Discrete Carleman estimates and application to controllability for a fully-discrete parabolic operator with dynamic boundary conditions

We consider a fully-discrete approximations of 1-D heat equation with dynamic boundary conditions for which we provide a controllability result. The proof of this result is based on a relaxed observability inequality for the corresponding adjoint system. This is done by using a suitable Carleman est...

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Bibliographic Details
Published in:arXiv.org 2022-09
Main Authors: Lecaros, Rodrigo, Morales, Roberto, Pérez, Ariel, Zamorano, Sebastián
Format: Article
Language:English
Subjects:
Boundary conditions
Controllability
Observability (systems)
Parameters
Thermodynamics
Online Access:Get full text
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Summary:We consider a fully-discrete approximations of 1-D heat equation with dynamic boundary conditions for which we provide a controllability result. The proof of this result is based on a relaxed observability inequality for the corresponding adjoint system. This is done by using a suitable Carleman estimate for such models where the discrete parameters \(h\) and \(\Delta t\) are connected to the one of the large Carleman parameters.
ISSN:2331-8422