tools of optimal control will be presented enabling further analysis of these controls from
the point of view of their optimality. We then will revisit our model pursuing its analysis.
The resulting optimal controls here represent the dosage of anti-angiogenic inhibitors. The
most important part of this analysis is computation of the singular optimal control which
corresponds to varying partial doses. Then these controls are combined with so-called bang-
bang controls which take value of 0 (no dose) or a (full dose) of the drug in the order which
depends on the initial conditions of the problem. The typical form of the optimal controls
u, will be "as0". This means that we start the therapy by giving full dose (u = a) and
then, at the right switching time, we change to administering a partial dosage according to
the singular controls (part s), until we run out of the drug. At the �nal part, after e�ects
of the medicine (u = 0) still lead to a further reduction in tumor volume. The last part of
this thesis will deal with numerical simulations comparing the e�ect of the parameters in the
objective on both the qualitative and quantitative characteristic of the solutions.
4
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