A dissertation submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of requirements for the degree of Master of Science. February 16, 2015. / The Adomian decomposition method is an effective procedure for the analytical solution of a wide class of dynamical systems without linearization or weak nonlinearity assumptions, closure approximations, perturbation theory, or restrictive assumptions on stochasticity. Our aim here is to apply the Adomian decomposition method to steady two-dimensional blood flow through a constricted artery in the presence of a uniform transverse magnetic field. Blood flow is the study of measuring blood pressure and determining flow through arteries. Blood flow is assumed to be Newtonian and is governed by the equation of continuity and the momentum balanced equation (which are known as the Navier-Stokes equations). This model is consistent with the principles of ferro-hydrodynamics and magnetohydrodynamics and takes into account both magnetization and electrical conductivity of blood. We apply the Adomian decomposition method to the equations governing blood flow through arteries in the presence of an external transverse magnetic field. The results show that the e ect of a uniform external transverse magnetic field applied to blood flow through arteries favors the physiological condition of blood. The motion of blood in stenosed arteries can be regulated by applying a magnetic field externally and increasing/decreasing the intensity of the applied field.

Chu Shun Yin. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2000. / Includes bibliographical references (leaves 63-65). / Abstracts in English and Chinese. / Acknowledgments --- p.i / Abstract --- p.ii / Introduction --- p.3 / Chapter 1 --- Preliminaries --- p.8 / Chapter 2 --- Singular Integrals --- p.15 / Chapter 2.1 --- Marcinkiewicz Integral --- p.15 / Chapter 2.2 --- Decomposition in cubes of open sets in Rn --- p.17 / Chapter 2.3 --- Interpolation Theorem for Lp --- p.18 / Chapter 2.4 --- Singular Integrals on homogeneous of degree 0 --- p.25 / Chapter 3 --- Solutions to the Euler Equations --- p.36 / Chapter 3.1 --- Existence and Uniqueness of smooth solutions for Euler Equations --- p.36 / Chapter 3.2 --- Rate of Convergence and Decay in Time --- p.43 / Chapter 3.2.1 --- Rate of Convergence --- p.43 / Chapter 3.2.2 --- Lp Decay for Solutions of the Navier-Stokes Equations --- p.46 / Chapter 3.3 --- Weak Solution to the Euler Equations --- p.48 / Chapter 3.3.1 --- Weak Solution to the Velocity Formulation --- p.49 / Chapter 3.3.2 --- Weak Solution to the Vorticity Formulation --- p.52 / Bibliography --- p.63

Chan Man-fai. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2002. / Includes bibliographical references (leaves 40-41). / Abstracts in English and Chinese. / Acknowledgement --- p.i / Abstract --- p.ii / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Equation of motion and main results --- p.3 / Chapter 3 --- The space K(x) --- p.9 / Chapter 4 --- Proof of the main theorem --- p.17 / Chapter 4.1 --- The passage to the limit as ε →0 --- p.18 / Chapter 4.2 --- The passage to the limit as δ→ 0 --- p.26 / Chapter 4.3 --- Properties of the solution --- p.29 / Chapter 5 --- Conclusion and comments on future works --- p.36 / Appendix --- p.38 / Bibliography --- p.40

Neste trabalho estudamos a existência de soluções de equações do tipo Navier-Stokes com retardo na força externa e no termo n~ao linear. Usando a teoria de semigrupos estudamos a existência de soluções para um problema da forma \'d. SUP. dt u(t) - v\'delta\'u(t) + (F(t, \'u IND.t\'). abla)u(t) + abla p = g(t, \'u IND.t\'), em \'OMEGA\' x (0, T), div u(t) = 0 em \'OMEGA\' x (0, T), u(0, x) = \'u POT.0 (x) x PERTENCE a \' OMEGA\', u(t, x) = 0 t > 0, X \'PERTENCE A\' \' PARTIAL\' \'OMEGA\', u(t, x) =\\phi (t, x) t \'PERTENCE A\' (- \'INFINITO\', 0) x \'PERTENCE A\' \'OMEGA\', onde F9t, \'uIND.t) = INT.IND.t SUP. -\' INFINITO\' \' ALFA1(s-t)u(s)ds + u(t-r), g(t, \'u IND.t\') = INT. SUP. t IND. - INFINITO \'BETA\' (s-t)u(s)ds. Similarmente, usando a tecnica de aproximac~oes de Galerkin, estudamos o problema anterior com F(.) e g(.) dadas por f(t; \'u INDS.t\') = u(t-r(t)); e g(t; \'u IND.t\') = G(u(t-\'rô\' (t))), para alguma função G apropriada. Neste caso, também estudamos a estabilidade de soluções estacionarias / In this work we stuy the existence of solutions for a Navier-Stokes typt equations with delay in the external force and in the nonlinear term. Using the semi-group theory we study the existence of solution for a problem in the form \'d. SUP. dt u(t) - v\'delta\'u(t) + (F(t, \'u IND.t\'). abla)u(t) + abla p = g(t, \'u IND.t\'), ijn \'OMEGA\' x (0, T), div u(t) = 0 in \'OMEGA\' x (0, T), u(0, x) = \'u POT.0 (x) x \'IT BELONGS \' OMEGA\', u(t, x) = 0 t > 0, X \'IT BELONGS\' \'PARTIAL\' \'OMEGA\', u(t, x) =\\phi (t, x) t \'IT BELONGS\' (- \'INFINITY\', 0) x \'IT BELONGS\' \'OMEGA\', where F(t, \'u .t) = INT.IND.t SUP. -\' INFINITY\' \' ALFA(s-t)u(s)ds + u(t-r), g(t, \'u IND.t\') = INT. SUP. t IND. - INFINITY \'BETA\' (s-t)u(s)ds. On another hand using the Galerkin appreoximations method we study the same with F(.) e g(.) given by f(t; \'u INDS.t\') = u(t-r(t)); and g(t; \'u IND.t\') = G(u(t-\'rô\' (t))), for some G appropriated. In thiis case, we study also the stability of stanionary solutions

In chapter 1, we focus on the noncharacteristic boundary layers for the parabolic regularization of quasi-linear hyperbolic problems, where the viscosity matrix is positive definite, with the zero Dirichlet boundary conditions. We adapt the method developed by Grenier and Gues [?] where the center-stable manifold theorem is used to prove the existence and exponential decay property of the leading boundary layer profile under suitable conditions on the boundary x = 0. With this boundary condition we prove the well-posedness of the initial boundary value problem of the inviscid flow. Then we prove the stability of the boundary layer by an energy estimate, where exponential decay property of the boundary layer profile plays an important role. Finally, we can specify the limit of the viscous solutions to the corresponding inviscid solution. / In chapter 2, we consider the noncharacteristic one-dimensional compressible full Navier-Stokes equations for the ideal gas with outflow boundary condition on the velocity and suitable initial conditions, which make all the three characteristics to the corresponding Euler equations negative up to some local time, especially on the boundary. By the aymptotic analysis, we derive an algebraic-differential equation for the leading boundary layer functions. The center-stable manifold theorem helps to prove the existence and exponential decay property of the leading boundary layer function. The outflow boundary condition makes it possible to estimate the normal derivatives. Combining this with the tangential derivative estimate, we can recover the H1 estimate of the error term. Thus we establish the stability of the boundary layers which satisfy an algebraic-differential equation in this case. With this stability result, we obtain the relation between the solutions to Navier-Stokes and Euler equations. / In chapter 3, we concentrate on the existence and nonlinear stability of the totally characteristic boundary layer for the quasi-linear equations with positive definite viscosity matrix under the assumption that the boundary matrix vanishes identically on the boundary x = 0. We carry out a weighted estimate to the boundary layer equations---Prandtl type equations to get the regularity and the far field behavior of the solutions. This allows us to perform a weighted energy estimate for the error equation to prove the stability of the boundary layers. The stability result finally implies the asymptotic limit of the viscous solutions. / In this thesis we study three kinds of asymptotic limiting behavior of the solutions to the initial boundary value problem of one-dimensional quasilinear equations with viscosity by carrying out the boundary layer analysis. / Wang, Jing. / Adviser: Zhouping Xin. / Source: Dissertation Abstracts International, Volume: 71-01, Section: B, page: 0407. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (leaves 107-112). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. Ann Arbor, MI : ProQuest Information and Learning Company, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese.

Finally, we prove that weak solutions to the compressible Navier-Stokes equations with the Navier boundary condition stabilize to static equilibrium states under a fair condition. / First, we show that the most general class of weak solutions to one-dimensional full compressible Navier-Stokes equations do not exhibit vacuum states in a finite time provided that no vacuum is present initially with the minimum physical assumptions on the data. Moreover, two initially non interacting vacuum regions will never meet each other in the future. / Secondly, we construct the local classical solutions to the compressible Navier-Stokes equations for initial vacuum far fields. In this case, we describe the blow-up phenomena of two-dimensional compact support smooth spherically symmetric solutions. When the far field of the initial state is away from vacuum, we obtain the global classical solutions and show the large time blow-up behavior of the gradient of the density. / This thesis deals with some important problems of compressible Navier-Stokes equations, including the well-posedness of the Cauchy problem, the regularity of the weak solutions constructed by Lions and Feireisl, and the dynamics of vacuum states, etc.. / Luo, Zhen. / Adviser: Zhouping Xin. / Source: Dissertation Abstracts International, Volume: 72-04, Section: B, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 152-161). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. Ann Arbor, MI : ProQuest Information and Learning Company, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese.

Abstract not available

University of Macau / Faculty of Science and Technology / Department of Electromechanical Engineering

No description available.

Thesis (M.S.)--Mississippi State University. Department of Computational Engineering. / Title from title screen. Includes bibliographical references.