Rottbrand, Klaus (1996)
A Canonical Diffraction Problem With Two Media.
In: Mathematical Methods in the Applied Sciences, 19 (15)
doi: 10.1002/(SICI)1099-1476(199610)19:15<1217::AID-MMA826>3.0.CO;2-S
Article
Abstract
A Wiener–Hopf equation in L2 being equivalent [5] to a boundary value problem (of the first kind) for a wave-scattering Sommerfeld half-plane Σ=ℝ+×{0} which faces two different media Ω-: x2<0, Ω+: x2>0, as a special configuration in [3], is solved by canonical Weiner–Hopf factorization of its L2-regular scalar symbol γo=γo- γo+. The factors are calculated by solving a Riemann–Hilbert boundary value problem on the semi-infinite branch cuts of tj(ξ):=(ξ2−k2j)1/2, kj∈ℂ++ for j=1,2: taken parallel to the imaginary axis. The procedure following this idea is known as the Wiener–Hopf–Hilbert(–Hurd) method [2] and requires the evaluation of elliptic-type integrals. Formula (3.7) seems not to be contained in tables of integrals.
| Item Type: | Article |
|---|---|
| Erschienen: | 1996 |
| Creators: | Rottbrand, Klaus |
| Type of entry: | Bibliographie |
| Title: | A Canonical Diffraction Problem With Two Media |
| Language: | English |
| Date: | 1 October 1996 |
| Publisher: | Wiley & Sons Ltd. |
| Journal or Publication Title: | Mathematical Methods in the Applied Sciences |
| Volume of the journal: | 19 |
| Issue Number: | 15 |
| DOI: | 10.1002/(SICI)1099-1476(199610)19:15<1217::AID-MMA826>3.0.CO;2-S |
| Abstract: | A Wiener–Hopf equation in L2 being equivalent [5] to a boundary value problem (of the first kind) for a wave-scattering Sommerfeld half-plane Σ=ℝ+×{0} which faces two different media Ω-: x2<0, Ω+: x2>0, as a special configuration in [3], is solved by canonical Weiner–Hopf factorization of its L2-regular scalar symbol γo=γo- γo+. The factors are calculated by solving a Riemann–Hilbert boundary value problem on the semi-infinite branch cuts of tj(ξ):=(ξ2−k2j)1/2, kj∈ℂ++ for j=1,2: taken parallel to the imaginary axis. The procedure following this idea is known as the Wiener–Hopf–Hilbert(–Hurd) method [2] and requires the evaluation of elliptic-type integrals. Formula (3.7) seems not to be contained in tables of integrals. |
| Divisions: | 04 Department of Mathematics |
| Date Deposited: | 19 Nov 2008 16:00 |
| Last Modified: | 27 Jul 2023 10:26 |
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