Asymptotics for the Spectrum of a Floquet-Parametric Family of Homogenization Problems Associated with a Dirichlet Waveguide

D. Gómez (), S. A. Nazarov (), R. Orive-Illera () and M. -E. Pérez-Martínez ()
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D. Gómez: Universidad de Cantabria
S. A. Nazarov: St. Petersburg State University
R. Orive-Illera: Universidad Autónoma de Madrid
M. -E. Pérez-Martínez: Universidad de Cantabria

Chapter Chapter 7 in Integral Methods in Science and Engineering, 2022, pp 95-111 from Springer

Abstract: Abstract In this chapter, we address the asymptotic behavior of the eigenvalues and eigenfunctions of a parametric family of problems for the Laplace operator posed on a rectangular perforated domain of the plane. The perforations are periodically placed along the ordinate axis. The two parameters of the problem are the period, which converges toward zero, and the so-called Floquet parameter. The boundary conditions are quasi-periodicity conditions on the lateral sides of the rectangle and Dirichlet over the rest. In particular, we provide bounds for convergence rates of the eigenvalues which are uniform in both parameters.

Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-07171-3_7

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DOI: 10.1007/978-3-031-07171-3_7

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