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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
##### Keywords:
Laplacian; singular perturbation; degenerate domain
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##### References:
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