Speaker
Description
Maxwell’s equations are considered in a half-waveguide Ω₊ := ℝ₊ × S where S ⊂ ℝ² is a bounded Lipschitz domain and ℝ₊ = (0,∞). The electric permittivity ε and the magnetic permeability μ are assumed to be strictly positive and periodic outside a compact set. Our Maxwell system is accompanied by a radiation condition that was introduced and investigated in [1]. 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 on Ω₊, then there is a unique solution for every right-hand side. Our approach is based on an energy method which was developed in [2] to study Helmholtz equations.
References:
[1] A. Kirsch and B. Schweizer, Time harmonic Maxwell’s equations in periodic waveguides, (submitted), TU Dortmund 2024-01
[2] B. Schweizer, Inhomogeneous Helmholtz equations in wave guides – existence and uniqueness results with energy methods in European J. Appl. Math. Vol. 34(2), pp. 211-237
