Long time approximations for solutions of wave equations via standing waves from quasimodes
type: Item
instance of: scholarly article
title: Long time approximations for solutions of wave equations via standing waves from quasimodes
zbMATH Open document ID: 1159.47057
published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série
publication date: 2008-10-30T00:00:00Z
review text: The author deals with second-order evolution problems, providing estimates for the time, in which standing waves approach their solutions, when the initial data are connected with quasimodes of the associated positive, symmetric and compact operations on a Hilbert space. Asymptotics for low and high frequency vibrations in certain singularly perturbed spectral problems, which depend on a small parameter, are thus described. These results are applied to vibrating systems with concentrated masses; it is thus possible to detect standing waves affecting only certain regions.
reviewed by: Petre P. Teodorescu
Mathematics Subject Classification ID: 47N20
Mathematics Subject Classification ID: 46N20
Mathematics Subject Classification ID: 74H45
zbMATH DE Number: 5359444
zbMATH Keywords: spectral analysis
zbMATH Keywords: asymptotic analysis
zbMATH Keywords: quasimodes
zbMATH Keywords: standing waves
author: E. Pérez
MaRDI profile type: Publication
full work available at URL: j.matpur.2008.06.003
OpenAlex ID: W2068386772
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DOI: 10.1016/J.MATPUR.2008.06.003
description: scientific article; zbMATH DE number 5359444