Periodic waveguides revisited: Radiation conditions, limiting absorption principles, and the space of bounded solutions

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
Hauptverfasser: Kirsch, A., Schweizer, B.
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Sprache:eng
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Absorption
Constraining
Helmholtz equation
Helmholtz equations
limiting absorption principle
radiation condition
waveguide
Waveguides
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description 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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subjects Absorption
Constraining
Helmholtz equation
Helmholtz equations
limiting absorption principle
radiation condition
waveguide
Waveguides
title Periodic waveguides revisited: Radiation conditions, limiting absorption principles, and the space of bounded solutions
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