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Mat. Sb. (N.S.), 1978, Volume 106(148), Number 4(8), Pages 604–621 (Mi msb2609)  

This article is cited in 55 scientific papers (total in 55 papers)

The asymptotic behavior of solutions of the second boundary value problem under fragmentation of the boundary of the domain

E. Ya. Khruslov


Abstract: The second boundary value problem is considered for the equation $\Delta u-cu=f$ in a domain $G^{(s)}$ of complicated structure of the form $G^{(s)}=\mathbf R_n\setminus F^{(s)}$, where $F^{(s)}$ is a closed finely partitioned set lying in a domain $\Omega\subset\mathbf R_n$ ($n\geqslant 2$) for all $s=1,2,…$. The asymptotic behavior of a solution $u^{(s)}(x)$ of this problem is studied as $s\to\infty$, when $F^{(s)}$ becomes more and more finely divided and is situated in $\Omega$ so that the distance from $F^{(s)}$ to any point $x\in\Omega$ tends to zero. It is proved that under specific conditions $u^{(s)}(x)$ converges in $\mathbf R_n\setminus\overline\Omega$ to a function $u(x)$ that is a solution of a conjugation problem. Sufficient conditions for convergence are formulated.
Bibliography: 9 titles.

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English version:
Mathematics of the USSR-Sbornik, 1979, 35:2, 266–282

Bibliographic databases:

UDC: 517.946.9
MSC: 35G15, 35B40
Received: 21.11.1977

Citation: E. Ya. Khruslov, “The asymptotic behavior of solutions of the second boundary value problem under fragmentation of the boundary of the domain”, Mat. Sb. (N.S.), 106(148):4(8) (1978), 604–621; Math. USSR-Sb., 35:2 (1979), 266–282

Citation in format AMSBIB
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\by E.~Ya.~Khruslov
\paper The asymptotic behavior of solutions of the second boundary value problem under fragmentation of the boundary of the domain
\jour Mat. Sb. (N.S.)
\yr 1978
\vol 106(148)
\issue 4(8)
\pages 604--621
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\transl
\jour Math. USSR-Sb.
\yr 1979
\vol 35
\issue 2
\pages 266--282
\crossref{https://doi.org/10.1070/SM1979v035n02ABEH001474}
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  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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