Asymptotic structure of the spectrum of a thin Dirichlet single-tee beam

Abstract

The asymptotic behaviour of eigenvalues and eigenfunctions of the Dirichlet problem for the Laplace operator in a tee-type junction of two thin parallelepiped plates is examined. The effect of a strong localization is observed for eigenfunctions near junction zones. Comparing with asymptotic results for analogous Neumann problem, the crucial difference between asymptotic behaviour of their spectra is observed.