On regular and singular perturbations of acoustic and quantum waveguides

TL;DR

This paper investigates how small and singular changes to boundary conditions affect eigenvalues in acoustic and quantum waveguides, providing insights into their existence and asymptotic behavior.

Contribution

It introduces new results on eigenvalue existence and asymptotics for perturbed Helmholtz problems in waveguides with boundary modifications.

Findings

Eigenvalues' existence under perturbations

Asymptotic formulas for eigenvalues

Impact of boundary conditions on spectral properties

Abstract

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.