English

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 hh and t\triangle t 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}
}