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 Mat. Zametki: Year: Volume: Issue: Page: Find

 Mat. Zametki, 2001, Volume 69, Issue 4, Pages 600–612 (Mi mz526)

Spectral Asymptotics for a Steady-State Heat Conduction Problem in a Perforated Domain

S. E. Pastukhova

Moscow State Institute of Radio-Engineering, Electronics and Automation (Technical University)

Abstract: In this paper we study the eigenvalues and eigenfunctions of a boundary-value problem for an elliptic equation of second order with oscillatory coefficients in a periodically perforated domain when the boundary condition on the external boundary is of the first type and on the boundary of “holes” of the third type, for the case in which the linear dimension $\varepsilon$ of the perforation period tends to zero. It is proved that these eigenvalues and eigenfunctions can be determined approximately via the eigenvalues and eigenfunctions of an essentially simpler Dirichlet problem for an elliptic equation with constant coefficients in a domain without holes. Estimates of errors in these approximations are given.

DOI: https://doi.org/10.4213/mzm526

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English version:
Mathematical Notes, 2001, 69:4, 546–558

Bibliographic databases:

UDC: 517.946.9

Citation: S. E. Pastukhova, “Spectral Asymptotics for a Steady-State Heat Conduction Problem in a Perforated Domain”, Mat. Zametki, 69:4 (2001), 600–612; Math. Notes, 69:4 (2001), 546–558

Citation in format AMSBIB
\Bibitem{Pas01} \by S.~E.~Pastukhova \paper Spectral Asymptotics for a Steady-State Heat Conduction Problem in a Perforated Domain \jour Mat. Zametki \yr 2001 \vol 69 \issue 4 \pages 600--612 \mathnet{http://mi.mathnet.ru/mz526} \crossref{https://doi.org/10.4213/mzm526} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1845999} \zmath{https://zbmath.org/?q=an:0992.35059} \elib{http://elibrary.ru/item.asp?id=582626} \transl \jour Math. Notes \yr 2001 \vol 69 \issue 4 \pages 546--558 \crossref{https://doi.org/10.1023/A:1010216415846} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000169324200024} 

• http://mi.mathnet.ru/eng/mz526
• https://doi.org/10.4213/mzm526
• http://mi.mathnet.ru/eng/mz/v69/i4/p600

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Piat V.Ch., Piatnitski A., “Gamma-CONVERGENCE APPROACH TO VARIATIONAL PROBLEMS IN PERFORATED DOMAINS WITH Fourier BOUNDARY CONDITIONS”, ESAIM-Control Optimisation and Calculus of Variations, 16:1 (2010), 148–175
2. Piat V.Ch., Pankratova I., Piatnitski A., “Localization Effect for a Spectral Problem in a Perforated Domain with Fourier Boundary Conditions”, SIAM J. Math. Anal., 45:3 (2013), 1302–1327
3. Cancedda A., “Spectral Homogenization For a Robin-Neumann Problem”, Boll. Unione Mat. Ital., 10:2 (2017), 199–222
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