<?xml version="1.0" encoding="utf-8"?>
<export-example>
  <doc>
    <id>1321</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2011-06-23</completedDate>
    <publishedDate>2011-06-23</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Symmetry analysis and exact solutions of semilinear heat flow in multi-dimensions</title>
    <abstract language="eng">A symmetry group method is used to obtain exact solutions for&#13;
a semilinear radial heat equation in $n&amp;amp;gt;1$ dimensions&#13;
with a general power nonlinearity.&#13;
The method involves an ansatz technique to solve&#13;
an equivalent first-order PDE system of similarity variables&#13;
given by group foliations of this heat equation,&#13;
using its admitted group of scaling symmetries. &#13;
This technique yields explicit similarity solutions as well as&#13;
other explicit solutions of a more general (non-similarity) form&#13;
having interesting analytical behavior connected with blow up and dispersion.&#13;
In contrast,&#13;
standard similarity reduction of this heat equation gives&#13;
a semilinear ODE that cannot be explicitly solved by familiar&#13;
integration techniques such as point symmetry reduction or integrating factors.</abstract>
    <identifier type="serial">11-26</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-13213</identifier>
    <enrichment key="SourceTitle">Appeared in: Journal of Mathematical Analysis and Applications, 379 (2011), 748-763.</enrichment>
    <author>Stephen Anco</author>
    <submitter>Winfried Neun</submitter>
    <author>Sajid Ali</author>
    <author>Thomas Wolf</author>
    <series>
      <title>ZIB-Report</title>
      <number>11-26</number>
    </series>
    <subject>
      <language>deu</language>
      <type>uncontrolled</type>
      <value>semilinear heat equation, similarity reduction, exact solutions, group foliation, symmetry</value>
    </subject>
    <collection role="msc" number="34-XX">ORDINARY DIFFERENTIAL EQUATIONS</collection>
    <collection role="msc" number="35-XX">PARTIAL DIFFERENTIAL EQUATIONS</collection>
    <collection role="msc" number="58-XX">GLOBAL ANALYSIS, ANALYSIS ON MANIFOLDS [See also 32Cxx, 32Fxx, 32Wxx, 46-XX, 47Hxx, 53Cxx](For geometric integration theory, see 49Q15)</collection>
    <collection role="institutes" number="sis">Digital Data and Information for Society, Science, and Culture</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/1321/ZR-11-26.pdf</file>
    <file>https://opus4.kobv.de/opus4-zib/files/1321/ZR-11-26.ps</file>
  </doc>
</export-example>
