Method of asymptotic partial decomposition of domain for multistructures. Issue 16 (10th December 2017)

• Record Type: Journal Article
• Authors: Panasenko, Grigory
• Is Part Of: Applicable analysis. Volume 96:Issue 16(2017)
• Page Start: 2771
• Page End: 2779
• Publication Date: 2017-12-10
• Subjects: Stokes equations -- multistructures -- asymptotic partial decomposition -- estimates -- hybrid dimension models; 35Q35 -- 76D07 -- 65N55; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2016.1240366
• Languages: English
• ISSNs: 0003-6811

Abstract

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.