Numerical impulse controllability for parabolic equations by a penalized HUM approach
Optimization and Control
2023-10-31 v1 Numerical Analysis
Analysis of PDEs
Numerical Analysis
Abstract
This work presents 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 -norms by adapting a penalized Hilbert Uniqueness Method (HUM) combined with a Conjugate Gradient (CG) method. We consider static boundary conditions (Dirichlet and Neumann) and dynamic boundary conditions. Some numerical experiments based on our developed algorithm are given to validate and compare the theoretical impulse controllability results.
Keywords
Cite
@article{arxiv.2310.18436,
title = {Numerical impulse controllability for parabolic equations by a penalized HUM approach},
author = {S. E. Chorfi and G. El Guermai and L. Maniar and W. Zouhair},
journal= {arXiv preprint arXiv:2310.18436},
year = {2023}
}