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.

中文翻译：

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由亥姆霍兹谐振器组成的边界模型

摘要

构建了边界由亥姆霍兹谐振器组成的谐振器模型。它基于对称算子的自伴随扩展理论。当谐振器的数量趋于无穷大时，我们考虑了一个限制程序，并考虑了诺依曼拉普拉斯算子的频谱。结果表明，存在一系列模型系统，相应地，存在收敛到具有特定边界条件的拉普拉斯算子的本征函数的模型算子的本征函数序列。