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Sbornik: Mathematics, 1996, Volume 187, Issue 6, Pages 869–880
DOI: https://doi.org/10.1070/SM1996v187n06ABEH000138
(Mi sm138)
 

This article is cited in 6 scientific papers (total in 6 papers)

On the nature of the temperature distribution in a perforated body with given values on the external boundary under conditions of heat transfer by Newton's law on the boundary of the cavities

S. E. Pastukhova

Moscow State Institute of Radio-Engineering, Electronics and Automation (Technical University)
References:
Abstract: For $\varepsilon \in (0,1)$ let $\Omega _\varepsilon =\Omega \cap \varepsilon \omega$, where $\Omega \subset \mathbb R^d$ is a bounded domain $\varepsilon \omega$ is the set obtained by an $\varepsilon ^{-1}$-fold contraction from an unbounded domain $\omega$ with a $1$-periodic structure, the set $\mathbb R^d \setminus \omega$ being dispersible. Then $\partial \Omega _\varepsilon =\Gamma _\varepsilon \cup S_\varepsilon$, where $\Gamma _\varepsilon$ is the external boundary of $\Omega _\varepsilon$ and $S_\varepsilon$ is the boundary of the cavities lying in $\Omega _\varepsilon$. We study the effect of the exponentially damping (as $\varepsilon \to 0$) influence of a non-zero temperature regime established on $\Gamma _\varepsilon$ on the temperature distribution inside an isotropic body occupying $\Omega _\varepsilon$ under the condition that the heat exchange on $S_\varepsilon$ with the medium filling the cavities of the body follows Newton's law with coefficient of proportionality $a_\varepsilon (x)=a(x/\varepsilon )$, where $a(y)$ is a $1$-periodic function defined on $\partial \omega~$ such that $\int _S a(y)\,ds>0$, if $S=\partial \omega \cap \bigl \{x\in \mathbb R^d:|x_i|<1/2,\ i=\overline {1,d}\bigr \}$.
Received: 27.06.1995
Russian version:
Matematicheskii Sbornik, 1996, Volume 187, Number 6, Pages 85–96
DOI: https://doi.org/10.4213/sm138
Bibliographic databases:
UDC: 517.953
MSC: 35J55, 73B30
Language: English
Original paper language: Russian
Citation: S. E. Pastukhova, “On the nature of the temperature distribution in a perforated body with given values on the external boundary under conditions of heat transfer by Newton's law on the boundary of the cavities”, Mat. Sb., 187:6 (1996), 85–96; Sb. Math., 187:6 (1996), 869–880
Citation in format AMSBIB
\Bibitem{Pas96}
\by S.~E.~Pastukhova
\paper On the nature of the~temperature distribution in a~perforated body with given values on the~external boundary under conditions of heat transfer by Newton's law on the~boundary of the~cavities
\jour Mat. Sb.
\yr 1996
\vol 187
\issue 6
\pages 85--96
\mathnet{http://mi.mathnet.ru/sm138}
\crossref{https://doi.org/10.4213/sm138}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1407681}
\zmath{https://zbmath.org/?q=an:0872.73002}
\transl
\jour Sb. Math.
\yr 1996
\vol 187
\issue 6
\pages 869--880
\crossref{https://doi.org/10.1070/SM1996v187n06ABEH000138}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1996VK60300014}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-0030519488}
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  • https://doi.org/10.1070/SM1996v187n06ABEH000138
  • https://www.mathnet.ru/eng/sm/v187/i6/p85
  • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Математический сборник - 1992–2005 Sbornik: Mathematics
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    Russian version PDF:173
    English version PDF:12
    References:43
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