Please use this identifier to cite or link to this item:
Title: Boundary-domain integral equation systems for the stokes system with variable viscosity and diffusion equation in inhomogeneous media
Authors: Fresneda-Portillo, Carlos
Advisors: Warby, M
Mikhailov, S
Keywords: Boundry domain integral equation;PDE;Variable coefficient;Boundary integral equation
Issue Date: 2016
Publisher: Brunel University London
Abstract: The importance of the Stokes system stems from the fact that the Stokes system is the stationary linearised form of the Navier Stokes system [Te01, Chapter1]. This linearisation is allowed when neglecting the inertial terms at a low Reinolds numbers Re << 1. The Stokes system essentially models the behaviour of a non - turbulent viscous fluid. The mixed interior boundary value problem related to the compressible Stokes system is reduced to two different BDIES which are equivalent to the original boundary value problem. These boundary-domain integral equation systems (BDIES) can be expressed in terms of surface and volume parametrix-based potential type operators whose properties are also analysed in appropriate Sobolev spaces. The invertibility and Fredholm properties related to the matrix operators that de ne the BDIES are also presented. Furthermore, we also consider the mixed compressible Stokes system with variable viscosity in unbounded domains. An analysis of the similarities and differences with regards to the bounded domain case is presented. Furthermore, we outline the mapping properties of the surface and volume parametrix-based potentials in weighted Sobolev spaces. Equivalence and invertibility results still hold under certain decay conditions on the variable coeffi cient The last part of the thesis refers to the mixed boundary value problem for the stationary heat transfer partial di erential equation with variable coe cient. This BVP is reduced to a system of direct segregated parametrix-based Boundary-Domain Integral Equations (BDIEs). We use a parametrix different from the one employed by Chkadua, Mikhailov and Natroshvili in the paper [CMN09]. Mapping properties of the potential type integral operators appearing in these equations are presented in appropriate Sobolev spaces. We prove the equivalence between the original BVP and the corresponding BDIE system. The invertibility and Fredholm properties of the boundary-domain integral operators are also analysed in both bounded and unbounded domains.
Description: This thesis was submitted for the award of Doctor of Philosophy and was awarded by Brunel University London
Appears in Collections:Dept of Mathematics Theses
Mathematical Sciences

Files in This Item:
File Description SizeFormat 
FulltextThesis.pdf 737.64 kBAdobe PDFView/Open

Items in BURA are protected by copyright, with all rights reserved, unless otherwise indicated.