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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">5</article-id>
      <article-id pub-id-type="doi">10.5862/JPM.230.5</article-id>
      <title-group>
        <article-title>Rough estimates and binomial approximations for the crocco equation in the boundary problems</article-title>
        <trans-title-group xml:lang="ru">
          <trans-title>Грубые оценки и биномиальные аппроксимации в предельных задачах для уравнения Крокко</trans-title>
        </trans-title-group>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <name>
            <surname>Petrichenko</surname>
            <given-names>Mikhail</given-names>
          </name>
          <xref ref-type="aff" rid="aff1"/>
          <email>fonpetrich@mail.ru</email>
        </contrib>
      </contrib-group>
      <aff id="aff1">Peter the Great St. Petersburg Polytechnic University</aff>
      <pub-date publication-format="electronic" date-type="pub" iso-8601-date="2015-12-10">
        <day>10</day>
        <month>12</month>
        <year>2015</year>
      </pub-date>
      <issue>4</issue>
      <issue-id pub-id-type="publisher-id">230</issue-id>
      <fpage>61</fpage>
      <lpage>72</lpage>
      <self-uri xmlns:xlink="http://www.w3.org/1999/xlink" content-type="pdf" xlink:href="https://physmath.spbstu.ru/userfiles/files/articles/2015/4/05_61_72_4_230_2015.pdf"/>
      <abstract xml:lang="en">
        <p>In order to solve the Crocco boundary problems known as the typical one and the uniform one, binomials (as approximants of exact solutions) and integral identities have been used. The extent of the closeness of the exact solution to its approximation was estimated using the ϕ(0) value. The solution of the typical Crocco boundary problem was proved to have a logarithmic singularity of the derivative at ϕ = 0. The Crocco equation was found to provide both necessary and sufficient conditions for the minimum of a positive distribution being vortex in dϕ/dh. The uniform Crocco boundary problem was demonstrated to be equivalent to the two typical Crocco boundary problems with a common critical point.</p>
      </abstract>
      <kwd-group xml:lang="en">
        <kwd>Crocco boundary problem</kwd>
        <kwd>approximation</kwd>
        <kwd>convex distribution</kwd>
        <kwd>minimum of positive functional</kwd>
      </kwd-group>
    </article-meta>
  </front>
</article>
