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 -