Optimal Control Problem for Cancer Invasion Reaction–Diffusion System. (26th October 2018) - Shangerganesh, Lingeshwaran; Sowndarrajan, Puthur Thangaraj
Abstract: An optimal control problem constrained by a reaction–diffusion mathematical model which incorporates the cancer invasion and its treatment is considered. The state equations consisting of three unknown variables namely tumor cell density, normal cell density, and drug concentration. The main goal of the considered optimal control problem is to minimize the density of cancer cells and decreasing the side effects of treatment. Moreover, existence of a weak solution of brain tumor reaction–diffusion system and the corresponding adjoint system of optimal control problem is also investigated. Further, existence of minimizer for the optimal control problem is established and also the first-order optimality conditions are derived.