Scattering by a periodic tube in R-3: part ii. A radiation condition

Kirsch, Andreas

Abstract:
This second part of a pair of papers complements the first part (see Kirsch 2018 (35 104004)) but can be read independently. Scattering of time-harmonic waves from periodic structures at some fixed real-valued wave number becomes analytically difficult whenever there arise surface waves: These nonzero solutions to the homogeneous scattering problem physically correspond to modes propagating along the periodic structure and clearly imply nonuniqueness of any solution to the scattering problem. As in the first part we consider a medium described by a refractive index which is periodic along the axis of an infinite cylinder in R3 and constant outside of the cylinder. We formulate a proper radiation condition which allows the existence of traveling modes (and is motivated by the limiting absorption principle proven in the first part) and prove uniqueness and existence.

 Zugehörige Institution(en) am KIT Institut für Angewandte und Numerische Mathematik (IANM) Publikationstyp Zeitschriftenaufsatz Publikationsmonat/-jahr 10.2019 Sprache Englisch Identifikator ISSN: 0266-5611, 1361-6420 KITopen-ID: 1000098679 Erschienen in Inverse problems Band 35 Heft 10 Seiten Art. Nr.: 104005 Vorab online veröffentlicht am 09.09.2019 Schlagwörter Helmholtz equation, periodic wave guide, radiation condition Nachgewiesen in ScopusWeb of Science
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