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    <id>390</id>
    <completedYear>2021</completedYear>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>1</belongsToBibliography>
    <completedDate>2021-05-23</completedDate>
    <publishedDate>2021-06-03</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Control of Hyperbolic and Parabolic Equations on Networks and Singular limits</title>
    <abstract language="eng">We study the controllability properties of the transport equation and of parabolic equations posed on a tree. Using a control localized on the exterior nodes, we prove that the hyperbolic and the parabolic systems are null-controllable. The hyperbolic proof relies on the method of characteristics, the parabolic one on duality arguments and Carleman inequalities. We also show that the parabolic system may not be controllable if we do not act on all exterior vertices because of symmetries. Moreover, we estimate the cost of the null-controllability of transport-diffusion equations with diffusivity ε &gt; 0ε&gt;0 and study its asymptotic behavior when ε → 0^+ε→0 &#13;
+&#13;
 . We prove that the cost of the controllability decays for a time sufficiently large and explodes for short times. This is done by duality arguments allowing to reduce the problem to obtain observability estimates which depend on the viscosity parameter. These are derived by using Agmon and Carleman inequalities.</abstract>
    <enrichment key="SubmissionStatus">under review</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <enrichment key="review.accepted_by">2</enrichment>
    <licence>Creative Commons - CC BY-SA - Namensnennung - Weitergabe unter gleichen Bedingungen 4.0 International</licence>
    <author>J.A. Bárcena-Petisco</author>
    <author>M. Cavalcante</author>
    <author>G.M. Coclite</author>
    <author>N. de Nitti</author>
    <author>E. Zuazua</author>
    <collection role="institutes" number="">Friedrich-Alexander-Universität Erlangen-Nürnberg</collection>
    <collection role="subprojects" number="">C03</collection>
    <file>https://opus4.kobv.de/opus4-trr154/files/390/SingularLimitsNetworks.pdf</file>
  </doc>
  <doc>
    <id>430</id>
    <completedYear>2021</completedYear>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>preprint</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>1</belongsToBibliography>
    <completedDate>2021-09-23</completedDate>
    <publishedDate>2021-10-08</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Averaged dynamics and control for heat equations with random diffusion</title>
    <abstract language="eng">This paper deals with the averaged dynamics for heat equations in the degenerate case where the diffusivity coefficient, assumed to be constant, is allowed to take the null value. First we prove that the averaged dynamics is analytic. This allows to show that, most often, the averaged dynamics enjoys the property of unique continuation and is approximately controllable. We then determine if the averaged dynamics is actually null controllable or not depending on how the density of averaging behaves when the diffusivity vanishes. In the critical density threshold the dynamics of the average is similar to the \frac{1}{2}-fractional Laplacian, which is wellknown to be critical in the context of the controllability of fractional diffusion processes. Null controllability then fails (resp. holds) when the density weights more (resp. less) in the null diffusivity regime than in this critical regime.</abstract>
    <enrichment key="SubmissionStatus">accepted for publication</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <enrichment key="opus.doi.autoCreate">false</enrichment>
    <enrichment key="opus.urn.autoCreate">false</enrichment>
    <enrichment key="review.accepted_by">2</enrichment>
    <licence>Creative Commons - CC BY-SA - Namensnennung - Weitergabe unter gleichen Bedingungen 4.0 International</licence>
    <author>J.A. Barcena-Petisco</author>
    <author>E Zuazua</author>
    <collection role="institutes" number="">Friedrich-Alexander-Universität Erlangen-Nürnberg</collection>
    <collection role="subprojects" number="">C03</collection>
    <collection role="subprojects" number="">C05</collection>
    <file>https://opus4.kobv.de/opus4-trr154/files/430/avgDyn-heatEq-randomDiff-V2.pdf</file>
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