Periodic wave-guides revisited: Radiation conditions, limiting absorption principles, and the space of boundes solutions
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Date
2023-07
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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.
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periodic