Stability analysis for acoustic waveguides. Part 3: Impedance boundary conditions
Leszek Demkowicz, Jay Gopalakrishnan, and Norbert Heuer
A model two-dimensional acoustic waveguide with lateral impedance boundary conditions
(and outgoing boundary conditions at the waveguide outlet) is considered.
The governing operator is proved to be bounded below with a constant inversely
proportional to the length of the waveguide.
The presence of impedance boundary conditions leads to a non self-adjoint operator
which considerably complicates the analysis.
The goal of this paper is to elucidate these complications,
and tools that are applicable, as simply as possible.
This work is a continuation of prior waveguide studies
(where self-adjoint operators arose) by Melenk et al.,
“Stability Analysis for Electromagnetic Waveguides.
Part 1: Acoustic and Homogeneous Electromagnetic Waveguides” (2023)
and Demkowicz et al.
“Stability Analysis for Acoustic and Electromagnetic Waveguides.
Part 2: Non-homogeneous Waveguides” (2023).