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<article article-type="research-article" dtd-version="1.3" xml:lang="ru">
  <front xmlns:xlink="http://www.w3.org/1999/xlink">
    <journal-meta>
      <journal-title-group>
        <journal-title>St. Petersburg Polytechnic University Journal: Physics and Mathematics</journal-title>
        <trans-title-group xml:lang="ru">
          <trans-title>Научно-технические ведомости СПбГПУ. Физико-математические науки</trans-title>
        </trans-title-group>
      </journal-title-group>
      <issn pub-type="epub">2304-9782, 2618-8686, 2405-7223</issn>
    </journal-meta>
    <article-meta xmlns:xlink="http://www.w3.org/1999/xlink">
      <article-id pub-id-type="publisher-id">4</article-id>
      <article-id pub-id-type="doi">10.18721/JPM.13304</article-id>
      <title-group>
        <article-title>The diffusion problem in a rectangular container with an internal source: exact solutions obtained by the fast expansion method</article-title>
        <trans-title-group xml:lang="ru">
          <trans-title>Точные решения задачи о диффузии в прямоугольной емкости с внутренним источником, полученные методом быстрых разложений</trans-title>
        </trans-title-group>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <name>
            <surname>Chernyshov</surname>
            <given-names>Alexander</given-names>
          </name>
          <xref ref-type="aff" rid="aff1"/>
          <email>chernyshovad@mail.ru</email>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Sajko</surname>
            <given-names>Dmitrij</given-names>
          </name>
          <xref ref-type="aff" rid="aff1"/>
          <email>dmsajko@mail.ru</email>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Goryainov</surname>
            <given-names>Vitalij</given-names>
          </name>
          <xref ref-type="aff" rid="aff2"/>
          <email>gorvit77@mail.ru</email>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Kuznetsov</surname>
            <given-names>Sergei</given-names>
          </name>
          <xref ref-type="aff" rid="aff1"/>
          <email>sfs134@mail.ru</email>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Nikiforova</surname>
            <given-names>Olga</given-names>
          </name>
          <xref ref-type="aff" rid="aff1"/>
          <email>niki22@mail.ru</email>
        </contrib>
      </contrib-group>
      <aff id="aff1">Voronezh State University of Engineering Technology</aff>
      <aff id="aff2">Voronezh State Technical University</aff>
      <pub-date publication-format="electronic" date-type="pub" iso-8601-date="2020-09-24">
        <day>24</day>
        <month>09</month>
        <year>2020</year>
      </pub-date>
      <volume>13</volume>
      <issue>3</issue>
      <fpage>42</fpage>
      <lpage>55</lpage>
      <self-uri xmlns:xlink="http://www.w3.org/1999/xlink" content-type="pdf" xlink:href="https://physmath.spbstu.ru/userfiles/files/articles/2020/3/04_42-55_13(3)2020.pdf"/>
      <abstract xml:lang="en">
        <p>The diffusion problem in a rectangular-shaped body with the Derichlet’s boundary conditions and an internal substance source depending on the rectangle points’ coordinates has been solved generally by the fast expansion method (FEM). The exact solution containing free parameters was obtained, and by changing them one could get many new exact solutions. Exact solutions to the problem with a constant internal source were shown as an example. From our analysis of the exact solutions it follows that the concentration and diffusion fluxes distributions should be symmetrical relative to the plane y = b/2, provided that the substance concentration in the corners of the rectangular area is equal to zero. An investigation into the difference in the diffusion fluxes along the coordinate axes showed that the constant internal source affected the difference in the nonsymmetrical fluxes, and the concentration of the substance in the area corners had no effect.</p>
      </abstract>
      <kwd-group xml:lang="en">
        <kwd>exact solution</kwd>
        <kwd>diffusion</kwd>
        <kwd>internal source</kwd>
        <kwd>rectangular shape</kwd>
        <kwd>fast expansion method</kwd>
      </kwd-group>
    </article-meta>
  </front>
</article>
