Authors: Kirsch, Andreas
Schweizer, Ben
Title: Periodic wave-guides revisited: Radiation conditions, limiting absorption principles, and the space of boundes solutions
Language (ISO): en
Abstract: We study the Helmholtz equation with periodic coefficients in a closed wave-guide. A functional analytic approach is used to formulate and to solve the radiation problem in a self-contained exposition. In this context, we simplify the non-degeneracy assumption on the frequency. Limiting absorption principles (LAPs) are studied and the radiation condition corresponding to the chosen LAP is derived; we include an example to show different LAPs lead, in general, to different solutions of the radiation problem. Finally, we characterize the set of all bounded solutions to the homogeneous problem.
Subject Headings: periodic
Issue Date: 2023-07
Appears in Collections:Preprints der Fakultät für Mathematik

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