Functional Analysis and Applications Seminar 

09/03/2007, 15:00 — 16:00 — Room P3.10, Mathematics Building
Anatoli Merzon, Universidad Michoacana de San Nicolás de Hidalgo, Morelia, Mexico

About the scattering of plane waves by wedges

We consider a nonstationary scattering of plane waves by a wedge. It is assumed that the incident wave does not depend on the coordinate parallel to the the edge of the wedge, so the problem is planar. Also we assume that, beginning with a certain time instant depending on a spatial position of the point, the incident wave is periodic in time with the frequency \(\omega\) in each point of the space. Let the profile of the wave be such that the incident wave has the front ahead of which it is zero. Therefore the incident wave establishes a harmonic vibration at any point of the complement of the wedge with the frequency \(\omega\). The main goal is to prove that the amplitude of the solution to the corresponding mixed problem for the D'Alembert equation with initial data determined by the incident wave, tends to the solutions of the classical stationary diffraction problem. Thus, these classical solutions can be represented as the limiting amplitudes of the solutions to the non-stationary problem, i.e. the Limiting Amplitude Principle holds. It is proved for the Dirichlet and Neumann boundary conditions and for Dirichlet-Neumann boundary conditions only for the right angle.