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Tr. Mat. Inst. Steklova, 2019, Volume 304, Pages 273–284 (Mi tm3972)  

On Applications of the Hamilton–Jacobi Equations and Optimal Control Theory to Problems of Chemotherapy of Malignant Tumors

N. N. Subbotinaab, N. G. Novoselovaab

a N. N. Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi 16, Yekaterinburg, 620990 Russia
b Ural Federal University named after the First President of Russia B. N. Yeltsin, ul. Mira 19, Yekaterinburg, 620002 Russia

Abstract: A chemotherapy model for a malignant tumor is considered, and the optimal control (therapy) problem of minimizing the number of tumor cells at a fixed final instant is investigated. In this problem, the value function is calculated, which assigns the value (the optimal achievable result) to each initial state. An optimal feedback (optimal synthesis) is constructed, using which for any initial state ensures the achievement of the corresponding optimal result. The proposed constructions are based on the method of Cauchy characteristics, the Pontryagin maximum principle, and the theory of generalized (minimax/viscosity) solutions of the Hamilton–Jacobi–Bellman equation describing the value function.

Funding Agency Grant Number
Russian Foundation for Basic Research 17-01-00074
This work was supported by the Russian Foundation for Basic Research, project no. 17-01-00074.


DOI: https://doi.org/10.4213/tm3972

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English version:
Proceedings of the Steklov Institute of Mathematics, 2019, 304, 257–267

Bibliographic databases:

UDC: 517.977
Received: October 10, 2018
Revised: October 25, 2018
Accepted: December 19, 2018

Citation: N. N. Subbotina, N. G. Novoselova, “On Applications of the Hamilton–Jacobi Equations and Optimal Control Theory to Problems of Chemotherapy of Malignant Tumors”, Optimal control and differential equations, Collected papers. On the occasion of the 110th anniversary of the birth of Academician Lev Semenovich Pontryagin, Tr. Mat. Inst. Steklova, 304, Steklov Math. Inst. RAS, Moscow, 2019, 273–284; Proc. Steklov Inst. Math., 304 (2019), 257–267

Citation in format AMSBIB
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\paper On Applications of the Hamilton--Jacobi Equations and Optimal Control Theory to Problems of Chemotherapy of Malignant Tumors
\inbook Optimal control and differential equations
\bookinfo Collected papers. On the occasion of the 110th anniversary of the birth of Academician Lev Semenovich Pontryagin
\serial Tr. Mat. Inst. Steklova
\yr 2019
\vol 304
\pages 273--284
\publ Steklov Math. Inst. RAS
\publaddr Moscow
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