The asymptotic analysis of gaps in the spectrum of a waveguide perturbed with a periodic family of small voids
This paper is devoted to the spectral analysis of the Laplace operator in a periodic waveguide. the waveguide consists in a straight tubular domain of \(\mathbb{R}^d\) containing periodically distributed inclusions. The Laplace operator is defined by means of Dirichlet boundary conditions at the boundary of the guide. It is proved that the essential spectrum of Laplace operator contains open spectral gaps when the diameter of the inclusion is small enough. Furthermore the author gives a precise discussion on the link between the behavior of the spectral band near the band edges and the opening of the corresponding spectral gap. The method employed is based on the asymptotic perturbation theory of linear operators These results are illustrated by some examples.
scientific article; zbMATH DE number 6156253
scientific article