Let H be a real Hilbert space and A : D(A) ⊂ H → H be an unbounded, linear, self-adjoint, and maximal monotone operator. The aim of this thesis is to solve u 0 (t) + Au(t) = 0, when A is linear but not bounded. The classical ...

In this thesis, we treated a Standard Finite Difference Scheme for a singularly perturbed parabolic reaction-diffusion equation. We proved that the Standard Finite Difference Scheme is not a robust technique for solving ...

Let E be a uniformly convex and uniformly smooth real Banach space and E ∗ be its dual. Let A : E → 2 E be a bounded maximal monotone map. Assume that A −1 (0) 6 = ∅. A new iterative sequence is constructed which converges ...

Let E be a real normed space with dual space E ∗ and let A : E → 2 E be any map. Let J : E → 2 E be the normalized duality map on E. A new class of mappings, J-pseudocontractive maps, is introduced and the notion of J-fixed ...

We consider classical Finite Difference Scheme for a system of singularly perturbed convection-diffusion equations coupled in their reactive terms, we prove that the classical SFD scheme is not a robust technique for solving ...

We show that a class of solutions of minimal supergravity in five dimensions is given by lifts of three-dimensional Einstein–Weyl structures of hyper-CR type. We characterise this class as most general near-horizon limits ...

The scope of Quadratic Form Theory is historically wide although it usually appears almost as an afterthought when needed to solve a variety of problems such as the classification of Hessian matrices in finite dimensional ...

Let X be a real Banach space, X ∗ its conjugate dual space. Let A be a monotone angle-bounded continuous linear mapping of X into X ∗ with constant of angle-boundedness c ≥ 0. Let N be a hemicontinuous (possibly non-linear) ...

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We consider classical Finite Difference Scheme for a system of singularly perturbed convection-diffusion equations coupled in their reactive terms, we prove that the classical SFD scheme is not a robust technique for solving ...

We prove a homological stability theorem for moduli spaces of manifolds of dimension 2$\textit{n}$, for attaching handles of index at least $\textit{n}$, after these manifolds have been stabilised by countably many copies ...

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 ...

This project is mainly focused on the theory of Monotone (increasing) Operators and its applications. Monotone operators play an important role in many branches of Mathematics such as Convex Analysis, Optimization Theory, ...

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 ...

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 Differential ...

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This Project is at the interface between Optimization, Functional analysis and Differential equation. It concerns one of the powerful methods often used to solve optimization problems with constraints; namely Minimum ...