Implications of sharp trace regularity results on boundary stabilization of the system of linear elasticity
type: Item
instance of: scholarly article
title: Implications of sharp trace regularity results on boundary stabilization of the system of linear elasticity
zbMATH Open document ID: 0913.93062
author: M. Horn
published in: Journal of Mathematical Analysis and Applications
publication date: 1998-10-26T00:00:00Z
review text: The purpose of this very important paper is the study of a question concerning the problem of uniform-exponential decay of solutions to the elastodynamic system of elasticity using boundary feedback control. Energy dissipation is introduced via linear velocity feedbacks acting through a portion of the boundary as traction forces. Two primary goals are achieved: First, these results are proven without the imposition of strong geometric assumptions on the controlled portion of the boundary (thus extending earlier work which required that the domain should be star shaped). Second, the feedback is only a function of velocity (as opposed to the previous one also containing the tangential derivative of the displacement), resulting in a physically viable feedback. The proof of the main result is based on the multiplier method and relies critically on sharp trace estimates for the tangential derivative of the displacement on the boundary as well as on unique continuation results for the corresponding static system.
Mathematics Subject Classification ID: 93D15
Mathematics Subject Classification ID: 93C20
zbMATH DE Number: 1215667
zbMATH Keywords: linear elasticity
zbMATH Keywords: uniform stabilization
zbMATH Keywords: weak solution
zbMATH Keywords: boundary feedback control
zbMATH Keywords: multiplier method
zbMATH Keywords: trace estimates
zbMATH Keywords: unique continuation results
reviewed by: Jan Lovíšek
MaRDI profile type: Publication
full work available at URL: jmaa.1998.5963
OpenAlex ID: W2027455744
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DOI: 10.1006/JMAA.1998.5963
description: scientific article; zbMATH DE number 1215667