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arXiv · 2012.02156

Carleman estimates and controllability results for fully-discrete approximations of 1-D parabolic equations

Víctor Hernández-Santamaría·Pedro González Casanova
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Abstract

In this paper, we prove a Carleman estimate for fully-discrete approximations of parabolic operators in which the discrete parameters $h$ and $\triangle t$ 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.

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Víctor Hernández-Santamaría, Pedro González Casanova. 2020-12-03. Carleman estimates and controllability results for fully-discrete approximations of 1-D parabolic equations. https://arxiv.org/abs/2012.02156

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