Periodic waveguides revisited: Radiation conditions, limiting absorption principles, and the space of bounded solutions
We study the Helmholtz equation with periodic coefficients in a closed waveguide. A functional analytic approach is used to formulate and solve the radiation problem in a self‐contained exposition. In this context, we simplify the non‐degeneracy assumption on the frequency. Limiting absorption princ...
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Veröffentlicht in: | Mathematical methods in the applied sciences 2025-01, Vol.48 (2), p.2267-2293 |
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Hauptverfasser: | , |
Format: | Artikel |
Sprache: | eng |
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Zusammenfassung: | We study the Helmholtz equation with periodic coefficients in a closed waveguide. A functional analytic approach is used to formulate and 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. |
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ISSN: | 0170-4214 1099-1476 |
DOI: | 10.1002/mma.10435 |