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Abstract: The spectral problem for the diffusion operator is considered in a domain containing thin tubes. A new version of the method of partial asymptotic decomposition of the domain is introduced to reduce the dimension inside the tubes. It truncates the tubes at some small distance from the ends of the tubes and replaces the tubes with segments. At the interface of the three-dimensional and one-dimensional subdomains, special junction conditions are set: the pointwise continuity of the flux and the continuity of the average over a cross-section of the eigenfunctions. The existence of the discrete spectrum is proved for this partially reduced problem of the hybrid dimension. The conditions of the closeness of two spectra, i.e., of the diffusion operator in the full-dimensional domain and the partially reduced one, are obtained.
Fuente: Mathematics, 2023, 11(16), 3592
Publisher: MDPI
Publication date: 01/08/2023
No. of pages: 25
Publication type: Article
DOI: 10.3390/math11163592
ISSN: 2227-7390
Publication Url: https://doi.org/10.3390/math11163592
Consult in UCrea Read publication
AMOSOV, ANDREY
DELFINA GOMEZ GANDARILLAS
PANASENKO, GRIGORY
MARIA EUGENIA PEREZ MARTINEZ
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