Carleman estimates with a second large parameter
type: Item
instance of: scholarly article
title: Carleman estimates with a second large parameter
zbMATH Open document ID: 0973.35044
author: Matthias Eller
published in: Journal of Mathematical Analysis and Applications
publication date: 2001-11-14T00:00:00Z
review text: Unique continuation of solutions to linear partial differential equations is of importance in many branches of applied mathematics, in particular, in control theory and inverse problems. The Carleman estimates are an important tool for proving the unique continuation for linear operators with non-analytic coefficients. In this paper, the author combines the approaches by \textit{D. Tataru} [Commun. Partial Differ. Equations 20, No.~5-6, 855-884 (1995; Zbl 0846.35021)] and \textit{V. Isakov} [Preprint, 1998] to obtain a new Carleman estimate with two large parameters for operators with time independent coefficients. This estimate is the foundation of the local uniqueness result for the thermoelastic system: \(w_{tt}-\gamma \Delta w_{tt} +\Delta^2 w +\operatorname {div} (\alpha (x) \nabla \theta)=0\),\quad \(\theta_t -\Delta\theta -\operatorname {div} (\alpha (x) \nabla w_t)=0\).
reviewed by: Song Jiang
Mathematics Subject Classification ID: 35B60
Mathematics Subject Classification ID: 35B45
Mathematics Subject Classification ID: 35S05
Mathematics Subject Classification ID: 74F05
zbMATH DE Number: 1533180
zbMATH Keywords: unique continuation
zbMATH Keywords: linear operators with non-analytic coefficients
zbMATH Keywords: local uniqueness result for the thermoelastic systems
zbMATH Keywords: time-independent coefficients
MaRDI profile type: Publication
full work available at URL: jmaa.2000.6903
OpenAlex ID: W2132528241
Wikidata QID: Q124858004
cites work: Q4496130
cites work: Simultaneous exact/approximate boundary controllability of thermo-elastic plates with variable thermal coefficient and moment control
cites work: Q5557257
cites work: Q3671563
cites work: Unique continuation for solutions to pde's; between hörmander's theorem and holmgren' theorem
cites work: Unique continuation for operators with partially analytic coefficients
DOI: 10.1006/JMAA.2000.6903
description: scientific article; zbMATH DE number 1533180