OPTIMIZATION OF A MODEL FOKKER-PLANCK EQUATION

We discuss optimal control problems for the Fokker-Planck equation arising in radiotherapy treatment planning. We prove existence and uniqueness of an optimal boundary control for a general tracking-type cost functional in three spatial dimensions. Under additional regularity assumptions we prove existence of a continuous necessary first order optimality system. In the one-dimensional case we analyse a numerical discretization of the Fokker-Planck equation. We prove that the resulting discrete optimality system is a suitable discretization of the continuous first-order system.