Method of asymptotic partial decomposition of domain for multistructures

Abstract

Method of asymptotic partial decomposition of a domain (MAPDD) proposed and justified earlier for thin domains (rod structures, tube structures) is generalized and justified for the multistructures, i.e. domains consisting of a set of thin cylinders connecting some massive 3D domains. In the present paper, the Dirichlet boundary value problem for the steady-state Stokes equations is considered. This problem is reduced to the Stokes equations in the massive domains coupled with the Poiseuille-type flows within the thin cylinders at some distance from the bases (the MAPDD approximation problem). The high-order estimates for the difference of the exact solution to the initial problem and the solution to the MAPDD approximation problem is proved.