<?xml version="1.0" encoding="utf-8"?>
<export-example>
  <doc>
    <id>429</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>2021-10-07</completedDate>
    <publishedDate>2021-10-08</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Flow decomposition for heat equations with memory</title>
    <abstract language="eng">We build up a decomposition for the flow generated by the heat equation with a real analytic memory kernel. It&#13;
consists of three components: The first one is of parabolic nature; the second one gathers the hyperbolic component&#13;
of the dynamics, with null velocity of propagation; the last one exhibits a finite smoothing effect. This decomposition reveals the hybrid parabolic-hyperbolic nature of the flow and clearly illustrates the significant impact of the memory term on the parabolic behavior of the system in the absence of memory terms.</abstract>
    <enrichment key="SubmissionStatus">accepted for publication</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>G Wang</author>
    <author>Y Zhang</author>
    <author>E Zuazua</author>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Heat equations with memory</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>decomposition of the flow</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>hybrid parabolic-hyperbolic behavior</value>
    </subject>
    <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/429/heat-with-memory-final-version.pdf</file>
  </doc>
</export-example>
