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

Leszek Demkowicz; Jay Gopalakrishnan; Norbert Heuer

Applications of Mathematics (2024)

  • Volume: 69, Issue: 5, page 633-651
  • ISSN: 0862-7940

Abstract

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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).

How to cite

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Demkowicz, Leszek, Gopalakrishnan, Jay, and Heuer, Norbert. "Stability analysis for acoustic waveguides. Part 3: impedance boundary conditions." Applications of Mathematics 69.5 (2024): 633-651. <http://eudml.org/doc/299318>.

@article{Demkowicz2024,
abstract = {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).},
author = {Demkowicz, Leszek, Gopalakrishnan, Jay, Heuer, Norbert},
journal = {Applications of Mathematics},
keywords = {acoustic waveguides; well-posedness analysis},
language = {eng},
number = {5},
pages = {633-651},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Stability analysis for acoustic waveguides. Part 3: impedance boundary conditions},
url = {http://eudml.org/doc/299318},
volume = {69},
year = {2024},
}

TY - JOUR
AU - Demkowicz, Leszek
AU - Gopalakrishnan, Jay
AU - Heuer, Norbert
TI - Stability analysis for acoustic waveguides. Part 3: impedance boundary conditions
JO - Applications of Mathematics
PY - 2024
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 69
IS - 5
SP - 633
EP - 651
AB - 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).
LA - eng
KW - acoustic waveguides; well-posedness analysis
UR - http://eudml.org/doc/299318
ER -

References

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  9. Melenk, J. M., Demkowicz, L., Henneking, S., 10.48550/arXiv.2307.04521, Available at https://arxiv.org/abs/2307.04521 (2023), 45 pages. (2023) MR4739882DOI10.48550/arXiv.2307.04521
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