ON THE ASYMPTOTICS AND STABILITY OF THE POINT SPECTRUM OF A WAVEGUIDE WITH THIN SHIELDING OBSTACLE

摘要

Some explicit conditions are found for the existence and absence of an eigenvalue in the interval (O,π~2) of the continuous spectrum of the Neumann problem for the Laplace operator in the unit strip with a thin (of width O(ε)) symmetric screen, which, as e → +0, shrinks into a line segment perpendicular to the 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 pattern near a frequency threshold in the continuous spectrum. Bibliography: 32 titles.