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Optimization of a model Fokker-Planck equation

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  • 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.
    Mathematics Subject Classification: Primary: 85A25, 76P05; Secondary: 49J20, 92C50.

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