Stabilization of the wave equation with acoustic and delay boundary conditions
type: Item
instance of: scholarly article
title: Stabilization of the wave equation with acoustic and delay boundary conditions
zbMATH Open document ID: 1403.35151
author: Gilbert R. Peralta
published in: Semigroup Forum
publication date: 2018-06-22T00:00:00Z
review text: The paper is devoted to analysis of the well-posedness and stability property of the wave equation with acoustic boundary conditions and boundary delay. The structure of the paper is as follows. First, the author writes the considered equation in the form of abstract first order evolution equation. Then, it is proved that the operator of this equation generates a strongly continuous semigroup in a corresponding space. Using known results by Lasiecka et al., the author establishes sufficient conditions of stability for the equation with delay in the wave component. The exponential decay of the energy functional is also proved. Finally, the author establishes the sufficient conditions of stability for the equation with delay in the oscillator component.
reviewed by: Vyacheslav I. Maksimov
Mathematics Subject Classification ID: 35L20
Mathematics Subject Classification ID: 35B35
Mathematics Subject Classification ID: 35L05
Mathematics Subject Classification ID: 93D15
Mathematics Subject Classification ID: 47D06
zbMATH DE Number: 6893040
zbMATH Keywords: feedback delays
zbMATH Keywords: energy method
zbMATH Keywords: strongly continuous semigroup
zbMATH Keywords: exponential decay
MaRDI profile type: Publication
full work available at URL: s00233-018-9930-9
OpenAlex ID: W2791832495
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Wikidata QID: Q130105840
DOI: 10.1007/S00233-018-9930-9
description: scientific article; zbMATH DE number 6893040