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Eurasian Mathematical Journal, 2017, Volume 8, Number 1, Pages 50–57 (Mi emj247)  

This article is cited in 3 scientific papers (total in 3 papers)

On an ill-posed problem for the Laplace operator with nonlocal boundary condition

T. Sh. Kal'menov, B. T. Torebek

Institute of Mathematics and Mathematical Modeling, 125 Pushkin St, 050010 Almaty, Kazakhstan
Full-text PDF (387 kB) Citations (3)
References:
Abstract: In this paper a nonlocal problem for the Poisson equation in a rectangular is considered. It is shown that this problem is ill-posed as well as the Cauchy problem for the Laplace equation. The method of spectral expansion via eigenfunctions of the nonlocal problem for equations with deviating argument allows us to establish a criterion of the strong solvability of the considered nonlocal problem. It is shown that the ill-posedness of the nonlocal problem is equivalent to the existence of an isolated point of the continuous spectrum for a nonself-adjoint operator with the deviating argument.
Keywords and phrases: Laplace operator, nonlocal boundary value problem, differential operator, criterion of well-posedness.
Funding agency Grant number
Ministry of Education and Science of the Republic of Kazakhstan 0820/GF4
0085/PTSF-14
This research is financially supported by a grant No. 0820/GF4 and by the target program 0085/PTSF-14 of the Ministry of Science and Education of the Republic of Kazakhstan.
Received: 28.11.2016
Bibliographic databases:
Document Type: Article
MSC: 31A30, 31B30, 35J40
Language: English
Citation: T. Sh. Kal'menov, B. T. Torebek, “On an ill-posed problem for the Laplace operator with nonlocal boundary condition”, Eurasian Math. J., 8:1 (2017), 50–57
Citation in format AMSBIB
\Bibitem{KalTor17}
\by T.~Sh.~Kal'menov, B.~T.~Torebek
\paper On an ill-posed problem for the Laplace operator with nonlocal boundary condition
\jour Eurasian Math. J.
\yr 2017
\vol 8
\issue 1
\pages 50--57
\mathnet{http://mi.mathnet.ru/emj247}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000411744800004}
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  • https://www.mathnet.ru/eng/emj/v8/i1/p50
  • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Eurasian Mathematical Journal
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