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Russian Academy of Sciences. Sbornik. Mathematics, 1995, Volume 82, Issue 2, Pages 293–313
DOI: https://doi.org/10.1070/SM1995v082n02ABEH003565 (Mi sm910) 		 
This article is cited in 2 scientific papers (total in 2 papers)

On scattering by bodies with narrow channels

R. R. Gadyl'shin

Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences
English version PDF (1093 kB) Citations (2)
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DOI: https://doi.org/10.1070/SM1995v082n02ABEH003565
Abstract: Boundary value problems are considered for the Helmholtz equation outside a domain having a finite cavity of small 'radius' $\varepsilon\ll1$. It is shown that in the case of Neumann boundary conditions the analytic continuation of the solution of the boundary value problem has poles with small imaginary part. The method of matching asymptotic expansions is used to construct asymptotic expressions for these poles with respect to the small parameter $\varepsilon$, and it is shown that they have a resonance character.
Received: 06.10.1992
Russian version:
Matematicheskii Sbornik, 1994, Volume 185, Number 7, Pages 39–62
Bibliographic databases:
UDC: 517.95
MSC: Primary 35J05, 35J25, 35P25; Secondary 35B60, 34B27, 76Q05
Language: English
Original paper language: Russian
Citation: R. R. Gadyl'shin, “On scattering by bodies with narrow channels”, Mat. Sb., 185:7 (1994), 39–62; Russian Acad. Sci. Sb. Math., 82:2 (1995), 293–313
Citation in format AMSBIB
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\by R.~R.~Gadyl'shin
\paper On scattering by bodies with narrow channels
\jour Mat. Sb.
\yr 1994
\vol 185
\issue 7
\pages 39--62
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\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1300131}
\zmath{https://zbmath.org/?q=an:0840.35024}
\transl
\jour Russian Acad. Sci. Sb. Math.
\yr 1995
\vol 82
\issue 2
\pages 293--313
\crossref{https://doi.org/10.1070/SM1995v082n02ABEH003565}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1995RV83000003}
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  • https://doi.org/10.1070/SM1995v082n02ABEH003565
  • https://www.mathnet.ru/eng/sm/v185/i7/p39
    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Математический сборник - 1992–2005 Sbornik: Mathematics
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    Abstract page:253
    Russian version PDF:80
    English version PDF:21
    References:40
    First page:1
     
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