<?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-04482225</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="2026-05-12T19:43:52+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">A two spaces extension of Cauchy-Lipschitz Theorem</title>
            <author role="aut">
              <persName>
                <forename type="first">Charles</forename>
                <surname>Bertucci</surname>
              </persName>
              <email type="md5">f985909587dcc8ced17002b05f0ba1f2</email>
              <email type="domain">polytechnique.edu</email>
              <idno type="idhal" notation="string">charles-bertucci</idno>
              <idno type="idhal" notation="numeric">749897</idno>
              <idno type="halauthorid" notation="string">43707-749897</idno>
              <affiliation ref="#struct-89626"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Pierre-Louis</forename>
                <surname>Lions</surname>
              </persName>
              <idno type="halauthorid">2068687-0</idno>
              <affiliation ref="#struct-1043508"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Charles</forename>
                <surname>Bertucci</surname>
              </persName>
              <email type="md5">f985909587dcc8ced17002b05f0ba1f2</email>
              <email type="domain">polytechnique.edu</email>
            </editor>
          </titleStmt>
          <editionStmt>
            <edition n="v1" type="current">
              <date type="whenSubmitted">2024-02-28 14:45:46</date>
              <date type="whenModified">2025-12-11 03:17:02</date>
              <date type="whenReleased">2024-02-29 13:20:28</date>
              <date type="whenProduced">2025-03</date>
              <date type="whenEndEmbargoed">2024-02-28</date>
              <ref type="file" target="https://hal.science/hal-04482225v1/document">
                <date notBefore="2024-02-28"/>
              </ref>
              <ref type="file" subtype="author" n="1" target="https://hal.science/hal-04482225v1/file/note.pdf" id="file-4482225-3887030">
                <date notBefore="2024-02-28"/>
              </ref>
              <ref type="externalLink" target="http://arxiv.org/pdf/2402.19092"/>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="603509">
                <persName>
                  <forename>Charles</forename>
                  <surname>Bertucci</surname>
                </persName>
                <email type="md5">f985909587dcc8ced17002b05f0ba1f2</email>
                <email type="domain">polytechnique.edu</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-04482225</idno>
            <idno type="halUri">https://hal.science/hal-04482225</idno>
            <idno type="halBibtex">bertucci:hal-04482225</idno>
            <idno type="halRefHtml">&lt;i&gt;Journal of Differential Equations&lt;/i&gt;, 2025, 421, pp.524-530. &lt;a target="_blank" href="https://dx.doi.org/10.1016/j.jde.2024.12.031"&gt;&amp;#x27E8;10.1016/j.jde.2024.12.031&amp;#x27E9;&lt;/a&gt;</idno>
            <idno type="halRef">Journal of Differential Equations, 2025, 421, pp.524-530. &amp;#x27E8;10.1016/j.jde.2024.12.031&amp;#x27E9;</idno>
            <availability status="restricted">
              <licence target="https://about.hal.science/hal-authorisation-v1/">HAL Authorization<ref corresp="#file-4482225-3887030"/></licence>
            </availability>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="X">École polytechnique</idno>
            <idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno>
            <idno type="stamp" n="CDF">Collège de France</idno>
            <idno type="stamp" n="INSMI">CNRS-INSMI - INstitut des Sciences Mathématiques et de leurs Interactions</idno>
            <idno type="stamp" n="X-CMAP" corresp="X">Centre de Mathématiques Appliquées (CMAP)</idno>
            <idno type="stamp" n="X-DEP-MATHA">Département de mathématiques appliquées de l’École polytechnique</idno>
            <idno type="stamp" n="CMAP">Centre de Mathématiques Appliquées (CMAP)</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="IP_PARIS">Institut Polytechnique de Paris</idno>
            <idno type="stamp" n="CDF-PSL" corresp="PSL">Collège de France - PSL </idno>
            <idno type="stamp" n="DEPARTEMENT-DE-MATHEMATIQUES">Collection du Département de Mathématiques</idno>
            <idno type="stamp" n="IP-PARIS-MATHEMATIQUES">IP Paris Département de Mathématiques</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">A two spaces extension of Cauchy-Lipschitz Theorem</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Charles</forename>
                    <surname>Bertucci</surname>
                  </persName>
                  <email type="md5">f985909587dcc8ced17002b05f0ba1f2</email>
                  <email type="domain">polytechnique.edu</email>
                  <idno type="idhal" notation="string">charles-bertucci</idno>
                  <idno type="idhal" notation="numeric">749897</idno>
                  <idno type="halauthorid" notation="string">43707-749897</idno>
                  <affiliation ref="#struct-89626"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Pierre-Louis</forename>
                    <surname>Lions</surname>
                  </persName>
                  <idno type="halauthorid">2068687-0</idno>
                  <affiliation ref="#struct-1043508"/>
                </author>
              </analytic>
              <monogr>
                <idno type="halJournalId" status="VALID">15346</idno>
                <idno type="issn">0022-0396</idno>
                <idno type="eissn">1090-2732</idno>
                <title level="j">Journal of Differential Equations</title>
                <imprint>
                  <publisher>Elsevier</publisher>
                  <biblScope unit="volume">421</biblScope>
                  <biblScope unit="pp">524-530</biblScope>
                  <date type="datePub">2025-03</date>
                </imprint>
              </monogr>
              <idno type="arxiv">2402.19092</idno>
              <idno type="doi">10.1016/j.jde.2024.12.031</idno>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <keywords scheme="author">
                <term xml:lang="en">Cauchy-Lipschitz Picard-Lindelöf theory</term>
                <term xml:lang="en">Evolution equation</term>
              </keywords>
              <classCode scheme="halDomain" n="math.math-ap">Mathematics [math]/Analysis of PDEs [math.AP]</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 adapt the classical theory of local well-posedness of evolution problems to cases in which the nonlinearity can be accurately quantified by two different norms. For ordinary differential equations, we consider ẋ = f (x, x) for a function f : V × E → E where E is a Banach space and V → E a normed vector space. This structure allows us to distinguish between the two dependencies of f in x and allows to generalize classical results. We also prove a similar results for partial differential equations.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="laboratory" xml:id="struct-89626" status="VALID">
          <idno type="IdRef">197373461</idno>
          <idno type="ISNI">000000010944436X</idno>
          <idno type="RNSR">199719340P</idno>
          <idno type="ROR">https://ror.org/012e1xn46</idno>
          <idno type="Wikidata">Q16008922</idno>
          <orgName>Centre de Mathématiques Appliquées de l'Ecole polytechnique</orgName>
          <orgName type="acronym">CMAP</orgName>
          <date type="start">2005-01-01</date>
          <desc>
            <address>
              <addrLine>Route de Saclay, 91128 Palaiseau Cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://cmap.ip-paris.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-300009" type="direct"/>
            <relation active="#struct-300340" type="direct"/>
            <relation active="#struct-563936" type="indirect"/>
            <relation name="UMR7641" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-1043508" status="VALID">
          <orgName>Collège de France - Chaire Équations aux dérivées partielles et applications</orgName>
          <date type="start">2003-05-22</date>
          <desc>
            <address>
              <addrLine>Collège de France, 11 Place Marcelin Berthelot, 75005 Paris</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.college-de-france.fr/site/pierre-louis-lions/index.htm</ref>
          </desc>
          <listRelation>
            <relation active="#struct-300026" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-300009" status="VALID">
          <idno type="ROR">https://ror.org/02kvxyf05</idno>
          <orgName>Institut National de Recherche en Informatique et en Automatique</orgName>
          <orgName type="acronym">Inria</orgName>
          <desc>
            <address>
              <addrLine>Domaine de VoluceauRocquencourt - BP 10578153 Le Chesnay Cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.inria.fr/en/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-300340" status="VALID">
          <idno type="IdRef">027309320</idno>
          <idno type="ISNI">0000000121581279</idno>
          <idno type="ROR">https://ror.org/05hy3tk52</idno>
          <idno type="Wikidata">Q273626</idno>
          <orgName>École polytechnique</orgName>
          <orgName type="acronym">X</orgName>
          <date type="start">1794-03-11</date>
          <desc>
            <address>
              <addrLine>Route de Saclay, 91128 Palaiseau Cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.polytechnique.edu/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-563936" type="direct"/>
          </listRelation>
        </org>
        <org type="regroupinstitution" xml:id="struct-563936" status="VALID">
          <idno type="IdRef">238327159</idno>
          <idno type="ISNI">0000000502717600</idno>
          <idno type="ROR">https://ror.org/042tfbd02</idno>
          <idno type="Wikidata">Q48759778</idno>
          <orgName>Institut Polytechnique de Paris</orgName>
          <orgName type="acronym">IP Paris</orgName>
          <date type="start">2019-06-02</date>
          <desc>
            <address>
              <addrLine>Route de Saclay, 91120 Palaiseau Cedex, France</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.ip-paris.fr</ref>
          </desc>
        </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-300026" status="VALID">
          <orgName>Collège de France</orgName>
          <orgName type="acronym">CdF (institution)</orgName>
          <desc>
            <address>
              <country key="FR"/>
            </address>
          </desc>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>