Optimal control problem for a general reaction-diffusion tumor-immune system with chemotherapy. (English) Zbl 1455.92071
Summary: An optimal control problem of a general reaction-diffusion tumor-immune system with chemotherapy is investigated to minimize the tumor burden and side effects as well as treatment costs. Firstly, the existence, uniqueness and some estimates of strong solution to the state system in spatial dimensions \(n=1,2,3\) are obtained by making use of the semigroup theory and truncation method. Subsequently, we prove the existence of optimal pair by utilizing the minimizing sequence technique. Furthermore, we show the differentiability of the control-to-state mapping and establish the first-order necessary optimality condition. Finally, several numerical simulations are presented to illustrate the practical application of the theoretical results obtained in this work and to validate some clinical observations.
MSC:
| 92C50 | Medical applications (general) |
| 49J20 | Existence theories for optimal control problems involving partial differential equations |
| 35K57 | Reaction-diffusion equations |
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