Geodesic
Stability analysis for acoustic waveguides. Part 3: impedance boundary conditions
Applications of Mathematics, Tome 69 (2024) no. 5, pp. 633-651 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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 applicable, as simply as possible. This work is a continuation of prior waveguide studies (where self-adjoint operators arose) by J. M. Melenk et al. (2023), and L. Demkowicz et al. (2024).
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 applicable, as simply as possible. This work is a continuation of prior waveguide studies (where self-adjoint operators arose) by J. M. Melenk et al. (2023), and L. Demkowicz et al. (2024).
DOI : 10.21136/AM.2024.0080-24
Classification : 35Q61, 78A50
Keywords: acoustic waveguides; well-posedness analysis 
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     title = {Stability analysis for acoustic waveguides. {Part} 3: impedance boundary conditions},
     journal = {Applications of Mathematics},
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Demkowicz, Leszek; Gopalakrishnan, Jay; Heuer, Norbert. Stability analysis for acoustic waveguides. Part 3: impedance boundary conditions. Applications of Mathematics, Tome 69 (2024) no. 5, pp. 633-651. doi: 10.21136/AM.2024.0080-24

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