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Sbornik: Mathematics, 2009, Volume 200, Issue 3, Pages 357–383
DOI: https://doi.org/10.1070/SM2009v200n03ABEH004000 (Mi sm4500) 		 
This article is cited in 13 scientific papers (total in 13 papers)

Asymptotic analysis of boundary-value problems in thick three-dimensional multi-level junctions

T. A. Mel'nika, G. A. Chechkinbc

a National Taras Shevchenko University of Kyiv, The Faculty of Mechanics and Mathematics
b M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
c Narvik University College
English version PDF (447 kB) Citations (13)
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DOI: https://doi.org/10.1070/SM2009v200n03ABEH004000
Abstract: We consider homogenization problems in a singularly perturbed three-dimensional domain of multi-level-junction type which consists of the junction body and a large number of alternating thin curvilinear cylinders that belong to two classes. Under the assumption that one class consists of cylinders of finite height, and the second class of cylinders of infinitesimal height, and that different inhomogeneous boundary conditions of the third kind with perturbed coefficients are given on the boundaries of the thin curvilinear cylinders, we prove the homogenization theorems and the convergence of the energy integrals.
Bibliography: 42 titles.
Keywords: homogenization, thick junctions, asymptotics.
Received: 18.12.2007 and 02.07.2008
Russian version:
Matematicheskii Sbornik, 2009, Volume 200, Number 3, Pages 49–74
DOI: https://doi.org/10.4213/sm4500
Bibliographic databases:
UDC: 517.956.225+517.956.8
MSC: Primary 35B40; Secondary 35B25, 35B27, 35J25
Language: English
Original paper language: Russian
Citation: T. A. Mel'nik, G. A. Chechkin, “Asymptotic analysis of boundary-value problems in thick three-dimensional multi-level junctions”, Mat. Sb., 200:3 (2009), 49–74; Sb. Math., 200:3 (2009), 357–383
Citation in format AMSBIB
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    • This publication is cited in the following 13 articles:
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