The goal of this chapter is to introduce the Optimal Control Problem (OCP) formulation which serves as the point of origin for all further investigations in this thesis. To this end we recapitulate elements of the theory of parabolic Partial Differential Equations (PDEs) in Section 2.1 and present a system of PDEs coupled with Ordinary Differential Equations (ODEs) in Section 2.2. The coupled system is one of the constraints among additional boundary and path constraints for the OCP which we describe in Section 2.3. We emphasize the particular aspects in which our problem setting differs and extends the setting most often found in PDE constrained optimization.
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