Asymptotic behavior of eigenvalues and eigenfunctions of the Fourier problem in a thick multilevel junction
A spectral boundary-value problem is considered in a plane thick two-level junction $\Omega_{\varepsilon}$, which is the union of a domain $\Omega_{0}$ and a large number $2N$ of thin rods with thickness of order $\varepsilon = \mathcal{O} (N^{-1})$. The thin rods are divided into two levels depen...
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| Datum: | 2006 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2006
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/3447 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | A spectral boundary-value problem is considered in a plane thick two-level junction $\Omega_{\varepsilon}$, which is the union of a
domain $\Omega_{0}$ and a large number $2N$ of thin rods with thickness of order $\varepsilon = \mathcal{O} (N^{-1})$. The thin rods are divided into
two levels depending on their length. In addition, the thin rods from each level are $\varepsilon$-periodically alternated.
The Fourier conditions are given on the lateral boundaries of the thin rods. The asymptotic behavior of the eigenvalues
and eigenfunctions is investigated as $\varepsilon \rightarrow 0$, i.e., when the number of the thin rods infinitely increases and their thickness tends to zero.
The Hausdorff convergence of the spectrum is proved as $\varepsilon \rightarrow 0$, the leading terms of asymptotics are constructed and the
corresponding asymptotic estimates are justified for the eigenvalues and eigenfunctions. |
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