Dissertation
GENERALIZING THE CAHN-HILLIARD EQUATION WITH APPLICATIONS IN MIGRATION MODELING
Doctor of Philosophy (PhD), Washington State University
01/2020
Handle:
https://hdl.handle.net/2376/111097
Abstract
The Cahn-Hilliard Equation is a nonlinear parabolic partial differential equation that was originally developed to model phase separation of a two-phase solution. A gener- alization of this equation has been derived via hybrid mixture theory and phase field theory as a means to model migration by using fluid flow through a porous media as an analogue for a population migrating over a given terrain.
We examine this generalized equation both numerically and analytically. Analytically, we show that there are solutions to the generalized equation, which includes anisotropy and a forcing function. Included in the numerical analysis is a novel method of time-stepping that reduces the stiffness of the problem by making a change of variables in the continuous setting.
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Details
- Title
- GENERALIZING THE CAHN-HILLIARD EQUATION WITH APPLICATIONS IN MIGRATION MODELING
- Creators
- Zachary James Hilliard
- Contributors
- Lynn Schreyer (Advisor)Nikolaos Voulgarakis (Committee Member)Hong-Ming Yin (Committee Member)Sergey Lapin (Committee Member)Tiziana Giorgi (Committee Member)
- Awarding Institution
- Washington State University
- Academic Unit
- Mathematics and Statistics, Department of
- Theses and Dissertations
- Doctor of Philosophy (PhD), Washington State University
- Number of pages
- 85
- Identifiers
- 99900581810901842
- Language
- English
- Resource Type
- Dissertation