Applications of Mathematics, Vol. 69, No. 5, pp. 633-651, 2024
Stability analysis for acoustic waveguides. Part 3: impedance boundary conditions
Leszek Demkowicz, Jay Gopalakrishnan, Norbert Heuer
Received April 2, 2024. Published online October 8, 2024.
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).
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Affiliations: Leszek Demkowicz (corresponding author), Oden Institute, The University of Texas at Austin, 201 E. 24th Street, Austin, Texas 78712-1229, USA, e-mail: leszek@oden.utexas.edu; Jay Gopalakrishnan, Fariborz Maseeh Department of Mathematics + Statistics, Portland State University, 1825 SW Broadway, Portland, OR 97201, USA, e-mail: gjay@pdx.edu Norbert Heuer, Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Avenida Vicuña Mackenna 4860, Santiago, Chile, e-mail: nheuer@mat.uc.cl
