<?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-00712553v2</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="2026-05-03T07:03:58+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">Traveling fronts guided by the environment for reaction-diffusion equations</title>
            <author role="aut">
              <persName>
                <forename type="first">Henri</forename>
                <surname>Berestycki</surname>
              </persName>
              <idno type="halauthorid">102521-0</idno>
              <affiliation ref="#struct-1318"/>
            </author>
            <author role="crp">
              <persName>
                <forename type="first">Guillemette</forename>
                <surname>Chapuisat</surname>
              </persName>
              <email type="md5">4b61d736a03546bda4188adcec3f91f6</email>
              <email type="domain">univ-amu.fr</email>
              <idno type="idhal" notation="numeric">926969</idno>
              <idno type="halauthorid" notation="string">417669-926969</idno>
              <affiliation ref="#struct-1318"/>
              <affiliation ref="#struct-400941"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Guillemette</forename>
                <surname>Chapuisat</surname>
              </persName>
              <email type="md5">4b61d736a03546bda4188adcec3f91f6</email>
              <email type="domain">univ-amu.fr</email>
            </editor>
            <funder>NSF FRG grant DMS-1065979</funder>
          </titleStmt>
          <editionStmt>
            <edition n="v1">
              <date type="whenSubmitted">2012-06-27 11:56:41</date>
            </edition>
            <edition n="v2" type="current">
              <date type="whenSubmitted">2016-03-09 08:59:39</date>
              <date type="whenWritten">2012-05-28</date>
              <date type="whenModified">2024-04-30 16:32:11</date>
              <date type="whenReleased">2016-03-09 20:56:40</date>
              <date type="whenProduced">2013-03</date>
              <date type="whenEndEmbargoed">2016-03-09</date>
              <ref type="file" target="https://hal.science/hal-00712553v2/document">
                <date notBefore="2016-03-09"/>
              </ref>
              <ref type="file" subtype="author" n="1" target="https://hal.science/hal-00712553v2/file/HAL_HBGC_2013_03_11_GRpdf.pdf" id="file-1285317-1365697">
                <date notBefore="2016-03-09"/>
              </ref>
              <ref type="externalLink" target="http://arxiv.org/pdf/1206.6575"/>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="173316">
                <persName>
                  <forename>Guillemette</forename>
                  <surname>Chapuisat</surname>
                </persName>
                <email type="md5">4b61d736a03546bda4188adcec3f91f6</email>
                <email type="domain">univ-amu.fr</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-00712553</idno>
            <idno type="halUri">https://hal.science/hal-00712553</idno>
            <idno type="halBibtex">berestycki:hal-00712553</idno>
            <idno type="halRefHtml">&lt;i&gt;Networks and Heterogeneous Media&lt;/i&gt;, 2013, 8 (1), pp.79-114</idno>
            <idno type="halRef">Networks and Heterogeneous Media, 2013, 8 (1), pp.79-114</idno>
            <availability status="restricted">
              <licence target="https://about.hal.science/hal-authorisation-v1/">HAL Authorization<ref corresp="#file-1285317-1365697"/></licence>
            </availability>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno>
            <idno type="stamp" n="UNIV-AMU">Aix Marseille Université</idno>
            <idno type="stamp" n="EHESS">Ecole des Hautes Etudes en Sciences Sociales</idno>
            <idno type="stamp" n="EC-MARSEILLE">Ecole Centrale de Marseille</idno>
            <idno type="stamp" n="INSMI">CNRS-INSMI - INstitut des Sciences Mathématiques et de leurs Interactions</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="CAMS" corresp="EHESS">Collection HAL du Centre d'Analyse et de Mathématique Sociales (CAMS, UMR CNRS-EHESS)</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">Traveling fronts guided by the environment for reaction-diffusion equations</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Henri</forename>
                    <surname>Berestycki</surname>
                  </persName>
                  <idno type="halauthorid">102521-0</idno>
                  <affiliation ref="#struct-1318"/>
                </author>
                <author role="crp">
                  <persName>
                    <forename type="first">Guillemette</forename>
                    <surname>Chapuisat</surname>
                  </persName>
                  <email type="md5">4b61d736a03546bda4188adcec3f91f6</email>
                  <email type="domain">univ-amu.fr</email>
                  <idno type="idhal" notation="numeric">926969</idno>
                  <idno type="halauthorid" notation="string">417669-926969</idno>
                  <affiliation ref="#struct-1318"/>
                  <affiliation ref="#struct-400941"/>
                </author>
              </analytic>
              <monogr>
                <idno type="halJournalId" status="VALID">162991</idno>
                <idno type="issn">1556-1801</idno>
                <idno type="eissn">1556-181X</idno>
                <title level="j">Networks and Heterogeneous Media</title>
                <imprint>
                  <publisher>American Institute of Mathematical Sciences</publisher>
                  <biblScope unit="volume">8</biblScope>
                  <biblScope unit="issue">1</biblScope>
                  <biblScope unit="pp">79-114</biblScope>
                  <date type="datePub">2013-03</date>
                </imprint>
              </monogr>
              <idno type="arxiv">1206.6575</idno>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <keywords scheme="author">
                <term xml:lang="en">traveling front</term>
                <term xml:lang="en">heterogeneous medium</term>
                <term xml:lang="en">reaction-diffusion</term>
              </keywords>
              <classCode scheme="classification">35K57</classCode>
              <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>This paper deals with the existence of traveling fronts guided by the medium for a KPP reaction-diffusion equation coming from a model in population dynamics in which there is spatial spreading as well as genetic mutation of a quantitative genetic trait that has a locally preferred value. The goal is to understand spreading and invasions in this heterogeneous context. We prove the existence of a threshold value on the existence of a nonzero asymptotic profile (a stationary limiting solution). When a nonzero asymptotic profile exists, we prove the existence of a traveling front. This allows us to completely identify the behavior of the solution of the parabolic problem in the KPP case. We also study here the bistable case. The equation provides a general framework for a model of cortical spreading depressions in the brain. We prove the existence of traveling front if the area where theere is reaction is large enough and the non-existence if it is too small.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="laboratory" xml:id="struct-1318" status="VALID">
          <idno type="RNSR">199812885U</idno>
          <idno type="ROR">00vb8fc53</idno>
          <orgName>Centre d'Analyse et de Mathématique sociales</orgName>
          <orgName type="acronym">CAMS</orgName>
          <date type="start">1998-01-01</date>
          <desc>
            <address>
              <addrLine>54 boulevard Raspail 75006 Paris</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://cams.ehess.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-99539" type="direct"/>
            <relation name="UMR8557" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-400941" status="OLD">
          <orgName>Laboratoire d'Analyse, Topologie, Probabilités</orgName>
          <orgName type="acronym">LATP</orgName>
          <date type="start">2012-01-01</date>
          <date type="end">2013-12-31</date>
          <desc>
            <address>
              <country key="FR"/>
            </address>
          </desc>
          <listRelation>
            <relation active="#struct-198056" type="direct"/>
            <relation active="#struct-300415" type="direct"/>
            <relation name="UMR7353" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-99539" status="VALID">
          <idno type="IdRef">026374889</idno>
          <idno type="ROR">https://ror.org/02d9dg697</idno>
          <orgName>École des hautes études en sciences sociales</orgName>
          <orgName type="acronym">EHESS</orgName>
          <date type="start">1975-01-01</date>
          <desc>
            <address>
              <addrLine>54, boulevard Raspail 75006 Paris</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.ehess.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-198056" status="VALID">
          <idno type="IdRef">15863621X</idno>
          <idno type="ISNI">0000 0001 2176 4817</idno>
          <idno type="ROR">https://ror.org/035xkbk20</idno>
          <orgName>Aix Marseille Université</orgName>
          <orgName type="acronym">AMU</orgName>
          <date type="start">2012-01-01</date>
          <desc>
            <address>
              <addrLine>Aix-Marseille UniversitéJardins du Pharo58 Boulevard Charles Livon13284 Marseille cedex 7</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.univ-amu.fr/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-300415" status="VALID">
          <idno type="ISNI">0000 0004 1762 2703</idno>
          <idno type="ROR">https://ror.org/040baw385</idno>
          <orgName>École Centrale de Marseille</orgName>
          <orgName type="acronym">ECM</orgName>
          <date type="start">2006-09-27</date>
          <desc>
            <address>
              <addrLine>Pôle de l'étoile - Technopole de Château-Gombert - 38 rue Frédéric Joliot-Curie - 13013 Marseille</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.centrale-marseille.fr/</ref>
          </desc>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>