Null controllability of coupled parabolic equations with first-order perturbations
Résumé
Recently, in \cite{benabdallah2020block}, the block moment method was introduced to study null controllability problems in the case where a condensation of the eigenvalues is compensated by a condensation of the eigenfunctions. In this paper, as an application of the block moment method, we analyze the boundary null controllability of two coupled one-dimensional heat equations with first-order perturbation. We can prove that if the perturbations satisfy suitable conditions, the system is null controllable for $T>0$. Moreover, in the case of constant perturbation, the controllability result holds without these restrictions.