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Vibrating Systems with Rigid Light-Weight Inclusions: Asymptotics of the Spectrum and Eigenspaces

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Ukrainian Mathematical Journal Aims and scope

We study the asymptotic behavior of eigenvalues and eigenfunctions of a singularly perturbed boundaryvalue problem for a second-order elliptic operator. The problem simulates natural vibrations of an elastic system with finitely many light-weight inclusions of any shape. The leading terms of the asymptotic representations of eigenelements are constructed with regard for their multiplicities. The justification of the asymptotic formulas is based on the uniform resolvent convergence of a certain family of unbounded self-adjoint operators.

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Authors and Affiliations

  1. Franko Lviv National University, Lviv, Ukraine

    Yu. D. Holovatyi & V. M. Hut

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  1. Yu. D. Holovatyi
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  2. V. M. Hut
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 64, No. 10, pp. 1314–1329, October, 2012.

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Holovatyi, Y.D., Hut, V.M. Vibrating Systems with Rigid Light-Weight Inclusions: Asymptotics of the Spectrum and Eigenspaces. Ukr Math J 64, 1495–1513 (2013). https://doi.org/10.1007/s11253-013-0731-8

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  • DOI: https://doi.org/10.1007/s11253-013-0731-8

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