<?xml version="1.0" encoding="utf-8"?>
<TEI xmlns="http://www.tei-c.org/ns/1.0" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:hal="http://hal.archives-ouvertes.fr/" xmlns:gml="http://www.opengis.net/gml/3.3/" xmlns:gmlce="http://www.opengis.net/gml/3.3/ce" version="1.1" xsi:schemaLocation="http://www.tei-c.org/ns/1.0 http://api.archives-ouvertes.fr/documents/aofr-sword.xsd">
  <teiHeader>
    <fileDesc>
      <titleStmt>
        <title>HAL TEI export of hal-00831402</title>
      </titleStmt>
      <publicationStmt>
        <distributor>CCSD</distributor>
        <availability status="restricted">
          <licence target="https://creativecommons.org/publicdomain/zero/1.0/">CC0 1.0 - Universal</licence>
        </availability>
        <date when="2026-05-12T15:59:10+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">Time-local dissipative formulation and stable numerical schemes for a class of integrodifferential wave equations</title>
            <author role="crp">
              <persName>
                <forename type="first">Céline</forename>
                <surname>Casenave</surname>
              </persName>
              <email type="md5">54c6b0b8c1ec8178f2229cc458f0a96c</email>
              <email type="domain">inrae.fr</email>
              <idno type="idhal" notation="string">casenave</idno>
              <idno type="idhal" notation="numeric">2091</idno>
              <idno type="halauthorid" notation="string">18238-2091</idno>
              <idno type="ORCID">https://orcid.org/0000-0003-0489-4665</idno>
              <idno type="IDREF">https://www.idref.fr/147895774</idno>
              <affiliation ref="#struct-1739870"/>
            </author>
            <author role="crp">
              <persName>
                <forename type="first">Emmanuel</forename>
                <surname>Montseny</surname>
              </persName>
              <email type="md5">bfd3133d574f3678d39342a5628c274d</email>
              <email type="domain">montseny.pro</email>
              <idno type="idhal" notation="numeric">959574</idno>
              <idno type="halauthorid" notation="string">858280-959574</idno>
              <orgName ref="#struct-389081"/>
              <affiliation ref="#struct-389059"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Céline</forename>
                <surname>Casenave</surname>
              </persName>
              <email type="md5">54c6b0b8c1ec8178f2229cc458f0a96c</email>
              <email type="domain">inrae.fr</email>
            </editor>
          </titleStmt>
          <editionStmt>
            <edition n="v1" type="current">
              <date type="whenSubmitted">2013-06-06 22:45:02</date>
              <date type="whenModified">2026-01-23 03:26:25</date>
              <date type="whenReleased">2013-06-07 08:10:25</date>
              <date type="whenProduced">2008-07</date>
              <date type="whenEndEmbargoed">2013-06-06</date>
              <ref type="file" target="https://hal.science/hal-00831402v1/document">
                <date notBefore="2013-06-06"/>
              </ref>
              <ref type="file" subtype="author" n="1" target="https://hal.science/hal-00831402v1/file/Preprint_-_Casenave_and_Montseny_-_2008_-_Time-local_dissipative_formulation_and_stable_nume.pdf" id="file-831402-1091570">
                <date notBefore="2013-06-06"/>
              </ref>
              <ref type="externalLink" target="http://hal.inria.fr/docs/00/83/14/02/PDF/Preprint_-_Casenave_and_Montseny_-_2008_-_Time-local_dissipative_formulation_and_stable_nume.pdf"/>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="184186">
                <persName>
                  <forename>Céline</forename>
                  <surname>Casenave</surname>
                </persName>
                <email type="md5">54c6b0b8c1ec8178f2229cc458f0a96c</email>
                <email type="domain">inrae.fr</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-00831402</idno>
            <idno type="halUri">https://hal.science/hal-00831402</idno>
            <idno type="halBibtex">casenave:hal-00831402</idno>
            <idno type="halRefHtml">&lt;i&gt;SIAM Journal on Applied Mathematics&lt;/i&gt;, 2008, 68 (6), pp.1763--1783. &lt;a target="_blank" href="https://dx.doi.org/10.1137/070693710"&gt;&amp;#x27E8;10.1137/070693710&amp;#x27E9;&lt;/a&gt;</idno>
            <idno type="halRef">SIAM Journal on Applied Mathematics, 2008, 68 (6), pp.1763--1783. &amp;#x27E8;10.1137/070693710&amp;#x27E9;</idno>
            <availability status="restricted">
              <licence target="https://about.hal.science/hal-authorisation-v1/">HAL Authorization<ref corresp="#file-831402-1091570"/></licence>
            </availability>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="UNIV-TLSE2">Université Toulouse 2</idno>
            <idno type="stamp" n="UNIV-TLSE3">Université de Toulouse</idno>
            <idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno>
            <idno type="stamp" n="INSA-TOULOUSE">Institut National des Sciences Appliquées de Toulouse</idno>
            <idno type="stamp" n="LAAS">Laboratoire d'analyse et d'architecture des systèmes</idno>
            <idno type="stamp" n="UT1-CAPITOLE">Université Toulouse 1 Capitole</idno>
            <idno type="stamp" n="LAAS-DISCO" corresp="LAAS-DECISION-ET-OPTIMISATION">Equipe diagnostic, supervision et COnduite</idno>
            <idno type="stamp" n="LAAS-RAP" corresp="LAAS-ROBOTIQUE">Équipe Robotique, Action et Perception</idno>
            <idno type="stamp" n="LAAS-ROBOTIQUE" corresp="LAAS">LAAS-Robotique</idno>
            <idno type="stamp" n="LAAS-DECISION-ET-OPTIMISATION" corresp="LAAS">LAAS-Décision et Optimisation</idno>
            <idno type="stamp" n="LAAS-GESTION-DE-L-ENERGIE" corresp="LAAS">LAAS-Gestion de l'énergie</idno>
            <idno type="stamp" n="TDS-MACS">Réseau de recherche en Théorie des Systèmes Distribués, Modélisation, Analyse et Contrôle des Systèmes</idno>
            <idno type="stamp" n="INSA-GROUPE">Groupe INSA</idno>
            <idno type="stamp" n="INRAE">Institut National de Recherche en Agriculture, Alimentation et Environnement</idno>
            <idno type="stamp" n="TOULOUSE-INP">Toulouse - INP</idno>
            <idno type="stamp" n="UNIV-UT3">Université Toulouse 3</idno>
            <idno type="stamp" n="UT3-INP">Université de Toulouse / Toulouse INP</idno>
            <idno type="stamp" n="UT3-TOULOUSEINP">Université de Toulouse / Toulouse INP</idno>
            <idno type="stamp" n="TEST7-HALCNRS">test 7 du portail hal cnrs</idno>
            <idno type="stamp" n="LAAS-MRS" corresp="LAAS-GESTION-DE-L-ENERGIE">Équipe Matériaux Réactifs et Stockage d'énergie</idno>
          </seriesStmt>
          <notesStmt>
            <note type="audience" n="2">International</note>
            <note type="popular" n="0">No</note>
            <note type="peer" n="1">Yes</note>
          </notesStmt>
          <sourceDesc>
            <biblStruct>
              <analytic>
                <title xml:lang="en">Time-local dissipative formulation and stable numerical schemes for a class of integrodifferential wave equations</title>
                <author role="crp">
                  <persName>
                    <forename type="first">Céline</forename>
                    <surname>Casenave</surname>
                  </persName>
                  <email type="md5">54c6b0b8c1ec8178f2229cc458f0a96c</email>
                  <email type="domain">inrae.fr</email>
                  <idno type="idhal" notation="string">casenave</idno>
                  <idno type="idhal" notation="numeric">2091</idno>
                  <idno type="halauthorid" notation="string">18238-2091</idno>
                  <idno type="ORCID">https://orcid.org/0000-0003-0489-4665</idno>
                  <idno type="IDREF">https://www.idref.fr/147895774</idno>
                  <affiliation ref="#struct-1739870"/>
                </author>
                <author role="crp">
                  <persName>
                    <forename type="first">Emmanuel</forename>
                    <surname>Montseny</surname>
                  </persName>
                  <email type="md5">bfd3133d574f3678d39342a5628c274d</email>
                  <email type="domain">montseny.pro</email>
                  <idno type="idhal" notation="numeric">959574</idno>
                  <idno type="halauthorid" notation="string">858280-959574</idno>
                  <orgName ref="#struct-389081"/>
                  <affiliation ref="#struct-389059"/>
                </author>
              </analytic>
              <monogr>
                <idno type="localRef">Rapport LAAS n° 07258</idno>
                <idno type="halJournalId" status="VALID">8475</idno>
                <idno type="issn">0036-1399</idno>
                <title level="j">SIAM Journal on Applied Mathematics</title>
                <imprint>
                  <publisher>Society for Industrial and Applied Mathematics</publisher>
                  <biblScope unit="volume">68</biblScope>
                  <biblScope unit="issue">6</biblScope>
                  <biblScope unit="pp">1763--1783</biblScope>
                  <date type="datePub">2008-07</date>
                </imprint>
              </monogr>
              <idno type="doi">10.1137/070693710</idno>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <keywords scheme="author">
                <term xml:lang="it">stability condition</term>
                <term xml:lang="it">energy functional</term>
                <term xml:lang="it">Cauchy problem</term>
                <term xml:lang="it">numerical scheme</term>
                <term xml:lang="it">diffusive representation</term>
                <term xml:lang="it">convolution operator</term>
                <term xml:lang="it">partial differential equation</term>
                <term xml:lang="it">integrodifferential equation</term>
              </keywords>
              <classCode scheme="halDomain" n="spi.auto">Engineering Sciences [physics]/Automatic</classCode>
              <classCode scheme="halDomain" n="math.math-na">Mathematics [math]/Numerical Analysis [math.NA]</classCode>
              <classCode scheme="halTypology" n="ART">Journal articles</classCode>
              <classCode scheme="halOldTypology" n="ART">Journal articles</classCode>
              <classCode scheme="halTreeTypology" n="ART">Journal articles</classCode>
            </textClass>
            <abstract xml:lang="en">
              <p>We consider integrodifferential equations of the abstract form H(∂t)Φ=G(∇)Φ+f, where H(∂t) is a diagonal convolution operator and G(∇) is a linear anti-selfadjoint differential operator. On the basis of an original approach devoted to integral causal operators, we propose and study a time-local augmented formulation under the form of a Cauchy problem ∂tΨ=AΨ+Bf such that Φ=CΨ. We show that under a suitable hypothesis on the symbol H(p), this new formulation is dissipative in the sense of a natural energy functional. We then establish the stability of numerical schemes built from this time-local formulation, thanks to the dissipation of appropriate discrete energies. Finally, the efficiency of these schemes is highlighted by concrete numerical results relating to a model recently proposed for 1D acoustic waves in porous media.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="researchteam" xml:id="struct-1739870" status="VALID">
          <orgName>Équipe Matériaux Réactifs et Stockage d'énergie</orgName>
          <orgName type="acronym">LAAS-MRS</orgName>
          <date type="start">2026-01-01</date>
          <desc>
            <address>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.laas.fr/fr/equipes/mrs/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-1612717" type="direct"/>
            <relation active="#struct-81148" type="indirect"/>
            <relation name="443875" active="#struct-443875" type="indirect"/>
            <relation active="#struct-116255" type="indirect"/>
            <relation active="#struct-301232" type="indirect"/>
            <relation active="#struct-443875" type="indirect"/>
            <relation active="#struct-116256" type="indirect"/>
            <relation name="UPR8001" active="#struct-441569" type="indirect"/>
            <relation active="#struct-448187" type="indirect"/>
            <relation active="#struct-1574795" type="indirect"/>
          </listRelation>
        </org>
        <org type="researchteam" xml:id="struct-389059" status="OLD">
          <orgName>Équipe DIagnostic, Supervision et COnduite</orgName>
          <orgName type="acronym">LAAS-DISCO</orgName>
          <date type="end">2025-01-01</date>
          <desc>
            <address>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.laas.fr/public/fr/disco</ref>
          </desc>
          <listRelation>
            <relation active="#struct-459" type="direct"/>
            <relation active="#struct-81148" type="indirect"/>
            <relation name="443875" active="#struct-443875" type="indirect"/>
            <relation active="#struct-116255" type="indirect"/>
            <relation active="#struct-301232" type="indirect"/>
            <relation active="#struct-443875" type="indirect"/>
            <relation active="#struct-116256" type="indirect"/>
            <relation active="#struct-217752" type="indirect"/>
            <relation name="UPR8001" active="#struct-441569" type="indirect"/>
            <relation active="#struct-448187" type="indirect"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-1612717" status="VALID">
          <idno type="IdRef">199278792</idno>
          <idno type="ISNI">0000 0001 2188 216X </idno>
          <idno type="RNSR">199517454Y</idno>
          <idno type="ROR">https://ror.org/03vcm6439</idno>
          <orgName>Laboratoire d'analyse et d'architecture des systèmes</orgName>
          <orgName type="acronym">LAAS</orgName>
          <date type="start">2025-01-01</date>
          <desc>
            <address>
              <addrLine>7 Av du colonel Roche 31077 TOULOUSE CEDEX 4</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.laas.fr</ref>
          </desc>
          <listRelation>
            <relation active="#struct-81148" type="direct"/>
            <relation name="443875" active="#struct-443875" type="indirect"/>
            <relation active="#struct-116255" type="direct"/>
            <relation active="#struct-301232" type="indirect"/>
            <relation active="#struct-443875" type="indirect"/>
            <relation active="#struct-116256" type="direct"/>
            <relation name="UPR8001" active="#struct-441569" type="direct"/>
            <relation active="#struct-448187" type="direct"/>
            <relation active="#struct-1574795" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-81148" status="VALID">
          <idno type="IdRef">026404354</idno>
          <idno type="ISNI">0000000121902837</idno>
          <idno type="ROR">https://ror.org/0443n9e75</idno>
          <orgName>Université Toulouse Capitole</orgName>
          <orgName type="acronym">UT Capitole</orgName>
          <date type="start">1970-01-01</date>
          <desc>
            <address>
              <addrLine>2 rue du Doyen-Gabriel-Marty - 31042 Toulouse Cedex 9</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.ut-capitole.fr/</ref>
          </desc>
          <listRelation>
            <relation name="443875" active="#struct-443875" type="direct"/>
          </listRelation>
        </org>
        <org type="regroupinstitution" xml:id="struct-443875" status="VALID">
          <idno type="ROR">https://ror.org/017tgbk05</idno>
          <orgName>Communauté d'universités et établissements de Toulouse</orgName>
          <orgName type="acronym">Comue de Toulouse</orgName>
          <desc>
            <address>
              <addrLine>41 Allée Jules Guesde, 31000 Toulouse</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.univ-toulouse.fr/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-116255" status="VALID">
          <idno type="IdRef">026388766</idno>
          <idno type="ISNI">0000 0001 2286 8343</idno>
          <idno type="ROR">https://ror.org/01h8pf755</idno>
          <idno type="Wikidata">Q858979</idno>
          <orgName>Institut National des Sciences Appliquées - Toulouse</orgName>
          <orgName type="acronym">INSA Toulouse</orgName>
          <date type="start">1963-10-21</date>
          <desc>
            <address>
              <addrLine>135, avenue de Rangueil - 31077 Toulouse cedex 4</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.insa-toulouse.fr</ref>
          </desc>
          <listRelation>
            <relation active="#struct-301232" type="direct"/>
            <relation active="#struct-443875" type="direct"/>
          </listRelation>
        </org>
        <org type="regroupinstitution" xml:id="struct-301232" status="VALID">
          <idno type="IdRef">162105150</idno>
          <orgName>Institut National des Sciences Appliquées</orgName>
          <orgName type="acronym">INSA</orgName>
          <desc>
            <address>
              <country key="FR"/>
            </address>
          </desc>
        </org>
        <org type="institution" xml:id="struct-116256" status="VALID">
          <idno type="IdRef">026403994</idno>
          <idno type="ROR">https://ror.org/04ezk3x31</idno>
          <orgName>Université Toulouse - Jean Jaurès</orgName>
          <orgName type="acronym">UT2J</orgName>
          <date type="start">1971-01-01</date>
          <desc>
            <address>
              <addrLine>5 allées Antonio Machado - 31058 Toulouse Cedex 9</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.univ-tlse2.fr</ref>
          </desc>
          <listRelation>
            <relation active="#struct-443875" type="direct"/>
          </listRelation>
        </org>
        <org type="regroupinstitution" xml:id="struct-441569" status="VALID">
          <idno type="IdRef">02636817X</idno>
          <idno type="ISNI">0000000122597504</idno>
          <idno type="ROR">https://ror.org/02feahw73</idno>
          <orgName>Centre National de la Recherche Scientifique</orgName>
          <orgName type="acronym">CNRS</orgName>
          <date type="start">1939-10-19</date>
          <desc>
            <address>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.cnrs.fr/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-448187" status="VALID">
          <idno type="IdRef">026388820</idno>
          <idno type="ISNI">0000000121766169</idno>
          <idno type="ROR">https://ror.org/033p9g875</idno>
          <orgName>Institut National Polytechnique (Toulouse)</orgName>
          <orgName type="acronym">Toulouse INP</orgName>
          <desc>
            <address>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.inp-toulouse.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-443875" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-1574795" status="VALID">
          <orgName>Université de Toulouse</orgName>
          <orgName type="acronym">EPE UT</orgName>
          <date type="start">2025-01-01</date>
          <desc>
            <address>
              <addrLine>118 toute de Narbonne, 31062 Toulouse cedex 9</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.univ-tlse3.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-443875" type="direct"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-459" status="OLD">
          <idno type="IdRef">199278792</idno>
          <idno type="ISNI">0000 0001 2188 216X </idno>
          <idno type="RNSR">199517454Y</idno>
          <idno type="ROR">https://ror.org/03vcm6439</idno>
          <orgName>Laboratoire d'analyse et d'architecture des systèmes</orgName>
          <orgName type="acronym">LAAS</orgName>
          <date type="start">1968-01-01</date>
          <date type="end">2025-01-01</date>
          <desc>
            <address>
              <addrLine>7 Av du colonel Roche 31077 TOULOUSE CEDEX 4</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.laas.fr</ref>
          </desc>
          <listRelation>
            <relation active="#struct-81148" type="direct"/>
            <relation name="443875" active="#struct-443875" type="indirect"/>
            <relation active="#struct-116255" type="direct"/>
            <relation active="#struct-301232" type="indirect"/>
            <relation active="#struct-443875" type="indirect"/>
            <relation active="#struct-116256" type="direct"/>
            <relation active="#struct-217752" type="direct"/>
            <relation name="UPR8001" active="#struct-441569" type="direct"/>
            <relation active="#struct-448187" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-217752" status="OLD">
          <idno type="IdRef">026404672</idno>
          <idno type="ISNI">0000000121617331</idno>
          <idno type="ROR">https://ror.org/02v6kpv12</idno>
          <idno type="Wikidata">Q1273188</idno>
          <orgName>Université Toulouse III - Paul Sabatier</orgName>
          <orgName type="acronym">UT3</orgName>
          <date type="end">2025-01-01</date>
          <desc>
            <address>
              <addrLine>118 route de Narbonne - 31062 Toulouse</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.univ-tlse3.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-443875" type="direct"/>
          </listRelation>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>