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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
Publisher: Springer Nature
Year of publication: 2021
No. of pages: 27
Publication type: Article
DOI: 10.1007/s10958-021-05506-z
ISSN: 1072-3374,1573-8795
Spanish project: MICINN PGC2018-098178-B-I00
Publication Url: https://doi.org/10.1007/s10958-021-05506-z
Consult in UCrea Read publication
DELFINA GOMEZ GANDARILLAS
NAZAROV, S. A.
ORIVE-ILLERA, R.
MARIA EUGENIA PEREZ MARTINEZ
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