Asymptotic Analysis of Eigenvalues for Concentrated Masses Approaching One Another

A spectral Dirichlet problem in a three-dimensional domain with several identical concentrated heavy masses (large density perturbations on small sets) is studied. Asymptotics of its eigenvalues and eigenfunctions are constructed depending on two parameters: a small one characterizing the size and t...

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Bibliographic Details
Published in:Computational mathematics and mathematical physics Vol. 64; no. 10; pp. 2285 - 2304
Main Author: Nazarov, S. A.
Format: Journal Article
Language:English
Published: Moscow Pleiades Publishing 01.10.2024
Springer Nature B.V
Subjects:
Asymptotic series
Computational Mathematics and Numerical Analysis
Density
Dirichlet problem
Eigenvalues
Eigenvectors
Estimates
Euclidean space
Inclusions
Mathematics
Mathematics and Statistics
Parameters
Partial Differential Equations
concentrated masses
timelike parameter
asymptotics of eigenvalues and eigenfunctions
uniform estimates
spectral Dirichlet problem
ISSN:0965-5425, 1555-6662
Online Access:Get full text
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Summary:A spectral Dirichlet problem in a three-dimensional domain with several identical concentrated heavy masses (large density perturbations on small sets) is studied. Asymptotics of its eigenvalues and eigenfunctions are constructed depending on two parameters: a small one characterizing the size and the density of the inclusions and a timelike parameter describing their approach to the origin (or to a point on the boundary of the domain). The basic novelty is the construction of two-scale asymptotic expansions and the derivation of uniform estimates for asymptotic remainders.
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ISSN:0965-5425
1555-6662
DOI:10.1134/S0965542524701276