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Asymptotic domain decomposition method for approximation the Spectrum of the diffusion operator in a domain containing thin tubes

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.

Otras publicaciones de la misma revista o congreso con autores/as de la Universidad de Cantabria

 Fuente: Mathematics, 2023, 11(16), 3592

Editorial: MDPI

 Fecha de publicación: 01/08/2023

Nº de páginas: 25

Tipo de publicación: Artículo de Revista

 DOI: 10.3390/math11163592

ISSN: 2227-7390

Url de la publicación: https://doi.org/10.3390/math11163592

Autoría

AMOSOV, ANDREY

PANASENKO, GRIGORY