Salah-Eddine Chorfi – Mathematics and Decision

$\begin{quote} \begin{center} \textbf{Impulsive control for parabolic equations with various boundary conditions} \end{center} \medskip We present a comparative study to numerically compute impulse approximate controls for parabolic equations with various boundary conditions. Theoretical controllability results have been recently investigated using a logarithmic convexity estimate at a single time based on a Carleman commutator approach. We propose a numerical algorithm for computing the impulse controls with minimal $L^2$-norms by adapting a penalized Hilbert Uniqueness Method (HUM) combined with a Conjugate Gradient (CG) method. We consider static boundary conditions (Dirichlet and Neumann) as well as dynamic boundary conditions. Some numerical experiments are given to validate and compare the theoretical impulse controllability results. \end{quote}$