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 Trudy Inst. Mat. i Mekh. UrO RAN, 2020, Volume 26, Number 1, Pages 173–181 (Mi timm1708)

Construction of the viability set in a problem of chemotherapy of a malignant tumor growing according to the Gompertz law

N. G. Novoselovaab, N. N. Subbotinaab

a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
b Ural Federal University named after the First President of Russia B. N. Yeltsin, Ekaterinburg

Abstract: The problem of chemotherapy of a malignant tumor growing according to the Gompertz law is considered. The mathematical model is a system of two ordinary differential equations. We study a problem of optimal control (optimal therapy) aiming at the minimization of the malignant cells in the body at a given terminal time $T$. The viability set of this problem, i.e., the set of initial states of the model (the volume of the tumor and the amount of the drug in the body) for which an optimal control guarantees that the dynamics of the system up to the time $T$ is compatible with life in terms of the volume of the tumor, is constructed analytically.

Keywords: viability set, optimal control, value function.

 Funding Agency Grant Number Russian Foundation for Basic Research 20-01-00362 This work was supported by the Russian Foundation for Basic Research (project no. 20-01-00362).

DOI: https://doi.org/10.21538/0134-4889-2020-26-1-173-181

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Bibliographic databases:

UDC: 517.977
MSC: 49L25, 49K15, 65K05
Revised: 17.01.2020
Accepted:20.01.2020

Citation: N. G. Novoselova, N. N. Subbotina, “Construction of the viability set in a problem of chemotherapy of a malignant tumor growing according to the Gompertz law”, Trudy Inst. Mat. i Mekh. UrO RAN, 26, no. 1, 2020, 173–181

Citation in format AMSBIB
\Bibitem{NovSub20} \by N.~G.~Novoselova, N.~N.~Subbotina \paper Construction of the viability set in a problem of chemotherapy of a malignant tumor growing according to the Gompertz law \serial Trudy Inst. Mat. i Mekh. UrO RAN \yr 2020 \vol 26 \issue 1 \pages 173--181 \mathnet{http://mi.mathnet.ru/timm1708} \crossref{https://doi.org/10.21538/0134-4889-2020-26-1-173-181} \elib{https://elibrary.ru/item.asp?id=42492202}