Two-dimensional Helmholtz resonator with two close point-like windows: regularization for the Neumann case

Authors

  • Ya. I. Belopolskaya Department of Higher Mathematics, ITMO University, 197101 St. Petersburg, Russian Federation https://orcid.org/0000-0002-8303-2571
  • A. A. Boitsev Department of Higher Mathematics, ITMO University, 197101 St. Petersburg, Russian Federation
  • S. Fassari Department of Higher Mathematics, ITMO University, 197101 St. Petersburg, Russian Federation, CERFIM, PO Box 1132, CH-6601 Locarno, Switzerland, Univ. degli Studi Guglielmo Marconi, Via Plinio 44, I-00193 Rome, Italy
  • I. Y. Popov Department of Higher Mathematics, ITMO University, 197101 St. Petersburg, Russian Federation
  • F. Rinaldi Univ. degli Studi Guglielmo Marconi, Via Plinio 44, I-00193 Rome, Italy, Istituto Nazionale di Fisica Nucleare, Sezione di Napoli, Naples, Italy

DOI:

https://doi.org/https://doi.org/10.31392/MFAT-npu26_2.2022.01

Keywords:

Operator extensions theory, Helmholtz resonator, solvable model

Abstract

Explicitly solvable model for two-dimensional Helmholtz resonator with two close point-like windows is constructed. The model is based on the theory of self-adjoint extensions of symmetric operators. Limiting procedure is studied for the case where the distance between the windows tends to zero. A regularization is suggested.

Побудовано явно розв'язувану модель для двовимірного резонатора Гельмгольца з двома близькими точковими вікнами. Модель базується на теорії самоспряжених розширень симетричних операторів. Вивчено процедуру граничного переходу для випадку, коли відстань між вікнами прямує до нуля, та запропоновано регуляризацію.

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Published

2022-06-25

Issue

Vol. 28 No. 2 (2022)

Section

Articles

How to Cite

Belopolskaya, Ya. I., et al. “Two-Dimensional Helmholtz Resonator With Two Close Point-Like Windows: Regularization for the Neumann Case”. Methods of Functional Analysis and Topology, vol. 28, no. 2, June 2022, pp. 95-104, https://doi.org/https://doi.org/10.31392/MFAT-npu26_2.2022.01.