Functional Analysis and Applications Seminar 

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.