@article{10902/18096,
year = {2019},
month = {6},
url = {http://hdl.handle.net/10902/18096},
abstract = {We consider a spectral problem for the Laplacian operator in a planar T-like shaped thin structure , where E; denotes the transversal thickness of both branches. We assume the homogeneous Dirichlet boundary condition on the ends of the branches and the homogeneous Neumann boundary condition on the remaining part of the boundary of . We study the asymptotic behavior, as ; tends to zero, of the high frequencies of such a problem. Unlike the asymptotic behavior of the low frequencies where the limit problem involves only longitudinal vibrations along each branch of the T-like shaped thin structure (i.e. 1D limit spectral problems), we obtain a two dimensional limit spectral problem which allows us to capture other kinds of vibrations. We also give a characterization of the asymptotic form of the eigenfunctions originating these vibrations.},
organization = {This work has partially been supported by MINECO grant MTM2013-44883-P and MICINN grant PGC2018-098178-B-I00. The first author is also member of the Gruppo Nazionale per l’Analisi Matematica, la Probabilita e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM).},
publisher = {Elsevier},
publisher = {Journal de Mathématiques Pures et Appliquées 
Volume 134, February 2020, Pages 299-327},
title = {Asymptotic analysis of the high frequencies for the Laplace operator in a thin T-like shaped structure},
author = {Gaudiello, Antonio and Gómez Gandarillas, Delfina and Pérez Martínez, María Eugenia},
}