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Partial dimension reduction for the heat equation in a domain containing thin tubes
Author(s) -
Amosov Andrey,
Panasenko Grigory
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5311
Subject(s) - dimension (graph theory) , domain (mathematical analysis) , reduction (mathematics) , neumann boundary condition , heat equation , mathematical analysis , mathematics , boundary (topology) , boundary value problem , partial differential equation , geometry , pure mathematics
The heat equation in considered in a domain containing thin cylindrical tubes with Neumann's boundary condition at the lateral boundary of these tubes. This problem is reduced to a hybrid dimension problem keeping the initial dimension out of thin tubes and reducing it to the one‐dimensional heat equation within the tubes at some distance from the bases of the cylinders. Junction of models of different dimensions is done according to the method of asymptotic partial decomposition of domain. The difference of solutions of the original and partially reduced problems is estimated. This result generalizes the method of partial dimension reduction for the case when the domain has only one restriction that it contains several thin cylinders possibly of different orders of diameters.