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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2017, Volume 141, Pages 42–47 (Mi into241)  
This article is cited in 1 scientific paper (total in 1 paper)

Convergence of eigenelements of a Steklov-type problem in a half-band with a small hole

D. B. Davletova, O. B. Davletovb

a Bashkir State Pedagogical University, Ufa
b Ufa State Petroleum Technological University
Full-text PDF (163 kB) Citations (1)
Abstract: We consider a Steklov-type problem for the Laplace operator in a half-band containing a small hole. On the lateral boundaries and the boundary of the hole, the Dirichlet conditions are stated, and on the base of the half-band the Steklov spectral condition. We prove that eigenvalues of this problem tend to zero as the small parameter (the “diameter” of the hole) vanishes.
Keywords: half-band, Steklov problem, eigenvalue, singular perturbation, small hole, convergence.
Funding agency Grant number
Russian Foundation for Basic Research 16-31-00066-мол
Grant of the Republic of Bashkortostan
This work was partially supported by the Russian Foundation for Basic Research (project No 16-31-00066-mol) and the Grant of the Republic of Bashkortostan for younf scientists and youth scientific teams (2016).
English version:
Journal of Mathematical Sciences, 2019, Volume 241, Issue 5, Pages 549–555
DOI: https://doi.org/10.1007/s10958-019-04444-1
Bibliographic databases:
Document Type: Article
UDC: 517.929.7, 517.929.8, 517.984
MSC: 47A10, 58J37
Language: Russian
Citation: D. B. Davletov, O. B. Davletov, “Convergence of eigenelements of a Steklov-type problem in a half-band with a small hole”, Differential equations. Spectral theory, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 141, VINITI, M., 2017, 42–47; Journal of Mathematical Sciences, 241:5 (2019), 549–555
Citation in format AMSBIB
\Bibitem{DavDav17}
\by D.~B.~Davletov, O.~B.~Davletov
\paper Convergence of eigenelements of a Steklov-type problem in a half-band with a small hole
\inbook Differential equations. Spectral theory
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2017
\vol 141
\pages 42--47
\publ VINITI
\publaddr M.
\mathnet{http://mi.mathnet.ru/into241}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3801336}
\zmath{https://zbmath.org/?q=an:07123831}
\transl
\jour Journal of Mathematical Sciences
\yr 2019
\vol 241
\issue 5
\pages 549--555
\crossref{https://doi.org/10.1007/s10958-019-04444-1}
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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