# American Institute of Mathematical Sciences

September  2012, 5(3): 485-503. doi: 10.3934/krm.2012.5.485

## Optimization of a model Fokker-Planck equation

 1 RWTH Aachen University, Templergraben 55, D-52056 Aachen, Germany, Germany, Germany

Received  October 2011 Revised  March 2012 Published  August 2012

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.
Citation: Michael Herty, Christian Jörres, Albert N. Sandjo. Optimization of a model Fokker-Planck equation. Kinetic & Related Models, 2012, 5 (3) : 485-503. doi: 10.3934/krm.2012.5.485
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