This research concerns the solution of certain undetermined coefficient problems in parabolic and elliptic partial differential equations where the unknown coefficients depend only on the dependent variables. The problems are related to the determination of laws or relationships governing physical systems, and the mathematical formulation is most often in the form of an elliptic or parabolic equation. The research is in the general area of Applied Mathematics and concerns the solutions of partial differential equations which arise in physical settings. In addition to the solutions of partial differential equations, the research will involve the study of inverse problems which have applications to the recovery of birth and death rates and initial distributions in age- dependent population models.
