Application of a Numerical Method and Optimal Control Theory to a Partial Differential Equation Model for a Bacterial Infection in a Chronic Wound

<p>In this work, we study the application both of optimal control techniques and a numerical method to a system of partial differential equations arising from a problem in wound healing. Optimal control theory is a generalization of calculus of variations, as well as the method of Lagrange Multipliers. Both of these techniques have seen prevalent use in the modern theories of Physics, Economics, as well as in the study of Partial Differential Equations. The numerical method we consider is the method of lines, a prominent method for solving partial differential equations. This method uses finite difference schemes to discretize the spatial variable over an N-point mesh, thereby converting each partial differential equation into N ordinary differential equations. These equations can then be solved using numerical routines defined for ordinary differential equations.</p>

Name thesis:degree_name

Master of Science

Discipline thesis:degree_discipline

Department of Mathematics

Year

2015

Author dc:creator

• Guffey, Stephen

Contributors dc:contributor

• Dr. Richard Schugart (Director), Dr. Nezam Iraniparast, Dr. Mikhail Khenner

• Method of lines
• Partial Differential Equations
• Optimal Control
• Applied Mathematics

Repository record dc:identifier

https://digitalcommons.wku.edu/theses/1494

OAI identifier oai:identifier

oai:digitalcommons.wku.edu:theses-2487