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Stability analysis for acoustic waveguides. Part 3: impedance boundary conditions

Leszek Demkowicz, Jay Gopalakrishnan, Norbert Heuer (2024)

Applications of Mathematics

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 stability 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...

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