An Optimal Control Problem for Acid-mediated Cancer Invasion Model
DOI:
https://doi.org/10.5890/JAND.2023.06.011Abstract
In this article, we investigate an optimal control problem for acid-mediated cancer invasion model which describes the normal cell density, the tumor cell density, the excess $H^+$ ion concentration, the extracellular matrix, and active metalloproteinases. The main objective of this paper is to minimize the growth of tumor cells by controlling the excess production of $H^+$ ions. First, we establish the existence of weak solutions by using the Faedo-Galerkin approximation method, then we prove the existence of optimal control. Further, we derive the necessary optimality condition for acid-mediated cancer invasion model. Finally, we illustrate the importance of the control term using some numerical simulations.References
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