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Mat. Sb., 1994, Volume 185, Number 3, Pages 3–24 (Mi msb883)  

This article is cited in 1 scientific paper (total in 1 paper)

Transfer of Sommerfeld's radiation conditions to an artificial boundary of a domain, based on a variational principle

I. V. Bezmenov

M. V. Keldysh Institute for Applied Mathematics, Russian Academy of Sciences

Abstract: To solve the Helmholtz equation interior to a bounded domain with artificial boundary, a new formulation of variational type is proposed for boundary conditions which have the property of suppressing waves reflected from the boundary. This formulation is based on the minimization of a functional constructed in a special way. Existence and uniqueness theorems are proved for a classical solution of the problem in the proposed variational formulation. It is proved that the solution of the interior problem converges uniformly to a solution of the problem posed in an unbounded domain with Sommerfeld's radiation conditions at infinity as the size of the domain increases without limit.

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English version:
Russian Academy of Sciences. Sbornik. Mathematics, 1995, 81:2, 261–279

Bibliographic databases:

UDC: 517.972.5
MSC: 35J05, 35A05, 35A35
Received: 15.10.1992

Citation: I. V. Bezmenov, “Transfer of Sommerfeld's radiation conditions to an artificial boundary of a domain, based on a variational principle”, Mat. Sb., 185:3 (1994), 3–24; Russian Acad. Sci. Sb. Math., 81:2 (1995), 261–279

Citation in format AMSBIB
\Bibitem{Bez94}
\by I.~V.~Bezmenov
\paper Transfer of Sommerfeld's radiation conditions to an~artificial boundary of a~domain, based on a~variational principle
\jour Mat. Sb.
\yr 1994
\vol 185
\issue 3
\pages 3--24
\mathnet{http://mi.mathnet.ru/msb883}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1268795}
\zmath{https://zbmath.org/?q=an:0831.35034}
\transl
\jour Russian Acad. Sci. Sb. Math.
\yr 1995
\vol 81
\issue 2
\pages 261--279
\crossref{https://doi.org/10.1070/SM1995v081n02ABEH003538}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1995RB51300001}


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    Erratum

    This publication is cited in the following articles:
    1. T. Sh. Kalmenov, D. Suragan, “Perenos uslovii izlucheniya Zommerfelda na granitsu ogranichennoi oblasti”, Zh. vychisl. matem. i matem. fiz., 52:6 (2012), 1063–1068  mathnet
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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