On regular and singular perturbations of acoustic and quantum waveguides

We consider regular and singular perturbations of the Dirichlet and Neumann boundary value problems for the Helmholtz equation in $n$-dimensional cylinders. Existence of eigenvalues and their asymptotics are studied

On boundary-value problems for the laplacian in bounded and in unbounded domains with perforated boundaries

AbstractIn this paper we consider boundary-value problems in domains with perforated boundaries. We use the classification of homogenized (limit) problems depending on the ratio of small parameters, which characterize the diameter of the holes and the distance between them. We study the analogue of the Helmholtz resonator for domains with a perforated boundary