Resumo: We treat a spectral problem for the Laplace operator defined in some multi-structures where the thickness of each component depends on a small parameter. We assume mixed boundary conditions. We address the asymptotic behavior of the eigenvalues and the corresponding eigenfunctions of such problems as the thickness vanish. In particular, we describe the behavior of the eigenfunctions associated with the so-called low and high frequencies.
Based on joint works with Antonio Gaudiello and Maria-Eugenia Pérez-Martínez.