Article
| Title: | Stability analysis for acoustic waveguides. Part 3: impedance boundary conditions (English) |
| Author: | Demkowicz, Leszek |
| Author: | Gopalakrishnan, Jay |
| Author: | Heuer, Norbert |
| Language: | English |
| Journal: | Applications of Mathematics |
| ISSN: | 0862-7940 (print) |
| ISSN: | 1572-9109 (online) |
| Volume: | 69 |
| Issue: | 5 |
| Year: | 2024 |
| Pages: | 633-651 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | 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). (English) |
| Keyword: | acoustic waveguides |
| Keyword: | well-posedness analysis |
| MSC: | 35Q61 |
| MSC: | 78A50 |
| DOI: | 10.21136/AM.2024.0080-24 |
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| Date available: | 2024-11-05T12:04:10Z |
| Last updated: | 2024-11-05 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/152635 |
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| Reference: | [9] Melenk, J. M., Demkowicz, L., Henneking, S.: Stability analysis for electromagnetic waveguides. I. Acoustic and Homogeneous Electromagnetic Waveguides.Available at https://arxiv.org/abs/2307.04521 (2023), 45 pages. MR 4739882, 10.48550/arXiv.2307.04521 |
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