Geodesic
Eigenvalue asymptotics of long Kirchhoff plates with clamped edges
Sbornik. Mathematics, Tome 210 (2019) no. 4, pp. 473-494

Voir la notice de l'article provenant de la source Math-Net.Ru

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 $\mathsf T$-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 $\mathsf T$ and describing a boundary-layer phenomenon. Open questions are stated for which the method developed gives no answer. Bibliography: 33 titles.
Keywords: Kirchhoff plate, eigenvalues and eigenfunctions, asymptotic behaviour, dimension reduction, boundary layer. 
@article{SM_2019_210_4_a0,
     author = {F. L. Bakharev and S. A. Nazarov},
     title = {Eigenvalue asymptotics of long {Kirchhoff} plates with clamped edges},
     journal = {Sbornik. Mathematics},
     pages = {473--494},
     publisher = {mathdoc},
     volume = {210},
     number = {4},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2019_210_4_a0/}
}
TY  - JOUR
AU  - F. L. Bakharev
AU  - S. A. Nazarov
TI  - Eigenvalue asymptotics of long Kirchhoff plates with clamped edges
JO  - Sbornik. Mathematics
PY  - 2019
SP  - 473
EP  - 494
VL  - 210
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SM_2019_210_4_a0/
LA  - en
ID  - SM_2019_210_4_a0
ER  - 
%0 Journal Article
%A F. L. Bakharev
%A S. A. Nazarov
%T Eigenvalue asymptotics of long Kirchhoff plates with clamped edges
%J Sbornik. Mathematics
%D 2019
%P 473-494
%V 210
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SM_2019_210_4_a0/
%G en
%F SM_2019_210_4_a0
F. L. Bakharev; S. A. Nazarov. Eigenvalue asymptotics of long Kirchhoff plates with clamped edges. Sbornik. Mathematics, Tome 210 (2019) no. 4, pp. 473-494. http://geodesic.mathdoc.fr/item/SM_2019_210_4_a0/