On the asymptotics of an eigenvalue of a waveguide with thin shielding obstacle and Wood's anomalies

Conditions are found out for the existence and absence of an eigenvalue in the interval $(0,\pi^2)$ of the continuous spectrum of the Neumann problem for the Laplace operator in the unit strip with a thin (of width $O(\varepsilon)$) symmetric screen which, as $\varepsilon\to+0$, shrinks into a line segment perpendicular to sides of the strip. An asymptotics of this eigenvalue is constructed as well as the asymptotics of the reflection coefficient which describes Wood's anomalies, namely quick changes of the diffraction characteristics near a frequency threshold in the continuous spectrum. Bibl. 32 titles.