Standard

Eigenvalue asymptotics of long Kirchhoff plates with clamped edges. / Bakharev, F.L; Nazarov, S.A.

In: Sbornik Mathematics, Vol. 210, No. 4, 2019, p. 473-494.

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

Harvard

Bakharev, FL & Nazarov, SA 2019, 'Eigenvalue asymptotics of long Kirchhoff plates with clamped edges', Sbornik Mathematics, vol. 210, no. 4, pp. 473-494. https://doi.org/10.1070/SM9008

APA

Bakharev, F. L., & Nazarov, S. A. (2019). Eigenvalue asymptotics of long Kirchhoff plates with clamped edges. Sbornik Mathematics, 210(4), 473-494. https://doi.org/10.1070/SM9008

Vancouver

Bakharev FL, Nazarov SA. Eigenvalue asymptotics of long Kirchhoff plates with clamped edges. Sbornik Mathematics. 2019;210(4):473-494. https://doi.org/10.1070/SM9008

Author

Bakharev, F.L ; Nazarov, S.A. / Eigenvalue asymptotics of long Kirchhoff plates with clamped edges. In: Sbornik Mathematics. 2019 ; Vol. 210, No. 4. pp. 473-494.

BibTeX

@article{981d10acbdcd423bb99c686c3658ac7c,
title = "Eigenvalue asymptotics of long Kirchhoff plates with clamped edges",
abstract = "Asymptotic expansions are constructed for the eigenvalues and eigenfunctions of the Dirichlet problem for the biharmonic operator in thin domains (Kirchhoff plates with clamped edges). For a rectangular plate the leading terms are asymptotically determined from the Dirichlet problem for a second-order ordinary differential equation, while for a T-junction of plates they are determined from another limiting problem in an infinite waveguide formed by three half-strips in the shape of a letter T and describing a boundary-layer phenomenon. Open questions are stated for which the method developed gives no answer.",
keywords = "Kirchhoff plate, asymptotic behaviour, boundary layer, dimension reduction, eigenvalues and eigenfunctions",
author = "F.L Bakharev and S.A. Nazarov",
year = "2019",
doi = "10.1070/SM9008",
language = "English",
volume = "210",
pages = "473--494",
journal = "Sbornik Mathematics",
issn = "1064-5616",
publisher = "Turpion Ltd.",
number = "4",

}

RIS

TY - JOUR

T1 - Eigenvalue asymptotics of long Kirchhoff plates with clamped edges

AU - Bakharev, F.L

AU - Nazarov, S.A.

PY - 2019

Y1 - 2019

N2 - Asymptotic expansions are constructed for the eigenvalues and eigenfunctions of the Dirichlet problem for the biharmonic operator in thin domains (Kirchhoff plates with clamped edges). For a rectangular plate the leading terms are asymptotically determined from the Dirichlet problem for a second-order ordinary differential equation, while for a T-junction of plates they are determined from another limiting problem in an infinite waveguide formed by three half-strips in the shape of a letter T and describing a boundary-layer phenomenon. Open questions are stated for which the method developed gives no answer.

AB - Asymptotic expansions are constructed for the eigenvalues and eigenfunctions of the Dirichlet problem for the biharmonic operator in thin domains (Kirchhoff plates with clamped edges). For a rectangular plate the leading terms are asymptotically determined from the Dirichlet problem for a second-order ordinary differential equation, while for a T-junction of plates they are determined from another limiting problem in an infinite waveguide formed by three half-strips in the shape of a letter T and describing a boundary-layer phenomenon. Open questions are stated for which the method developed gives no answer.

KW - Kirchhoff plate

KW - asymptotic behaviour

KW - boundary layer

KW - dimension reduction

KW - eigenvalues and eigenfunctions

UR - http://www.scopus.com/inward/record.url?scp=85071194595&partnerID=8YFLogxK

UR - https://elibrary.ru/item.asp?id=41648060

U2 - 10.1070/SM9008

DO - 10.1070/SM9008

M3 - Article

VL - 210

SP - 473

EP - 494

JO - Sbornik Mathematics

JF - Sbornik Mathematics

SN - 1064-5616

IS - 4

ER -

ID: 46296094