Year: 2025
Type: article
Abstract: Maxwell’s equations are considered in a half-waveguide Ω+ := R+ × S ⊂ R3 where S ⊂ R2 is a bounded Lipschitz domain in R2. The electric permittivity ε and the magnetic permeability μ are assumed to be strictly positive and periodic outside a compact set. A standard radiation condition accompanies the equations. We give a result on existence and uniqueness in the form of a Fredholm alternative: When there is no bound state, i.e., no non-trivial solution of the homogeneous problem, then there is a unique solution for every right-hand side.
Authors: Lamacz-Keymling, Agnes, Schubert, Tim, Schweizer, Ben
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6887936845
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