Abstract: We consider the spectral problem for the diffusion operator 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, getting a model of hybrid dimensions. The method truncates the tubes at some small distance from the ends of the tubes and replaces the longer part of 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. We obtain conditions on the ratio of the characteristic sizes in the transverse and longitudinal directions that ensure the closeness of two spectra, i.e. of the diffusion operator in the full-dimensional domain and the partially reduced one, keeping the conservation of the multiplicity, all up to a prescribed accuracy.

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