07/11/2003, 15:00 — 16:00 — Room P3.10, Mathematics Building
Frank-Olme Speck, Instituto Superior Técnico, U.T. Lisboa
Diffraction by Rectangular Wedges with Different Face Impedances
Some basic hitherto open boundary value problems are treated by
a new potential approach, using so-called reproducing half-line
potentials. It involves symmetry properties, operator relations,
factorization methods and normalization techniques for convolution
type operators with symmetry that were recently developed by
various members of the CEMAT operator theory group. Interior wedge
problems of normal type for the Helmholtz equation could be
completely analyzed and explictly solved by analytical formulas
which also allow fine results about the solutions' regularity
properties. It turns out that these results are also good for
reducing exterior wedge problems in a most efficient way to scalar
boundary pseudodifferential equations. However, their nature is
much more complicated and cumbersome compared with the class of
interior wedge diffration problems. Only very particular boundary
conditions allow a detailed comparable analysis. The lecture is
based upon common work with L. P. Castro and F. S. Teixeira.