E Theses
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This collection contains Theses of Masters students of AUST, who have successfully completed their programme in attendance and haven passed all required examinations to earn them a postgraduate certificate in their chosen field of study.
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Solutions to identified Mathematical Problems.
This material is not for commercial purpose and so should not be used by a third party without permission from the author and university. When permitted, proper acknowledgement should be given to the author and university.
Recent Submissions

Sobolev Spaces and Variational Method Applied to Elliptic Partial Differential Equations
(20101206)Variational methods have proved to be very important in the study of optimal shape, time, velocity, volume or energy. Laws existing in mechanics, physics, astronomy, economics and other fields of natural sciences and ...

Characteristic Inequalities in Banach Spaces and Applications
(20130514)The contribution of this project falls within the general area of nonlinear functional analysis and applications. We focus on an important topic within this area: Inequalities in Banach spaces and applications. As is well ...

Differential Forms and Applications
(20111206)This project deals mainly with Differential Forms on smooth Riemannian manifolds and their applications through the properties of their classical Differential and Integral Operators. The calculus of Differential Forms ...

Evolution Equations and Applications
(20111206)This project concerns Evolution Equations in Banach spaces and lies at the interface between Functional Analysis, Dynamical Systems, Modeling Theory and Natural Sciences. Evolution Equations include Partial Di erential ...

Sobolev Spaces and Linear Elliptic Partial Differential Equations
(20111206)The cardinal goal to the study of theory of Partial Differential Equations (PDEs) is to insure or find out properties of solutions of PDE that are not directly at tainable by direct analytical means. Certain function ...

Spectral Theory of Compact Linear Operators and Applications
(20111208)This Project primarily falls into the field of Linear Functional Analysis and its Applications to Eigenvalue problems. It concerns the study of Compact Lin ear Operators (i.e., bounded linear operators which map the ...

The Mountain Pass Theorem and Applications
(20101206)This project lies at the interface between Nonlinear Functional Anal ysis, unconstrained Optimization and Critical point theory. It concerns mainly the AmbrosettiRabinowitz's Mountain Pass Theorem which is a minmax ...

Isoperimetric Variational Techniques and Applications
(20101206)This project is at the interface between Nonlinear Functional Analysis, Con vex Analysis and Di erential Equations. It concerns one of the most powerful methods often used to solve optimization problems with constraints; ...

Floquet Theory and Applications
(20101207)This project is at the interface between Analysis, Natural Sciences and Modeling Theory. It deals with Floquet Theory (also re ered to as FloquetLyapunov theory) which is the main tool of the theory of periodic ordinary ...

Semigroups Of Linear Operators And Application To Differential Equations
(20091204)This work concerns one of the most important tools to solve wellposed problems in the the ory of evolution equations (e.g di usion equation, wave equations, ...) and in the theory of stochastic process, namely the ...

Controllability And Stabilizability Of Linear Systems In Hilbert Spaces
(20101206)Questions about controllability and stability arise in almost every dynamical system problem. As a result, controllability and stability are one of the most extensively studied subjects in system theory. A departure point ...