Publication Date


Advisor(s) - Committee Chair

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

Degree Program

Department of Mathematics

Degree Type

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