Carleman estimate and null controllability of a fourth order parabolic equation in dimension \(N\geq 2\)
type: Item
instance of: scholarly article
title: Carleman estimate and null controllability of a fourth order parabolic equation in dimension \(N\geq 2\)
zbMATH Open document ID: 1405.35073
author: Y. Aharonov
published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série
publication date: 2018-12-19T00:00:00Z
review text: The authors consider a fourth order parabolic equation in a bounded smooth domain \(\Omega\) with homogeneous Dirichlet boundary conditions on the solution and the Laplacian of the solution. The main result of the work is establishing a Carleman inequality with observation in an arbitrarily small open set \(\omega\subset\Omega\), which leads to a null controllability result at any time \(T>0\) for the associated control system with a control function acting through \(\omega\). Much attention in the work is paid to analysis of known results in the area of existence and uniqueness of solutions to a fourth order parabolic equation, as well as to issues of stability of such equations. It is noted that Carleman estimates for these equations in a domain with dimension of two or greater are first established in this work. They were known previously for a 1-dimensional domain only.
reviewed by: Vyacheslav I. Maksimov
Mathematics Subject Classification ID: 35K35
Mathematics Subject Classification ID: 93B05
Mathematics Subject Classification ID: 93B07
zbMATH DE Number: 6995651
zbMATH Keywords: fourth order parabolic equation
zbMATH Keywords: global Carleman estimate
zbMATH Keywords: controllability
zbMATH Keywords: observability
MaRDI profile type: Publication
full work available at URL: j.matpur.2018.04.004
OpenAlex ID: W2802338388
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DOI: 10.1016/J.MATPUR.2018.04.004
description: scientific article; zbMATH DE number 6995651