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.
Key words: Operator extensions theory, Helmholtz resonator, solvable model.
Full Text
Article Information
| Title | Two-dimensional Helmholtz resonator with two close point-like windows: regularization for the Neumann case |
| Source | Methods Funct. Anal. Topology, Vol. 28 (2022), no. 2, 95-104 |
| DOI | 10.31392/MFAT-npu26_2.2022.01 |
| MathSciNet |
MR4548146 |
| Milestones | Received 27/01/2022 |
| Copyright | The Author(s) 2022 (CC BY-SA) |
Authors Information
A. G. Belolipetskaia
Department of Higher Mathematics, ITMO University, 197101 St. Petersburg, Russian Federation
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
Citation Example
A. G. Belolipetskaia, A. A. Boitsev, S. Fassari, I. Y. Popov, and F. Rinaldi, Two-dimensional Helmholtz resonator with two close point-like windows: regularization for the Neumann case, Methods Funct. Anal. Topology 28
(2022), no. 2, 95-104.
BibTex
@article {MFAT1772,
AUTHOR = {A. G. Belolipetskaia and A. A. Boitsev and S. Fassari and I. Y. Popov and F. Rinaldi},
TITLE = {Two-dimensional Helmholtz resonator with two close point-like windows: regularization for the Neumann case},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {28},
YEAR = {2022},
NUMBER = {2},
PAGES = {95-104},
ISSN = {1029-3531},
MRNUMBER = {MR4548146},
DOI = {10.31392/MFAT-npu26_2.2022.01},
URL = {http://mfat.imath.kiev.ua/article/?id=1772},
}
