ABSTRACT A number of phenomena in modern science can be conveniently described in terms of problem for hyperbolic equation with Carleman estimates to the solution of inverse problem. The purpose of this study is to give a survey of the solution of the inverse problems for hyperbolic equation by Carleman estimates. We extend the results and prove the Carleman estimate focusing on an inverse problem for a simple hyperbolic equation. Also we derive the Lipschitz's stability by energy estimate; w...
ABSTRACT This dissertation investigates the magnetic field and Soret influence on MHD unsteady free convection radiating and reacting fluid past an exponentially accelerated inclined infinite porous plate of uniform permeability with variable temperature and concentration numerically. In this model the fluid is considered a gray, emitting absorbing radiation but a non-scattering medium and a magnetic field of intensity B0 is imposed in the perpendicular direction to the plate. The governing e...
ABSTRACT We find new exact solutions to Einstein-Maxwell's field equation for charged anisotropic stellar objects. We use the linear equations of the state consistent with quark matter and metric function. In our model, we choose a new measure of anisotropy. Through the transformation of Einstein-Maxwell field equations, new solutions for charged anisotropic matter are obtained. The models generated enable us to regain previous isotropic and anisotropic results as a specific case. We regain ...
Abstract In this paper, the effects of chemical reaction on unsteady MHD flow of viscous incompressible electrically conducting fluid past an impulsively started oscillating vertical plate with variable temperature and constant mass diffusion in the presence of Hall current have been presented. The dimensionless governing partial differential equations of the flow have been solved numerically by using the Crank-Nicolson implicit finite difference scheme. The numerical solutions for primary fl...
Abstract. We generate two new exact models for the Einstein–Maxwell field equations. In our models, we consider the stellar object that is anisotropic and charged with linear equation of state consistent with quark stars. We have a new choice of measure of anisotropy that is physically reasonable. It is interesting that in our models we regain previous isotropic results as special cases. Isotropic exact solutions regained include models by Komathiraj and Maharaj; Mak and Harko; and Misner ...
ABSTRACT This dissertation contains materials on numerical solutions to partial differential equations only appropriate for senior level undergraduate. The reader based on this dissertation should have had introductory courses in Calculus, linear algebra and general numerical analysis. A formal course in ordinary or partial differential equations would be useful. In our study, it should be understood that, there are many procedures that come under the name numerical methods. We shall see how...
ABSTRACT The objective of this study is to investigate the effects of chemical reaction on an unsteady hydro - magnetic natural convection heat and mass transfer flow of incompressible, viscous, rotating and radiating fluid past an infinite vertical porous flat plate in the presence of heat sink. The Rosseland approximation is used to describe the radiative heat flux for optically thick fluid in the energy equation. The system of non - dimensional partial differential equations governing the...
ABSTRACT This dissertation consists of four chapters. The first chapter is about general review of partial differential equations. The second chapter is devoted to the numerical solutions of partial differential equations. The third chapter is about applications of partial differential equations in mathematical physics and the fourth chapter is about mathematical modeling with partial differential equations.
ABSTRACT Present work determined with analytical solution of steady state onedimensional heat conduction problems in cylindrical and spherical coordinates and simplifications of general forms of heat equation are often possible . Also ,discussed on Newton's law of cooling on two ways conduction and radiation the result obtained that Newton's law of cooling is consequence of conduction and not radiation . Through internal body interactions in cylindrical coordinates with boundary conditions t...
The effects of chemical reaction on a transient MHD mixed convection flow with mass transfer past an impulsively fixed infinite vertical plate under the influence of a transverse magnetic field have been presented. The medium is considered to be non-scattering and the fluid to be non-gray having emitting-absorbing and optically thick radiation limit properties. The dimensionless governing equations of the flow and mass transfer with boundary conditions are solved numerically by using the Ritz...
ABSTRACT Mathematical models describing the variations in the plasma glucose and J insulin levels over time in an insulin - dependent diabetic person (IDD patient) were formulated. We showed that these models can correctly describe these variations when we solved them sirnuttaneously by andytical approach rather than the normal numerical approach employed for solving non-linear differential equations. The effect of the various parameters involved in the model were tested and it was shown tha...
Abstract In this paper, we present the q-analogues of some inequalities concerning the digamma function.
ABSTRACT This study investigated the types of strategies used by Grade 12 ordinary level mathematics learners to solve algebraic word problems in Namibian settings in the Kavango East Educational Region. The study used a descriptive qualitative research approach in which the researcher identified the strategies used by Grade 12 learners to solve algebraic word problems. The study used observations and focus group discussions as methods for data collection. The researcher independently conduc...
Abstract This study will investigate the strongness property for nearness and nearness partial frames. We initially revisit the concepts of strong and totally strong nearness frame and study their closures under completion. We also explore the properties of totally strong and uniformly completely regular nearness frames, and study the relationship between them. We show that the category of totally strong nearness frames is coreflective in the category of uniformly completely regular nearness...
ABSTRACT Unsteady heat and mass transfers are important transport phenomena that are found in many engineering and industrial applications. In such systems, the variations in the fluid flow result in variations in the heat flux for fluid-solid temperature difference. In this study, analytical and theoretical investigations of some non-linear problems arising from unsteady heat and mass transfer through porous media are considered. Analytical models are developed. These are non-linear mathem...