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

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]).