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