@article{10902/31519,
year = {2023},
month = {8},
url = {https://hdl.handle.net/10902/31519},
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.},
organization = {The study by the first author was supported by a grant from the Russian Science Foundation
(project no. 19-11-00033); the second and fourth authors were supported by the grant Gob. Cantabria-
UC, Ref. 20.VP66.64662; and the third author was supported by the European Social Fund (project No
09.3.3-LMT-K-712-17-003) under a grant agreement with the Research Council of Lithuania (LMTLT).},
publisher = {MDPI},
publisher = {Mathematics, 2023, 11(16), 3592},
title = {Asymptotic domain decomposition method for approximation the Spectrum of the diffusion operator in a domain containing thin tubes},
author = {Amosov, Andrey and Gómez Gandarillas, Delfina and Panasenko, Grigory and Pérez Martínez, María Eugenia},
}