Existence of eigenvalues of a linear operator pencil in a curved waveguide -- localized shelf waves on a curved coast

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/72670The study of the possibility of existence of the non-propagating, trapped continental shelf waves (CSWs)along curved coasts reduces mathematically to a spectral problem for a self-adjoint operator pencil in a curved strip. Using the methods developed in the setting of the waveguide trapped mode problem, we show that such CSWs exist for a wide class of coast curvature and depth profiles.21 pages, 1 figureSpectral Theory35P05;35P15;86A05;76U05Existence of eigenvalues of a linear operator pencil in a curved waveguide -- localized shelf waves on a curved coasttext