<?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-02159903</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="2026-05-04T09:48:49+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">NULL CONTROLLABILITY OF THE STRUCTURALLY DAMPED WAVE EQUATION ON THE TWO-DIMENSIONAL TORUS</title>
            <author role="aut">
              <persName>
                <forename type="first">Patricio</forename>
                <surname>Guzmán</surname>
              </persName>
              <idno type="halauthorid">1512487-0</idno>
              <affiliation ref="#struct-391039"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Lionel</forename>
                <surname>Rosier</surname>
              </persName>
              <email type="md5">c65833548ab0b6bf44700b3353efff83</email>
              <email type="domain">univ-littoral.fr</email>
              <idno type="idhal" notation="string">lionel-rosier</idno>
              <idno type="idhal" notation="numeric">14724</idno>
              <idno type="halauthorid" notation="string">2813-14724</idno>
              <idno type="IDREF">https://www.idref.fr/081301146</idno>
              <idno type="ORCID">https://orcid.org/0000-0002-5602-9799</idno>
              <idno type="GOOGLE SCHOLAR">deLqIscAAAAJ&amp;hl=fr</idno>
              <idno type="ISNI">http://isni.org/isni/0000000114928094</idno>
              <idno type="VIAF">https://viaf.org/viaf/64894912</idno>
              <affiliation ref="#struct-13898"/>
              <affiliation ref="#struct-27997"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Lionel</forename>
                <surname>Rosier</surname>
              </persName>
              <email type="md5">c65833548ab0b6bf44700b3353efff83</email>
              <email type="domain">univ-littoral.fr</email>
            </editor>
            <funder ref="#projanr-45571"/>
          </titleStmt>
          <editionStmt>
            <edition n="v1" type="current">
              <date type="whenSubmitted">2019-06-19 10:17:34</date>
              <date type="whenWritten">2019-06-19</date>
              <date type="whenModified">2026-01-09 09:52:01</date>
              <date type="whenReleased">2019-06-20 10:46:39</date>
              <date type="whenProduced">2019-06-19</date>
              <date type="whenEndEmbargoed">2019-06-19</date>
              <ref type="file" target="https://hal.science/hal-02159903v1/document">
                <date notBefore="2019-06-19"/>
              </ref>
              <ref type="file" subtype="author" n="1" target="https://hal.science/hal-02159903v1/file/GR-subm.pdf" id="file-2159903-2151278">
                <date notBefore="2019-06-19"/>
              </ref>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="147930">
                <persName>
                  <forename>Lionel</forename>
                  <surname>Rosier</surname>
                </persName>
                <email type="md5">c65833548ab0b6bf44700b3353efff83</email>
                <email type="domain">univ-littoral.fr</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-02159903</idno>
            <idno type="halUri">https://hal.science/hal-02159903</idno>
            <idno type="halBibtex">guzman:hal-02159903</idno>
            <idno type="halRefHtml">2019</idno>
            <idno type="halRef">2019</idno>
            <availability status="restricted">
              <licence target="https://about.hal.science/hal-authorisation-v1/">HAL Authorization<ref corresp="#file-2159903-2151278"/></licence>
            </availability>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="ENSMP" corresp="PARISTECH">MINES ParisTech</idno>
            <idno type="stamp" n="ENSMP_CAOR" corresp="ENSMP">CAO et robotique (CAOR)</idno>
            <idno type="stamp" n="ENSMP_CAS" corresp="ENSMP">Automatique et systèmes (CAS)</idno>
            <idno type="stamp" n="PARISTECH">ParisTech</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="PSL">Université Paris sciences et lettres</idno>
            <idno type="stamp" n="ENSMP_DEP_MS">Département Mathématiques et systèmes</idno>
            <idno type="stamp" n="ENSMP_DR" corresp="ENSMP">ENSMP_DR</idno>
            <idno type="stamp" n="ENSMP-PSL" corresp="PSL">MINES ParisTech - École nationale supérieure des mines de Paris - PSL</idno>
            <idno type="stamp" n="ANR">ANR</idno>
          </seriesStmt>
          <notesStmt/>
          <sourceDesc>
            <biblStruct>
              <analytic>
                <title xml:lang="en">NULL CONTROLLABILITY OF THE STRUCTURALLY DAMPED WAVE EQUATION ON THE TWO-DIMENSIONAL TORUS</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Patricio</forename>
                    <surname>Guzmán</surname>
                  </persName>
                  <idno type="halauthorid">1512487-0</idno>
                  <affiliation ref="#struct-391039"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Lionel</forename>
                    <surname>Rosier</surname>
                  </persName>
                  <email type="md5">c65833548ab0b6bf44700b3353efff83</email>
                  <email type="domain">univ-littoral.fr</email>
                  <idno type="idhal" notation="string">lionel-rosier</idno>
                  <idno type="idhal" notation="numeric">14724</idno>
                  <idno type="halauthorid" notation="string">2813-14724</idno>
                  <idno type="IDREF">https://www.idref.fr/081301146</idno>
                  <idno type="ORCID">https://orcid.org/0000-0002-5602-9799</idno>
                  <idno type="GOOGLE SCHOLAR">deLqIscAAAAJ&amp;hl=fr</idno>
                  <idno type="ISNI">http://isni.org/isni/0000000114928094</idno>
                  <idno type="VIAF">https://viaf.org/viaf/64894912</idno>
                  <affiliation ref="#struct-13898"/>
                  <affiliation ref="#struct-27997"/>
                </author>
              </analytic>
              <monogr>
                <imprint/>
              </monogr>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <keywords scheme="author">
                <term xml:lang="en">Wave equation</term>
                <term xml:lang="en">Kelvin-Voigt damping</term>
                <term xml:lang="en">null controllability</term>
                <term xml:lang="en">parabolic-transport system</term>
                <term xml:lang="en">moving control</term>
                <term xml:lang="en">Carleman estimates</term>
                <term xml:lang="en">Diophantine approximations</term>
              </keywords>
              <classCode scheme="halDomain" n="math.math-ap">Mathematics [math]/Analysis of PDEs [math.AP]</classCode>
              <classCode scheme="halTypology" n="UNDEFINED">Preprints, Working Papers, ...</classCode>
              <classCode scheme="halOldTypology" n="UNDEFINED">Preprints, Working Papers, ...</classCode>
              <classCode scheme="halTreeTypology" n="UNDEFINED">Preprints, Working Papers, ...</classCode>
            </textClass>
            <abstract xml:lang="en">
              <p>We investigate the null controllability of the wave equation with a Kelvin-Voigt damping on the two-dimensional torus T 2. We consider a distributed control supported in a moving domain ω(t) with a uniform motion at a constant velocity c = (1, ζ). The results we obtain depend strongly on the topological features of the geodesics of T 2 with constant velocity c. When ζ ∈ Q, writing ζ = p/q with p, q relatively prime, we prove that the null controllability holds if roughly the diameter of ω(0) is larger than 1/p and if the control time is larger than q. We prove also that for almost every ζ ∈ R + \ Q, and also for some particular values including e.g. ζ = e, the null controllability holds for any choice of ω(0) and for a sufficiently large control time. The proofs rely on a delicate construction of the weight function in a Carleman estimate which gets rid of a topogical assumption on the control region often encountered in the literature. Diophantine approximations are also needed when ζ is irrationnal. 2010 Mathematics Subject Classification: 35Q74, 93B05, 93B07, 93C20.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="laboratory" xml:id="struct-391039" status="VALID">
          <orgName>Departamento de Matematica [Vaparaiso]</orgName>
          <desc>
            <address>
              <addrLine>Universidad Tecnica Federico Santa MariaAvenida España 1680. Casilla 110-V, Valparaíso</addrLine>
              <country key="CL"/>
            </address>
            <ref type="url">https://matematica.usm.cl/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-406898" type="direct"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-13898" status="VALID">
          <idno type="IdRef">151285128</idno>
          <idno type="ISNI">0000 0004 6102 8496</idno>
          <idno type="ROR">https://ror.org/018786988</idno>
          <orgName>Centre Automatique et Systèmes</orgName>
          <orgName type="acronym">CAS</orgName>
          <desc>
            <address>
              <addrLine>35 rue Saint-Honoré 77305 Fontainebleau cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://cas.ensmp.fr</ref>
          </desc>
          <listRelation>
            <relation active="#struct-301492" type="direct"/>
            <relation active="#struct-564132" type="indirect"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-27997" status="VALID">
          <idno type="IdRef">151891001</idno>
          <idno type="ROR">https://ror.org/0180r7w69</idno>
          <orgName>Centre de Robotique</orgName>
          <orgName type="acronym">CAOR</orgName>
          <desc>
            <address>
              <addrLine>60, boulevard Saint-Michel 75272 Paris cedex 06</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.caor.minesparis.psl.eu/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-301492" type="direct"/>
            <relation active="#struct-564132" type="indirect"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-406898" status="VALID">
          <idno type="IdRef">032696221</idno>
          <idno type="ISNI">000000011958645X</idno>
          <idno type="ROR">https://ror.org/05510vn56</idno>
          <orgName>Universidad Tecnica Federico Santa Maria [Valparaiso]</orgName>
          <orgName type="acronym">UTFSM</orgName>
          <date type="start">1926-01-01</date>
          <desc>
            <address>
              <addrLine>Avenida España 1680, Valparaíso</addrLine>
              <country key="CL"/>
            </address>
            <ref type="url">http://www.usm.cl/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-301492" status="VALID">
          <idno type="IdRef">026375249</idno>
          <idno type="ROR">https://ror.org/04y8cs423</idno>
          <orgName>Mines Paris - PSL (École nationale supérieure des mines de Paris)</orgName>
          <date type="start">1783-01-01</date>
          <desc>
            <address>
              <addrLine>60, boulevard Saint-Michel 75006 Paris</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.minesparis.psl.eu/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-564132" type="direct"/>
          </listRelation>
        </org>
        <org type="regroupinstitution" xml:id="struct-564132" status="VALID">
          <idno type="IdRef">241597595</idno>
          <idno type="ISNI">0000 0004 1784 3645</idno>
          <idno type="ROR">https://ror.org/013cjyk83</idno>
          <orgName>Université Paris Sciences et Lettres</orgName>
          <orgName type="acronym">PSL</orgName>
          <desc>
            <address>
              <addrLine>60 rue Mazarine 75006 Paris</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.psl.eu/</ref>
          </desc>
        </org>
      </listOrg>
      <listOrg type="projects">
        <org type="anrProject" xml:id="projanr-45571" status="VALID">
          <idno type="anr">ANR-15-CE23-0007</idno>
          <idno type="program">Fondements du numérique</idno>
          <orgName>Finite4SoS</orgName>
          <desc>Commande et estimation en temps fini pour les Systèmes de Systèmes</desc>
          <date type="start">2015</date>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>