strategies, Carleman inequalities, parabolic systems

Hernández-Santamaría Víctor, de Teresa Luz, Poznyak Alexander: Corrigendum and addendum to ‘‘Hierarchic control for a coupled parabolic system’’, Portugaliae Math. 73 (2016), 2: 115–137. *Port. Math.* 74 (2017), 161-168. doi: 10.4171/PM/1998