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Zapiski Nauchnykh Seminarov POMI, 2000, Volume 264, Pages 66–82 (Mi znsl1159)  
This article is cited in 54 scientific papers (total in 54 papers)

An augmented scattering matrix and an exponentially decreasing solution of elliptic boundary-value problem in the domain with cylindrical outlets

I. V. Kamotskii, S. A. Nazarov

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences
Full-text PDF (262 kB) Citations (54)
Abstract: Self-adjoint elliptic boundary-value problem in domain with cylindrical outlets to infinity is considered. The notion of augmented scattering matrix is introduced due to artificial radiation conditions. The properties of augmented scattering matrix are studied and the connection with classical scattering matrix is demonstrated. The central point is possibility to calculate the number of leaner independent solutions of homogeneous problem with fixed rate of decreasing at infinity by analyzing the spectrum of augmented scattering matrix. This property is applied to problem of diffraction on periodical boundary as example.
Received: 23.12.1999
English version:
Journal of Mathematical Sciences (New York), 2002, Volume 111, Issue 4, Pages 3657–3666
DOI: https://doi.org/10.1023/A:1016377707919
Bibliographic databases:
UDC: 517.43
Language: Russian
Citation: I. V. Kamotskii, S. A. Nazarov, “An augmented scattering matrix and an exponentially decreasing solution of elliptic boundary-value problem in the domain with cylindrical outlets”, Mathematical problems in the theory of wave propagation. Part 29, Zap. Nauchn. Sem. POMI, 264, POMI, St. Petersburg, 2000, 66–82; J. Math. Sci. (New York), 111:4 (2002), 3657–3666
Citation in format AMSBIB
\Bibitem{KamNaz00}
\by I.~V.~Kamotskii, S.~A.~Nazarov
\paper An augmented scattering matrix and an exponentially decreasing solution of elliptic boundary-value problem in the domain with cylindrical outlets
\inbook Mathematical problems in the theory of wave propagation. Part~29
\serial Zap. Nauchn. Sem. POMI
\yr 2000
\vol 264
\pages 66--82
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl1159}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1796996}
\zmath{https://zbmath.org/?q=an:1040.35053}
\transl
\jour J. Math. Sci. (New York)
\yr 2002
\vol 111
\issue 4
\pages 3657--3666
\crossref{https://doi.org/10.1023/A:1016377707919}
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    • This publication is cited in the following 54 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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