PittsburghV1, France, Analysis, bibRecord, 000187

A hybrid variational principle for the Keller-Segel system in $\mathbb R^2$

Identifieur interne : 000187 ( France/Analysis ); précédent : 000186; suivant : 000188

A hybrid variational principle for the Keller-Segel system in $\mathbb R^2$

Auteurs : Adrien Blanchet [France] ; José Carrillo [Royaume-Uni] ; David Kinderlehrer [États-Unis] ; Michal Kowalczyk [Chili] ; Philippe Laurençot [France] ; Stefano Lisini [Italie]

Source :

RBID : Hal:hal-01026281

Abstract

We construct weak global in time solutions to the classical Keller-Segel system cell movement by chemotaxis in two dimensions when the total mass is below the well-known critical value. Our construction takes advantage of the fact that the Keller-Segel system can be realized as a gradient flow in a suitable functional product space. This allows us to employ a hybrid variational principle which is a generalisation of the minimising implicit scheme for Wasserstein distances introduced by Jordan, Kinderlehrer and Otto (1998).

Url:

https://hal.archives-ouvertes.fr/hal-01026281

Affiliations:

Chili, France, Italie, Royaume-Uni, États-Unis

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to stream Main, to step Exploration: 000699
to stream France, to step Extraction: 000187

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Le document en format XML

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          <orgName>Université Toulouse 2</orgName>
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          <date type="start">1971-01-01</date>
          <desc>            <address>              <addrLine>5 allées Antonio Machado - 31058 Toulouse Cedex 9 </addrLine>
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            <ref type="url">http://www.univ-tlse2.fr</ref>
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          <orgName>Institut National des Sciences Appliquées - Toulouse</orgName>
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          <orgName>Centre National de la Recherche Scientifique</orgName>
          <orgName type="acronym">CNRS</orgName>
          <date type="start">1939-10-19</date>
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            </address>
            <ref type="url">http://www.cnrs.fr/</ref>
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</hal:affiliation>
<country>France</country>
</affiliation>
</author>
<author><name sortKey="Lisini, Stefano" sort="Lisini, Stefano" uniqKey="Lisini S" first="Stefano" last="Lisini">Stefano Lisini</name>
<affiliation wicri:level="1"><hal:affiliation type="laboratory" xml:id="struct-25635" status="VALID">          <orgName>Dipartimento di Matematica - Università di Pavia</orgName>
          <desc>            <address>              <addrLine>Università di Pavia Dipartimento di Matematica Strada Nuova, 65 27100 Pavia</addrLine>
              <country key="IT"></country>
            </address>
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          <desc>            <address>              <country key="FR"></country>
            </address>
          </desc>
        </org>
</tutelle>
</tutelles>
</hal:affiliation>
<country>Italie</country>
</affiliation>
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<profileDesc><textClass><keywords scheme="mix" xml:lang="de"><term>Kantorovich-Rubinstein-Wasserstein distance</term>
<term>Keller-Segel model</term>
<term>Wasserstein distance</term>
<term>chemotaxis</term>
<term>minimising scheme</term>
</keywords>
</textClass>
</profileDesc>
</teiHeader>
<front><div type="abstract" xml:lang="en">We construct weak global in time solutions to the classical Keller-Segel system cell movement by chemotaxis in two dimensions when the total mass is below the well-known critical value. Our construction takes advantage of the fact that the Keller-Segel system can be realized as a gradient flow in a suitable functional product space. This allows us to employ a hybrid variational principle which is a generalisation of the minimising implicit scheme for Wasserstein distances introduced by Jordan, Kinderlehrer and Otto (1998).</div>
</front>
</TEI>
<affiliations><list><country><li>Chili</li>
<li>France</li>
<li>Italie</li>
<li>Royaume-Uni</li>
<li>États-Unis</li>
</country>
</list>
<tree><country name="France"><noRegion><name sortKey="Blanchet, Adrien" sort="Blanchet, Adrien" uniqKey="Blanchet A" first="Adrien" last="Blanchet">Adrien Blanchet</name>
</noRegion>
<name sortKey="Laurencot, Philippe" sort="Laurencot, Philippe" uniqKey="Laurencot P" first="Philippe" last="Laurençot">Philippe Laurençot</name>
</country>
<country name="Royaume-Uni"><noRegion><name sortKey="Carrillo, Jose" sort="Carrillo, Jose" uniqKey="Carrillo J" first="José" last="Carrillo">José Carrillo</name>
</noRegion>
</country>
<country name="États-Unis"><noRegion><name sortKey="Kinderlehrer, David" sort="Kinderlehrer, David" uniqKey="Kinderlehrer D" first="David" last="Kinderlehrer">David Kinderlehrer</name>
</noRegion>
</country>
<country name="Chili"><noRegion><name sortKey="Kowalczyk, Michal" sort="Kowalczyk, Michal" uniqKey="Kowalczyk M" first="Michal" last="Kowalczyk">Michal Kowalczyk</name>
</noRegion>
</country>
<country name="Italie"><noRegion><name sortKey="Lisini, Stefano" sort="Lisini, Stefano" uniqKey="Lisini S" first="Stefano" last="Lisini">Stefano Lisini</name>
</noRegion>
</country>
</tree>
</affiliations>
</record>

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A hybrid variational principle for the Keller-Segel system in $\mathbb R^2$

A hybrid variational principle for the Keller-Segel system in $\mathbb R^2$

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