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Asymptotic analysis of a spectral problem in a periodic thick junction of type 3:2:1. (English) Zbl 0983.35044
The author investigates a mixed boundary value problem for the Laplacian in a domain \(\Omega_\varepsilon\subset \mathbb{R}^3\) depending on a small parameter \(\varepsilon\). It consists of a ‘body’ \(\Omega_0:= \{(x', x_3)\in \mathbb{R}^3: x'\in K\), \(0< x_3< \gamma(x')\}\) and a large number of thin cylinders connected to \(\Omega_0\) at \(K\) and degenerating to segments as \(\varepsilon\to 0\). The author derives an asymptotic expansion (as \(\varepsilon\to 0\)) of the spectral decomposition of the corresponding operator.
Reviewer: N.Weck (Essen)

MSC:
35J25 Boundary value problems for second-order elliptic equations
35P20 Asymptotic distributions of eigenvalues in context of PDEs
35C20 Asymptotic expansions of solutions to PDEs
35B25 Singular perturbations in context of PDEs
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