On the Eigenvalues and Eigenfunctions of the Dirichlet and Neumann Problems in a Domain with Perforated Partitions

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On the Eigenvalues and Eigenfunctions of the Dirichlet and Neumann Problems in a Domain with Perforated Partitions. / Nazarov, S. A.

In: Differential Equations, Vol. 57, No. 6, 06.2021, p. 736-752.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{c6f0091e6b0e48dc9a6bd2982dc251d8,

title = "On the Eigenvalues and Eigenfunctions of the Dirichlet and Neumann Problems in a Domain with Perforated Partitions",

abstract = "Abstract: We find the asymptotics of the eigenpairs of the Dirichlet and Neumann spectral problemsfor the Laplace operator in a domain separated by several partitions with holes of small diametersand splitting into several independent cells in the limit as the diameters tend to zero. Usingasymptotic methods for singularly perturbed domains, we study the splitting of a multipleeigenvalue of the limit problems, for example, the zero eigenvalue under the Neumann boundaryconditions, and the localization of the eigenfunction in the case of a simple eigenvalue.",

keywords = "BOUNDARY-VALUE-PROBLEMS, PERTURBATION, LAPLACIAN",

author = "Nazarov, {S. A.}",

note = "Publisher Copyright: {\textcopyright} 2021, Pleiades Publishing, Ltd.",

year = "2021",

month = jun,

doi = "10.1134/s0012266121060045",

language = "English",

volume = "57",

pages = "736--752",

journal = "Differential Equations",

issn = "0012-2661",

publisher = "Pleiades Publishing",

number = "6",

}

RIS

TY - JOUR

T1 - On the Eigenvalues and Eigenfunctions of the Dirichlet and Neumann Problems in a Domain with Perforated Partitions

AU - Nazarov, S. A.

PY - 2021/6

Y1 - 2021/6

N2 - Abstract: We find the asymptotics of the eigenpairs of the Dirichlet and Neumann spectral problemsfor the Laplace operator in a domain separated by several partitions with holes of small diametersand splitting into several independent cells in the limit as the diameters tend to zero. Usingasymptotic methods for singularly perturbed domains, we study the splitting of a multipleeigenvalue of the limit problems, for example, the zero eigenvalue under the Neumann boundaryconditions, and the localization of the eigenfunction in the case of a simple eigenvalue.

AB - Abstract: We find the asymptotics of the eigenpairs of the Dirichlet and Neumann spectral problemsfor the Laplace operator in a domain separated by several partitions with holes of small diametersand splitting into several independent cells in the limit as the diameters tend to zero. Usingasymptotic methods for singularly perturbed domains, we study the splitting of a multipleeigenvalue of the limit problems, for example, the zero eigenvalue under the Neumann boundaryconditions, and the localization of the eigenfunction in the case of a simple eigenvalue.

KW - BOUNDARY-VALUE-PROBLEMS

KW - PERTURBATION

KW - LAPLACIAN

UR - http://www.scopus.com/inward/record.url?scp=85109779021&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/602057ff-3e13-3ee0-b6c0-f1be15c720d6/

U2 - 10.1134/s0012266121060045

DO - 10.1134/s0012266121060045

M3 - Article

AN - SCOPUS:85109779021

VL - 57

SP - 736

EP - 752

JO - Differential Equations

JF - Differential Equations

SN - 0012-2661

IS - 6

ER -

ID: 88365827