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Asymptotic Analysis of Spectral Problems in Thick Multi-Level Junctions

In: Integral Methods in Science and Engineering, Volume 1

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  • T. A. Mel’nyk

    (National Taras Shevchenko University of Kyiv)

Abstract

Spectral boundary-value problems are considered in a new kind of perturbed domain, namely, thick multi-level junctions. Boundary-value problems in thick one-level junctions (thick junctions) have been intensively investigated recently (see, for instance, [BlGaGr07], [BlGaMe08], [Me08] and, the references there). In [MeNa97]–[Me(3)01], classification of thick one-level junctions was given and basic results were obtained both for boundary-value and spectral problems in thick junctions of different types. It was shown that qualitative properties of solutions essentially depend on the junction type and on the conditions given on the boundaries of the attached thin domains. It is known that the asymptotic behavior of the spectrum of a perturbed spectral problem is highly sensitive to perturbation, and it is unexpected. This was also observed for spectral problems in thick junctions with Neumann conditions ([MeNa97] and [Me00]), with Dirichlet conditions ([Me99] and [Me(3)01]), with Fourier conditions ([Me(2)01]) and with Steklov ones ([Me(1)01]).

Suggested Citation

  • T. A. Mel’nyk, 2010. "Asymptotic Analysis of Spectral Problems in Thick Multi-Level Junctions," Springer Books, in: Christian Constanda & M.E. Pérez (ed.), Integral Methods in Science and Engineering, Volume 1, chapter 21, pages 205-215, Springer.
    • Handle: RePEc:spr:sprchp:978-0-8176-4899-2_21
    DOI: 10.1007/978-0-8176-4899-2_21
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