Carleman estimates and controllability results for the one-dimensional heat equation with BV coefficients
type: Item
instance of: scholarly article
title: Carleman estimates and controllability results for the one-dimensional heat equation with BV coefficients
zbMATH Open document ID: 1128.35020
published in: Journal of Differential Equations
publication date: 2007-02-26T00:00:00Z
review text: Global Carleman estimates for one-dimensional linear parabolic equations with a coefficient of bounded variations are derived. First, the author constructs limit weight functions by approaching the bounded variation coefficient \(c\) by piecewise constant coefficients \(c_{\varepsilon}\). Then he proves a Carleman estimate associated to \(\partial_t \pm \partial_x (c\partial_x)\) by proving that the constants in the Carleman estimate \(\partial_t \pm \partial_x (c_{\varepsilon}\partial_x)\) can be taken uniform with respect to the parameter \(\varepsilon\) and passing to the limit in each term of the estimate. In the conclusive part of the work, the author derives a Carleman estimate for a linear parabolic system with the right-hand side in \(L^2(0,T,H^{-1}(\Omega))\). This estimate is used for the analysis of the controllability of a semilinear system.
reviewed by: Vyacheslav I. Maksimov
Mathematics Subject Classification ID: 35B37
Mathematics Subject Classification ID: 93B05
Mathematics Subject Classification ID: 35K20
Mathematics Subject Classification ID: 35B45
zbMATH DE Number: 5129693
zbMATH Keywords: Carleman estimate
zbMATH Keywords: observability
zbMATH Keywords: non-smooth coefficients
zbMATH Keywords: parabolic equations
zbMATH Keywords: control
author: Jérôme Le Rousseau
MaRDI profile type: Publication
full work available at URL: j.jde.2006.10.005
OpenAlex ID: W2001950147
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DOI: 10.1016/J.JDE.2006.10.005
description: scientific article; zbMATH DE number 5129693