Analysis of positive solutions for classes of nonlinear reaction diffusion equations and systems
- UNCG Author/Contributor (non-UNCG co-authors, if there are any, appear on document)
- Amila K. Muthunayake (Creator)
- Institution
- The University of North Carolina at Greensboro (UNCG )
- Web Site: http://library.uncg.edu/
- Advisor
- Ratnasingham Shivaji
Abstract: The focus of this thesis is to study positive solutions for classes of nonlinear reaction diffusion equations and systems. In particular, we consider three focuses. In Focus 1, we establish existence and uniqueness of positive solutions for a class of infinite semipositone problems with nonlinear boundary conditions. In Focus 2, we explore the consequences of fragmentation and trait-mediated dispersal on the coexistence of a system of two mutualists by employing a model built upon the reaction diffusion framework. We establish several coexistence and nonexistence results. Finally, in Focus 3, we develop and analyze a radial finite difference method that directly approximate solutions for classes of semipositone problems with Dirichlet boundary conditions. Our existence results in Focus 1 and Focus 2 are achieved by methods of sub and supersolutions. In Focus 3, via computational methods, we obtain bifurcation diagrams describing the structure of positive solutions. Namely, we obtain these bifurcation diagrams via a modified finite difference method and MATLAB computations in the case when the domain is the unit disc in R2. This dissertation aims to significantly enrich the mathematical and computational analysis literature on reaction diffusion equations and systems. [This abstract may have been edited to remove characters that will not display in this system. Please see the PDF for the full abstract.]
Analysis of positive solutions for classes of nonlinear reaction diffusion equations and systems
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Created on 8/1/2021
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Additional Information
- Publication
- Dissertation
- Language: English
- Date: 2021
- Keywords
- Reaction-diffusion systems, Nonlinear systems, Positive solutions
- Subjects
- Differential equations, Nonlinear $x Numerical solutions
- Reaction-diffusion equations $x Numerical solutions
- Nonlinear systems $x Mathematical models
- Diffusion $x Mathematical models