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.
Acknowledgments
This work was partially financially supported by the Government of the Russian Federation (grant 08-08) and Russian Science Foundation (grant 16-11-10330). IYP thanks Professor A. Khrabustovskyi for useful discussions.
Disclosure statement
No potential conflict of interest was reported by the author(s).