@article{10902/31520,
year = {2023},
month = {10},
url = {https://hdl.handle.net/10902/31520},
abstract = {In this paper, we provide uniform bounds for convergence rates of the low frequencies of a parametric family of problems for the Laplace operator posed on a rectangular perforated domain of the plane of height H. The perforations are periodically placed along the ordinate axis at a distance  between them, where ε is a parameter that converges toward zero. Another parameter η, the Floquet-parameter, ranges in the interval. The boundary conditions are quasi-periodicity conditions on the lateral sides of the rectangle and Neumann over the rest. We obtain precise bounds for convergence rates which are uniform on both parameters ε and η and strongly depend on H. As a model problem associated with a waveguide, one of the main difficulties in our analysis comes near the nodes of the limit dispersion curves.},
organization = {The work has been partially supported by MICINN through PGC2018-098178-B-I00, PID2020-114703GB-I00 and Severo Ochoa Programme for Centres of Excellence in R&D (CEX2019-000904-S).},
publisher = {Wiley-VCH-Verl.},
publisher = {Mathematische Nachrichten, 2023, 296(10), 4888-4910},
title = {Asymptotic stability of the spectrum of a parametric family of homogenization problems associated with a perforated waveguide},
author = {Gómez Gandarillas, Delfina and Nazarov, Sergei A. and Orive Illera, Rafael and Pérez Martínez, María Eugenia},
}