Asymptotic expansions of eigenvalues and eigenfunctions of a vibrating system with rigid light-weight inclusions
type: Item
instance of: scholarly article
zbMATH Open document ID: 1289.35071
author: V. M. Hut
publication date: 2014-01-17T00:00:00Z
Mathematics Subject Classification ID: 35J15
Mathematics Subject Classification ID: 35J70
zbMATH DE Number: 6247737
zbMATH Keywords: asymptotics construction
zbMATH Keywords: substantiation of asymptotic expansions
MaRDI profile type: Publication
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title: Asymptotic expansions of eigenvalues and eigenfunctions of a vibrating system with rigid light-weight inclusions
published in: Matematychni Metody ta Fizyko-Mekhanichni Polya
review text: The author studies spectral properties of a boundary value problem for second-order elliptic operator with singularly perturbed coefficients. The problem describes eigenmodes of an elastic system with a finite number of rigid light-weight inclusions of arbitrary shape. It is assumed that the ratio of rigidity coefficients of the inclusions and the main body has the order \(\varepsilon^{-1}\) as \(\varepsilon\to 0\), and the ratio of their mass densities is of order \(\varepsilon^{\varkappa}\) for \(\varkappa>0\). Complete asymptotic expansions of the eigenvalues and eigenfunctions of the problem are constructed and justified.
description: scientific article; zbMATH DE number 6247737