Operator Pencil in a Domain with Concentrated Masses. A Scalar Analog of Linear Hydrodynamics

Part of the International Mathematical Series book series (IMAT, volume 12)


The problem describing low-frequency oscillations of a heavy viscousfluid in a vessel with a fine-meshed net on thefluid surface is studied in the case where thefluid density is inhomogeneous near the net. The obtained spectral problem for the operator pencil is treated by means of the Krein scheme [18]. To construct a homogenization for the quadratic operator pencil, the method of matching asymptotic expansions is used.


Weak Solution Asymptotic Expansion Spectral Problem Concentrate Mass Integral Identity 
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Authors and Affiliations

  1. 1.Department of MathematicsMoscow State UniversityMoscowRussia

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