OPTIMAL RADIOTHERAPY TREATMENT PLANNING GOVERNED BY KINETIC EQUATIONS

In this paper we study a problem in radiotherapy treatment planning. This problem is formulated as an optimization problem of a functional of the radiative flux. It is constrained by the condition that the radiative flux, which depends on position, energy and direction of the particles, is governed by a Boltzmann integro-differential equation. We show the existence, uniqueness and regularity of solutions to this constrained optimization problem in an appropriate function space. The main new difficulty is the treatment of the energy loss term. Furthermore, we characterize optimal controls by deriving first-order optimality conditions.

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