Corrigendum and addendum to ``Hierarchic control for a coupled parabolic system'' (Q1687821)

Summary: In [Port. Math. (N.S.) 73, No. 2, 115--137 (2016; Zbl 1342.49006)] 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 [loc. cit.] 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 [loc. cit.]).