Carleman estimates and controllability results for fully-discrete approximations of 1-D parabolic equations
Analysis of PDEs
2020-12-04 v1 Numerical Analysis
Numerical Analysis
Optimization and Control
Abstract
In this paper, we prove a Carleman estimate for fully-discrete approximations of parabolic operators in which the discrete parameters and are connected to the large Carleman parameter. We use this estimate to obtain relaxed observability inequalities which yield, by duality, controllability results for fully-discrete linear and semilinear parabolic equations.
Keywords
Cite
@article{arxiv.2012.02156,
title = {Carleman estimates and controllability results for fully-discrete approximations of 1-D parabolic equations},
author = {Víctor Hernández-Santamaría and Pedro González Casanova},
journal= {arXiv preprint arXiv:2012.02156},
year = {2020}
}