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Series Solutions Of Multi-Layer Boundary Value Problems, Amr Saad Hassan Bolbol
Series Solutions Of Multi-Layer Boundary Value Problems, Amr Saad Hassan Bolbol
Theses
It is well known that differential equations (DEs) play an important role in many sciences. They are mathematical representations of many physical systems. By studying such DEs, one gains many important insights about the physical system. Solutions of DEs provide information on the physical system behavior. As many physical systems are nonlinear in nature, this naturally gives rise to nonlinear differential equations (NLDEs). Such NLDEs are, in most cases, hard or sometimes impossible to solve analytically. In such situations, we resort to numerical techniques to approximate the solutions. The purpose of this thesis is to consider nonlinear multi-layer boundary value …
Moduli Space And Deformations Of Special Lagrangian Submanifolds With Edge Singularities, Josue Rosario-Ortega
Moduli Space And Deformations Of Special Lagrangian Submanifolds With Edge Singularities, Josue Rosario-Ortega
Electronic Thesis and Dissertation Repository
Special Lagrangian submanifolds are submanifolds of a Calabi-Yau manifold calibrated by the real part of the holomorphic volume form. In this thesis we use elliptic theory for edge- degenerate differential operators on singular manifolds to study general deformations of special Lagrangian submanifolds with edge singularities. We obtain a general theorem describing the local structure of the moduli space. When the obstruction space vanishes the moduli space is a smooth, finite dimensional manifold.
A Fractional Boundary Value Problem, Grant Yost
A Fractional Boundary Value Problem, Grant Yost
Honors Theses
We consider a fractional boundary value problem with various boundary conditions. This boundary value problem has two components, one fractional derivative of alpha degree with alpha between n-1 and n, and a fractional derivative of beta degree with beta between 0 and n-2. We prove existence and uniqueness of solutions, and show some examples that were found using a MATLAB simulation.