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Zapiski Nauchnykh Seminarov POMI, 2006, Volume 332, Pages 193–219 (Mi znsl270)  
This article is cited in 9 scientific papers (total in 9 papers)

Asymptotics of a solution to the Neumann problem in a thin domain with the sharp edge

S. A. Nazarova, Ya. Taskinenb

a Institute of Problems of Mechanical Engineering, Russian Academy of Sciences
b University of Helsinki, Department of Mathematics and Statistics
Full-text PDF (299 kB) Citations (9)
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Abstract: The asymptotic expansion of the solution of the Neumann problem for the second order equation in a thin domain with the sharp edge is constructed and justified. Because of the presence of a edge with the zero casp the limit equation on the longitudinal section of a domain obtained as a result of the procedure of lowering a dimention proves to be degenerating and its solution has a nonregular behavior near a boundary.
Received: 25.04.2006
English version:
Journal of Mathematical Sciences (New York), 2007, Volume 142, Issue 6, Pages 2630–2644
DOI: https://doi.org/10.1007/s10958-007-0151-0
Bibliographic databases:
UDC: 517.946
Language: Russian
Citation: S. A. Nazarov, Ya. Taskinen, “Asymptotics of a solution to the Neumann problem in a thin domain with the sharp edge”, Mathematical problems in the theory of wave propagation. Part 35, Zap. Nauchn. Sem. POMI, 332, POMI, St. Petersburg, 2006, 193–219; J. Math. Sci. (N. Y.), 142:6 (2007), 2630–2644
Citation in format AMSBIB
\Bibitem{NazTas06}
\by S.~A.~Nazarov, Ya.~Taskinen
\paper Asymptotics of a~solution to the Neumann problem in a~thin domain with the sharp edge
\inbook Mathematical problems in the theory of wave propagation. Part~35
\serial Zap. Nauchn. Sem. POMI
\yr 2006
\vol 332
\pages 193--219
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl270}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2252995}
\zmath{https://zbmath.org/?q=an:05051345}
\elib{https://elibrary.ru/item.asp?id=9172505}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2007
\vol 142
\issue 6
\pages 2630--2644
\crossref{https://doi.org/10.1007/s10958-007-0151-0}
\elib{https://elibrary.ru/item.asp?id=13534912}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-34247242717}
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  • https://www.mathnet.ru/eng/znsl/v332/p193
    • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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