Homogenization of Boundary Value Problems in Two-Level Thick Junctions Consisting of Thin Disks with Rounded or Sharp Edges

We consider a linear elliptic boundary value problem in a two-level thick junction of type 3 : 2 : 2 which consists of a cylinder with ε-periodically stringed thin disks. The thin disks are divided into two levels depending on their geometric structure and boundary conditions on their surfaces. The...

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Bibliographic Details
Published inJournal of mathematical sciences (New York, N.Y.) Vol. 191; no. 2; pp. 254 - 279
Main Authors Mel’nik, T. A., Sadovyi, D. Yu
Format Journal Article
LanguageEnglish
Published Boston Springer US 13.05.2013
Springer
Subjects
Mathematics
Mathematics and Statistics
Thin Disk
Integral Identity
Weak Derivative
Weak Solution
Unique Weak Solution
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Summary:We consider a linear elliptic boundary value problem in a two-level thick junction of type 3 : 2 : 2 which consists of a cylinder with ε-periodically stringed thin disks. The thin disks are divided into two levels depending on their geometric structure and boundary conditions on their surfaces. The first-level thin disks have variable thickness vanishing at their edges. Hence some coefficients of the corresponding homogenized problem degenerate and its solution has a singular behavior near the boundary. We extract three qualitatively different cases of the asymptotic behavior of the solution as ε → 0. Bibliography: 26 titles. Illustrations: 2 figures.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-013-1315-8