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Zapiski Nauchnykh Seminarov POMI, 1998, Volume 250, Pages 83–96 (Mi znsl644)  
This article is cited in 8 scientific papers (total in 8 papers)

Helmgoltz equation solutions concentrated near periodical boundary

V. Yu. Gotlib

St-Petersburg Branch of P. P. Shirshov institute of Oceanology of RAS
Full-text PDF (198 kB) Citations (8)
Abstract: Existence of solutions of Helmholtz equation exponentially decaying away from a periodical boundary in the upper half-plane is proved. These solutions can exist for special form of the boundary under Dirichlet or Neumann boundary conditions. In both cases the boundary has a form of the resonator chain connected by narrow splits with the upper half-plane.
Received: 19.09.1997
English version:
Journal of Mathematical Sciences (New York), 2000, Volume 102, Issue 4, Pages 4188–4194
DOI: https://doi.org/10.1007/BF02673850
Bibliographic databases:
UDC: 517
Language: Russian
Citation: V. Yu. Gotlib, “Helmgoltz equation solutions concentrated near periodical boundary”, Mathematical problems in the theory of wave propagation. Part 27, Zap. Nauchn. Sem. POMI, 250, POMI, St. Petersburg, 1998, 83–96; J. Math. Sci. (New York), 102:4 (2000), 4188–4194
Citation in format AMSBIB
\Bibitem{Got98}
\by V.~Yu.~Gotlib
\paper Helmgoltz equation solutions concentrated near periodical boundary
\inbook Mathematical problems in the theory of wave propagation. Part~27
\serial Zap. Nauchn. Sem. POMI
\yr 1998
\vol 250
\pages 83--96
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl644}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1701861}
\zmath{https://zbmath.org/?q=an:1071.35512}
\transl
\jour J. Math. Sci. (New York)
\yr 2000
\vol 102
\issue 4
\pages 4188--4194
\crossref{https://doi.org/10.1007/BF02673850}
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    • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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