Inhomogeneous Helmholtz equations in wave guides โ existence and uniqueness results with energy methods
Inhomogeneous Helmholtz equations in wave guides โ existence and uniqueness results with energy methods
The Helmholtz equation $-\nabla\cdot (a\nabla u) - \omega^2 u = f$ is considered in an unbounded wave guide $\Omega := \mathbb{R} \times S \subset \mathbb{R}^d$ , $S\subset \mathbb{R}^{d-1}$ a bounded domain. The coefficient a is strictly elliptic and either periodic in the unbounded direction $x_1 \in \mathbb{R}$ or periodic outside โฆ