17/04/2009, 11:00 — 12:00 — Sala P3.10, Pavilhão de Matemática
Sergey Nazarov, Laboratory for Mathematical Modelling of Wave Phenomena, Institute of Problems in Mechanical Engineering, Russian Academy of Sciences, St. Petersburg, Russia
The continuous spectrum of the water-wave problem in a pond with a shoal shore
The problem on water-waves is described, within the linearized theory, by a boundary-value problem for the Laplace equation with a spectral boundary condition of Steklov type. The spectrum of the problem is known to be be continuous in infinite channels and layers. In this talk, we will demonstrate that the spectrum can have a nonempty continuous component also in a pond with a gently sloped bottom topography due to the boundary singularity of cuspidal edge type.
