Carleman estimates and controllability for a semi-discrete fourth-order parabolic equation
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Date
2022
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Abstract
The boundary controllability of fourth-order parabolic equations has been addressed in recent literature. However, there are no results concerning their numerical approximation and the behavior of discrete controls when the discretization parameter goes to zero. This paper is intended to cover this gap by studying this issue when the space operator is discretized and the time is kept as a continuous variable (semi-discrete approximation case). The proof is based on a relaxed observability inequality for the corresponding semi-discrete adjoint system and a suitable semi-discrete Carleman estimate.(c) 2022 Elsevier Masson SAS. All rights reserved.
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Keywords
Parabolicoperator, Semi-discretesystem, Semi-discreteCarlemanestimates, Observability, Nullcontrollability