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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. [ABSTRACT FROM AUTHOR]

Our aim in this paper is to study an optimal control problem for a tumor growth model. The state system couples an Allen-Cahn equation and a reaction diffusion equation that models the evolution of tumor in the presence of nutrient supply. Elimination of cancer cells via cytotoxic drug is considered and the concentration of the cytotoxic drug is represented as a control variable. [ABSTRACT FROM AUTHOR]