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Remark on Justification of Asymptotics of Spectra of Cylindrical Waveguides with Periodic Singular Perturbations of Boundary and Coefficients

Abstract: To perform an asymptotic analysis of spectra of singularly perturbed periodic waveguides, it is required to estimate remainders of asymptotic expansions of eigenvalues of a model problem on the periodicity cell uniformly with respect to the Floquet parameter. We propose two approaches to this problem. The first is based on the max?min principle and is sufficiently easily realized, but has a restricted application area. The second is more universal, but technically complex since it is required to prove the unique solvability of the problem on the cell for some value of the spectral parameter and the Floquet parameter in a nonempty closed segment, which is verified by constructing an almost inverse operator of the operator of an inhomogeneous model problem in variational setting. We consider boundary value problems on the simplest periodicity cell: a rectangle with a row of fine holes.

 Fuente: Journal of Mathematical Sciences 2021. 257, 597-623

 Editorial: Springer Nature

 Año de publicación: 2021

 Nº de páginas: 27

 Tipo de publicación: Artículo de Revista

 DOI: 10.1007/s10958-021-05506-z

 ISSN: 1072-3374,1573-8795

 Proyecto español: MICINN PGC2018-098178-B-I00

 Url de la publicación: https://doi.org/10.1007/s10958-021-05506-z