Term of Award

Summer 2020

Degree Name

Master of Science in Mathematics (M.S.)

Document Type and Release Option

Thesis (open access)

Copyright Statement / License for Reuse

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.

Department

Department of Mathematical Sciences

Committee Chair

Zhan Chen

Committee Member 1

Martha Abell

Committee Member 2

Shijun Zheng

Committee Member 3

Yuanzhen Shao

Committee Member 3 Email

yshao8@georgiasouthern.edu

Non-Voting Committee Member

Yi Hu

Abstract

In biology, minimizing a free energy functional gives an equilibrium shape that is the most stable in nature. The formulation of these functionals can vary in many ways, in particular they can have either a smooth or sharp interface. Minimizing a functional can be done through variational calculus or can be proved to exist using various analysis techniques. The functionals investigated here have a smooth and sharp interface and are analyzed using analysis and variational calculus respectively. From the former we find the condition for extremum and its second variation. The second variation is commonly used to analyze stability of a surface that is a solution to the functional so having a surface is necessary. Comparatively, from the latter we find that there exists a minimizing surface for the functional; from this numerical and variational approaches to the problem can be justified.

Research Data and Supplementary Material

No

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