TY - JOUR

T1 - Infinite Kirchhoff Plate on a Compact Elastic Foundation May Have an Arbitrarily Small Eigenvalue

AU - Nazarov, S. A.

PY - 2019/9/1

Y1 - 2019/9/1

N2 - Abstract: An inhomogeneous Kirchhoff plate composed of a semi-infinite strip waveguide and a compact resonator that is in contact with a Winkler foundation of low variable compliance is considered. It is shown that, for any ε > 0, a compliance coefficient O(ε2) can be found such that the described plate possesses the eigenvalue ε4 embedded into the continuous spectrum. This result is quite surprising, because, in an acoustic waveguide (the spectral Neumann problem for the Laplace operator) a small eigenvalue does not exist for any slight perturbation. The cause of this disagreement is explained.

AB - Abstract: An inhomogeneous Kirchhoff plate composed of a semi-infinite strip waveguide and a compact resonator that is in contact with a Winkler foundation of low variable compliance is considered. It is shown that, for any ε > 0, a compliance coefficient O(ε2) can be found such that the described plate possesses the eigenvalue ε4 embedded into the continuous spectrum. This result is quite surprising, because, in an acoustic waveguide (the spectral Neumann problem for the Laplace operator) a small eigenvalue does not exist for any slight perturbation. The cause of this disagreement is explained.

UR - http://www.scopus.com/inward/record.url?scp=85075220470&partnerID=8YFLogxK

U2 - 10.1134/S1064562419050144

DO - 10.1134/S1064562419050144

M3 - Article

AN - SCOPUS:85075220470

VL - 100

SP - 491

EP - 495

JO - Doklady Mathematics

JF - Doklady Mathematics

SN - 1064-5624

IS - 2

ER -