Abstract
Altered metabolism, characterized by high concentration levels of lactate enzyme, contributes to tumor development, malignancy, and metastasis and introduces metabolic liabilities that can be employed in cancer treatment. Here, this paper aims to reach a desired lactate concentration, under the action of an optimal treatment dose, represented by a control, at an optimal treatment time. We consider an objective functional to be minimized associated with a system modeling lactate dynamics in the presence of control. We show the existence of a minimizer of this functional, and we derive a first-order necessary optimality condition.
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