###
**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 |

PPN: | |

Export: | |

Suche nach Titel in: | TUfind oder in Google |

Send an inquiry |

**Options (only for editors)**

Show editorial Details |