Advisor(s) - Committee Chair
Dr. Richard Schugart (Director), Dr. Nezam Iraniparast, Dr. Mikhail Khenner
Department of Mathematics
Master of Science
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.
Applied Mathematics | Partial Differential Equations
Guffey, Stephen, "Application of a Numerical Method and Optimal Control Theory to a Partial Differential Equation Model for a Bacterial Infection in a Chronic Wound" (2015). Masters Theses & Specialist Projects. Paper 1494.