Partial Decomposition of a Domain Containing Thin Tubes for Solving the Heat Equation
- Autores: Amosov A.1, Panasenko G.2
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Afiliações:
- National Research University “Moscow Power Engineering Institute,”
- Institute Camille Jordan UMR CNRS 5208 University of Lyon
- Edição: Volume 97, Nº 1 (2018)
- Páginas: 69-72
- Seção: Mathematics
- URL: https://journals.rcsi.science/1064-5624/article/view/225460
- DOI: https://doi.org/10.1134/S1064562418010222
- ID: 225460
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Resumo
An initial–boundary value problem for the heat equation in a three-dimensional domain containing thin cylindrical tubes is considered. The Neumann condition is set on the lateral boundaries of the tubes. The original three-dimensional problem is reduced to a hybrid-dimensional one in which the heat equation in the tubes is replaced by the one-dimensional heat equation in shorter cylinders (subtubes), and the three- and one-dimensional equations are matched on the bases of the subtubes. The difference between the solutions of the original and hybrid-dimensional problems is estimated using two geometric characteristics: the distance between the bases of the tubes and subtubes and the reciprocals of the minimal positive eigenvalues of the Neumann problem for the Laplace operator in the tube cross sections.
Sobre autores
A. Amosov
National Research University “Moscow Power Engineering Institute,”
Autor responsável pela correspondência
Email: amosovaa@mpei.ru
Rússia, Moscow, 111250
G. Panasenko
Institute Camille Jordan UMR CNRS 5208 University of Lyon
Email: amosovaa@mpei.ru
França, Saint-Etienne, 42023