TY - JOUR

T1 - Constructing a Trapped Mode at Low Frequencies in an Elastic Waveguide

AU - Nazarov, S. A.

N1 - Nazarov, S.A. Constructing a Trapped Mode at Low Frequencies in an Elastic Waveguide. Funct Anal Its Appl 54, 31–44 (2020). https://doi.org/10.1134/S0016266320010049

PY - 2020/1

Y1 - 2020/1

N2 - For any small ε > 0, a two-dimensional elastic waveguide is constructed such that λe = ε4 is the only eigenvalue in the vicinity of the lower bound λ† = 0 of the continuous spectrum. This result is rather unexpected, because an acoustic waveguide (the Neumann problem for the Laplace operator) with an arbitrary small localized perturbation cannot support a trapped mode at a low frequency.

AB - For any small ε > 0, a two-dimensional elastic waveguide is constructed such that λe = ε4 is the only eigenvalue in the vicinity of the lower bound λ† = 0 of the continuous spectrum. This result is rather unexpected, because an acoustic waveguide (the Neumann problem for the Laplace operator) with an arbitrary small localized perturbation cannot support a trapped mode at a low frequency.

KW - continuous spectrum

KW - orthotropic elastic waveguide

KW - trapped waves at low frequencies

UR - http://www.scopus.com/inward/record.url?scp=85090049523&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/e75e5aee-fde5-39f4-a1a7-2ab64e709f58/

U2 - 10.1134/S0016266320010049

DO - 10.1134/S0016266320010049

M3 - Article

AN - SCOPUS:85090049523

VL - 54

SP - 31

EP - 44

JO - Functional Analysis and its Applications

JF - Functional Analysis and its Applications

SN - 0016-2663

IS - 1

ER -