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Periodic wave-guides revisited: Radiation conditions, limiting absorption principles, and the space of bounded solutions
  • Andreas Kirsch,
  • Ben Schweizer
Andreas Kirsch
Karlsruher Institut fur Technologie Fakultat fur Mathematik

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Ben Schweizer
Technische Universitat Dortmund Fakultat fur Mathematik
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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.
17 Jul 2023Submitted to Mathematical Methods in the Applied Sciences
17 Jul 2023Assigned to Editor
17 Jul 2023Submission Checks Completed
26 Jul 2023Review(s) Completed, Editorial Evaluation Pending
28 Jan 2024Reviewer(s) Assigned