Spectral asymptotics for the vectorial damped wave equation

Spectral asymptotics for the vectorial damped wave equation

The eigenfrequencies associated to a scalar damped wave equation are known to belong to a band parallel to the real axis. In [Sj{\"o}00] J. Sj{\"o}strand showed that up to a set of density 0, the eigenfrequencies are confined in a thinner band determined by the Birkhoff limits of the dampi...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:arXiv.org 2021-11
1. Verfasser: Klein, Guillaume
Format: Artikel
Sprache:eng
Schlagworte:
Damping
Liapunov exponents
Resonant frequencies
Wave equations
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page
container_issue
container_start_page
container_title arXiv.org
container_volume
creator Klein, Guillaume
description The eigenfrequencies associated to a scalar damped wave equation are known to belong to a band parallel to the real axis. In [Sj{\"o}00] J. Sj{\"o}strand showed that up to a set of density 0, the eigenfrequencies are confined in a thinner band determined by the Birkhoff limits of the damping term. In this article we show that this result is still true for a vectorial damped wave equation. In this setting the Lyapunov exponents of the cocycle given by the damping term play the role of the Birkhoff limits of the scalar setting.
format Article
fullrecord <record><control><sourceid>proquest</sourceid><recordid>TN_cdi_proquest_journals_2598841121</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2598841121</sourcerecordid><originalsourceid>FETCH-proquest_journals_25988411213</originalsourceid><addsrcrecordid>eNqNyr0KwjAUQOEgCBbtOwScC8lNoxFHUdx1L6G9xZS2SfNT8e3t4AM4neE7K5KBELxQJcCG5CF0jDE4HEFKkZHzw2Edve6pDp_BRRtNHWhrPY0vpPNi1ptFGz04bOhbz0hxSjoaO-7IutV9wPzXLdnfrs_LvXDeTglDrDqb_LhQBfKkVMk5cPHf9QVI2TfF</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2598841121</pqid></control><display><type>article</type><title>Spectral asymptotics for the vectorial damped wave equation</title><source>Free E- Journals</source><creator>Klein, Guillaume</creator><creatorcontrib>Klein, Guillaume</creatorcontrib><description>The eigenfrequencies associated to a scalar damped wave equation are known to belong to a band parallel to the real axis. In [Sj{\"o}00] J. Sj{\"o}strand showed that up to a set of density 0, the eigenfrequencies are confined in a thinner band determined by the Birkhoff limits of the damping term. In this article we show that this result is still true for a vectorial damped wave equation. In this setting the Lyapunov exponents of the cocycle given by the damping term play the role of the Birkhoff limits of the scalar setting.</description><identifier>EISSN: 2331-8422</identifier><language>eng</language><publisher>Ithaca: Cornell University Library, arXiv.org</publisher><subject>Damping ; Liapunov exponents ; Resonant frequencies ; Wave equations</subject><ispartof>arXiv.org, 2021-11</ispartof><rights>2021. This work is published under http://arxiv.org/licenses/nonexclusive-distrib/1.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>780,784</link.rule.ids></links><search><creatorcontrib>Klein, Guillaume</creatorcontrib><title>Spectral asymptotics for the vectorial damped wave equation</title><title>arXiv.org</title><description>The eigenfrequencies associated to a scalar damped wave equation are known to belong to a band parallel to the real axis. In [Sj{\"o}00] J. Sj{\"o}strand showed that up to a set of density 0, the eigenfrequencies are confined in a thinner band determined by the Birkhoff limits of the damping term. In this article we show that this result is still true for a vectorial damped wave equation. In this setting the Lyapunov exponents of the cocycle given by the damping term play the role of the Birkhoff limits of the scalar setting.</description><subject>Damping</subject><subject>Liapunov exponents</subject><subject>Resonant frequencies</subject><subject>Wave equations</subject><issn>2331-8422</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><recordid>eNqNyr0KwjAUQOEgCBbtOwScC8lNoxFHUdx1L6G9xZS2SfNT8e3t4AM4neE7K5KBELxQJcCG5CF0jDE4HEFKkZHzw2Edve6pDp_BRRtNHWhrPY0vpPNi1ptFGz04bOhbz0hxSjoaO-7IutV9wPzXLdnfrs_LvXDeTglDrDqb_LhQBfKkVMk5cPHf9QVI2TfF</recordid><startdate>20211117</startdate><enddate>20211117</enddate><creator>Klein, Guillaume</creator><general>Cornell University Library, arXiv.org</general><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>HCIFZ</scope><scope>L6V</scope><scope>M7S</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope></search><sort><creationdate>20211117</creationdate><title>Spectral asymptotics for the vectorial damped wave equation</title><author>Klein, Guillaume</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-proquest_journals_25988411213</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Damping</topic><topic>Liapunov exponents</topic><topic>Resonant frequencies</topic><topic>Wave equations</topic><toplevel>online_resources</toplevel><creatorcontrib>Klein, Guillaume</creatorcontrib><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science &amp; Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</collection><collection>Publicly Available Content Database</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Klein, Guillaume</au><format>book</format><genre>document</genre><ristype>GEN</ristype><atitle>Spectral asymptotics for the vectorial damped wave equation</atitle><jtitle>arXiv.org</jtitle><date>2021-11-17</date><risdate>2021</risdate><eissn>2331-8422</eissn><abstract>The eigenfrequencies associated to a scalar damped wave equation are known to belong to a band parallel to the real axis. In [Sj{\"o}00] J. Sj{\"o}strand showed that up to a set of density 0, the eigenfrequencies are confined in a thinner band determined by the Birkhoff limits of the damping term. In this article we show that this result is still true for a vectorial damped wave equation. In this setting the Lyapunov exponents of the cocycle given by the damping term play the role of the Birkhoff limits of the scalar setting.</abstract><cop>Ithaca</cop><pub>Cornell University Library, arXiv.org</pub><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier EISSN: 2331-8422
ispartof arXiv.org, 2021-11
issn 2331-8422
language eng
recordid cdi_proquest_journals_2598841121
source Free E- Journals
subjects Damping
Liapunov exponents
Resonant frequencies
Wave equations
title Spectral asymptotics for the vectorial damped wave equation
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-26T09%3A18%3A51IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest&rft_val_fmt=info:ofi/fmt:kev:mtx:book&rft.genre=document&rft.atitle=Spectral%20asymptotics%20for%20the%20vectorial%20damped%20wave%20equation&rft.jtitle=arXiv.org&rft.au=Klein,%20Guillaume&rft.date=2021-11-17&rft.eissn=2331-8422&rft_id=info:doi/&rft_dat=%3Cproquest%3E2598841121%3C/proquest%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2598841121&rft_id=info:pmid/&rfr_iscdi=true