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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Vydané v:	Computational mathematics and mathematical physics Ročník 64; číslo 10; s. 2285 - 2304
Hlavný autor:	Nazarov, S. A.
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Moscow Pleiades Publishing 01.10.2024 Springer Nature B.V
Predmet:	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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Abstract	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.
AbstractList	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.
Author	Nazarov, S. A.
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Copyright	Pleiades Publishing, Ltd. 2024 ISSN 0965-5425, Computational Mathematics and Mathematical Physics, 2024, Vol. 64, No. 10, pp. 2285–2304. © Pleiades Publishing, Ltd., 2024. Pleiades Publishing, Ltd. 2024.
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SubjectTerms	Asymptotic series Computational Mathematics and Numerical Analysis Density Dirichlet problem Eigenvalues Eigenvectors Estimates Euclidean space Inclusions Mathematics Mathematics and Statistics Parameters Partial Differential Equations
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Title	Asymptotic Analysis of Eigenvalues for Concentrated Masses Approaching One Another
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