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

### Víctor Hernández-Santamaría

CINVESTAV del IPN, México DF, Mexico### Luz de Teresa

Universidad Nacional Autónoma de México, México DF, Mexico### Alexander Poznyak

CINVESTAV del IPN, México DF, Mexico

## Abstract

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]).

## Cite this article

Víctor Hernández-Santamaría, Luz de Teresa, Alexander Poznyak, Corrigendum and addendum to ‘‘Hierarchic control for a coupled parabolic system’’, Portugaliae Math. 73 (2016), 2: 115–137. Port. Math. 74 (2017), no. 2, pp. 161–168

DOI 10.4171/PM/1998