Geodesic
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
Sbornik. Mathematics, Tome 187 (1996) no. 6, pp. 869-880 Cet article a éte moissonné depuis la source Math-Net.Ru

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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 $S=\partial \omega \cap \bigl \{x\in \mathbb R^d:|x_i|<1/2,\ i=\overline {1,d}\bigr \}$. 
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     author = {S. E. Pastukhova},
     title = {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},
     journal = {Sbornik. Mathematics},
     pages = {869--880},
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     volume = {187},
     number = {6},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1996_187_6_a5/}
}
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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. Sbornik. Mathematics, Tome 187 (1996) no. 6, pp. 869-880. http://geodesic.mathdoc.fr/item/SM_1996_187_6_a5/

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