Partial Decomposition of a Domain Containing Thin Tubes for Solving the Diffusion Equation

摘要

In a domain containing thin cylindrical tubes, we consider the diffusion equation with the Neumann boundary condition on the lateral surface of the tubes. The problem is reduced to a problem of hybrid dimension so that the reduced problem has the original dimension outside the tubes, but is reduced to the one-dimensional diffusion equation inside the tubes. The docking of models of different dimensions is carried out according to the method of asymptotic partial decompositions of domains. We estimate the difference between the solutions to the initial problem and the problem of different dimension.