A model of a boundary composed of the Helmholtz resonators. Issue 8 (3rd August 2021)

• Record Type: Journal Article
• Authors: Popov, I. Y.; Blinova, I. V.; Popov, A. I.
• Is Part Of: Complex variables and elliptic equations. Volume 66:Issue 8(2021)
• Page Start: 1256
• Page End: 1263
• Publication Date: 2021-08-03
• Subjects: Spectrum -- self-adjoint extension -- Helmholtz resonator; 47B25 -- 35P15; Functions of complex variables -- Periodicals; Differential equations, Elliptic -- Periodicals; 515.905
• DOI: 10.1080/17476933.2020.1751138
• Languages: English
• ISSNs: 1747-6933

Abstract

ABSTRACT: A model of resonators for which boundary is composed of the Helmholtz resonators is constructed. It is based on the theory of self-adjoint extensions of symmetric operators. We consider a limiting procedure when the number of resonators tends to infinity and look after the spectrum of the Neumann Laplacian. It is shown that there is a sequence of the model systems and, correspondingly, a sequence of eigenfunctions of the model operators which converge to an eigenfunction of the Laplacian with a specific boundary condition.