TY - GEN

T1 - Resonances for the beam equation

AU - Korotyaev, E.

AU - Badanin, A.

PY - 2016

Y1 - 2016

N2 - We consider resonances for the beam equation on the half-line. We assume that the coefficients of this equation are constants outside a finite interval. We show that this equation has no eigenvalues and resonances iff the coefficients are constants on the whole half-line. Moreover, we get estimates of the counting function of resonances and describe the forbidden domain. In order to obtain these results, we consider resonances for a standard fourth order differential operator on the half-line with compactly supported coefficients.

AB - We consider resonances for the beam equation on the half-line. We assume that the coefficients of this equation are constants outside a finite interval. We show that this equation has no eigenvalues and resonances iff the coefficients are constants on the whole half-line. Moreover, we get estimates of the counting function of resonances and describe the forbidden domain. In order to obtain these results, we consider resonances for a standard fourth order differential operator on the half-line with compactly supported coefficients.

KW - eigenvalues and eigenfunctions

KW - Scattering

KW - Diffraction

KW - boundary conditions

KW - Standards

UR - https://ieeexplore.ieee.org/document/7756845

UR - http://www.pdmi.ras.ru/~dd/download/PROC16.pdf

M3 - Conference contribution

SN - 9781509058013

SP - 218

EP - 222

BT - Days on Diffraction

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2016 International Conference Days on Diffraction, DD 2016

Y2 - 27 June 2016 through 1 July 2016

ER -