Averaging in a perforated domain with an oscillating third boundary condition

A. G. Belyaev; A. L. Pyatnitskiǐ; G. A. Chechkin

doi:10.1070/sm2001v192n07ABEH000576

Averaging in a perforated domain with an oscillating third boundary condition

A. G. Belyaev
, A. L. Pyatnitskiǐ
, G. A. Chechkin

Research output: Contribution to journal › Article › peer-review

29 Citations (Scopus)

Abstract

We study an example averaging problem for a second-order elliptic equation in a periodically perforated domain with a third boundary condition (Fourier condition) on the boundary of the holes. Under the assumption that the coefficients of the boundary operator are bounded and the corresponding averages are small we construct the leading terms of the asymptotic expansion of the solution and estimate the error.

Original language	English
Pages (from-to)	933-949
Number of pages	17
Journal	Sbornik Mathematics
Volume	192
Issue number	7-8
DOIs	https://doi.org/10.1070/sm2001v192n07ABEH000576
Publication status	Published - 2001

ASJC Scopus subject areas

Mathematics (miscellaneous)

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title = "Averaging in a perforated domain with an oscillating third boundary condition",

abstract = "We study an example averaging problem for a second-order elliptic equation in a periodically perforated domain with a third boundary condition (Fourier condition) on the boundary of the holes. Under the assumption that the coefficients of the boundary operator are bounded and the corresponding averages are small we construct the leading terms of the asymptotic expansion of the solution and estimate the error.",

author = "Belyaev, \{A. G.\} and Pyatnitskiǐ, \{A. L.\} and Chechkin, \{G. A.\}",

year = "2001",

doi = "10.1070/sm2001v192n07ABEH000576",

language = "English",

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journal = "Sbornik Mathematics",

issn = "1064-5616",

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AU - Belyaev, A. G.

AU - Pyatnitskiǐ, A. L.

AU - Chechkin, G. A.

PY - 2001

Y1 - 2001

N2 - We study an example averaging problem for a second-order elliptic equation in a periodically perforated domain with a third boundary condition (Fourier condition) on the boundary of the holes. Under the assumption that the coefficients of the boundary operator are bounded and the corresponding averages are small we construct the leading terms of the asymptotic expansion of the solution and estimate the error.

AB - We study an example averaging problem for a second-order elliptic equation in a periodically perforated domain with a third boundary condition (Fourier condition) on the boundary of the holes. Under the assumption that the coefficients of the boundary operator are bounded and the corresponding averages are small we construct the leading terms of the asymptotic expansion of the solution and estimate the error.

UR - https://www.scopus.com/pages/publications/0035647938

U2 - 10.1070/sm2001v192n07ABEH000576

DO - 10.1070/sm2001v192n07ABEH000576

M3 - Article

AN - SCOPUS:0035647938

SN - 1064-5616

VL - 192

SP - 933

EP - 949

JO - Sbornik Mathematics

JF - Sbornik Mathematics

IS - 7-8

ER -

Averaging in a perforated domain with an oscillating third boundary condition

Abstract

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