Radial and Non-radial Numerical Solutions to the Non-linear Elliptic BVP on the Disk

Degbe, Elliott (2018) Radial and Non-radial Numerical Solutions to the Non-linear Elliptic BVP on the Disk. Masters thesis, Northern Arizona University.

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Abstract

In the last few decades, much research has gone into proving the existence of solutions to the non-linear elliptic partial differential equations (PDEs) with 0 - Dirichlet boundary conditions on the unit disk. Following the work of Luna and Swift in [15], we seek to find numerical solutions to a PDE of this type and investigate certain salient accompanying questions. We concentrate on find- ing radial-only solutions and investigating the behavior of secondary solution branches bifurcating from those radial ones.

Item Type:	Thesis (Masters)
Publisher’s Statement:	© Copyright is held by the author. Digital access to this material is made possible by the Cline Library, Northern Arizona University. Further transmission, reproduction or presentation of protected items is prohibited except with permission of the author.
Keywords:	Laplacian; numerical solutions; partial differential equations; unit disk
Subjects:	Q Science > QA Mathematics
NAU Depositing Author Academic Status:	Student
Department/Unit:	Graduate College > Theses and Dissertations College of the Environment, Forestry, and Natural Sciences > Mathematics and Statistics
Date Deposited:	22 Apr 2021 19:30
URI:	http://openknowledge.nau.edu/id/eprint/5275

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