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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Veröffentlicht in:Computational mathematics and mathematical physics Jg. 64; H. 10; S. 2285 - 2304
1. Verfasser: Nazarov, S. A.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Moscow Pleiades Publishing 01.10.2024
Springer Nature B.V
Schlagworte:
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
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Zusammenfassung: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.
Bibliographie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0965-5425
1555-6662
DOI:10.1134/S0965542524701276