18/09/2009, 14:00 — 16:00 — Room P3.10, Mathematics Building
Norbert Gorenflo, Beuth Hochschule für Technik Berlin
On searching for explicit solution formulas for the diffraction by
a strip and the diffraction by a circular disk
We consider mixed boundary value problems for the scalar
Helmholtz equation describing the diffraction by a (acoustically)
soft strip and the diffraction by a (acoustically) soft circular
disk, respectively. The talk focuses on representations of the
solutions of the underlying boundary integral equations. Firstly,
some of the speaker's earlier results are presented which are based
on the reformulation as a Wiener-Hopf problem which differs from
the hitherto known Wiener-Hopf formulations in that it is posed in
the original space and not in the frequency space. Then, newer
results are given, which admit series expansions of the solutions
of the boundary integral equations in terms of functions and
expansion coefficients that both are given in a closed form.